Download Chapter 8: Functions and modelling

Level
Number
5.0
5.0
Standard/Progression Point
At Level 5, students identify complete factor sets
for natural numbers and express these natural
numbers as products of powers of primes (for
example,
36 000 = 25 × 32 × 53).
They know the decimal equivalents for the unit
fractions ½, 1/3, ¼, 1/5, 1/8, 1/9 and find
equivalent representations of fractions as
decimals, ratios and percentages (for example, a
subset: set ratio of 4:9 can be expressed
equivalently as
4/9 = 0.4 ≈ 44.44%).
MathsWorld 9
MathsWorld 10
Chapter 1: Real numbers
*Chapter pre-test Q 9, 10, 11
1.3: Factors and prime factors
Examples 1, 2, 3
Ex. 1.3 Q 1 – 3
Chapter 1: Real numbers
*Chapter pre-test Q 3, 13
Ex. 1.1 Q 2, 3, 4, 5, 6
Chapter 5: Ratio and rates
5.3 Percentages
Ex. 5.3 Q 1, 2
Chapter 9: Chance
*Chapter pre-test Q 1, 3
Examples 1, 2, 3
5.0
Students use knowledge of perfect squares when
calculating and estimating squares and square
roots of numbers
(for example, 202 = 400 and
302 = 900 so √700 is between 20 and 30).
5.0
They evaluate natural numbers and simple
fractions given in base-exponent form (for
example, 54 = 625 and (2/3)2 = 4/9).
5.0
They calculate squares and square roots of rational
numbers that are perfect squares (for example,
√0.81 = 0.9 and √(9/16) = ¾).
They calculate cubes and cube roots of perfect
cubes (for example, 3√64 = 4).
5.0
Chapter 1: Real numbers
*Chapter pre-test Q 1e,f, 6g-j, 13-16
1.4: Irrational numbers
Example 1
Ex. 1.4 Q 3
Chapter 1: Real numbers
*Chapter pre-test Q 1e,f, 6g,h, 14b,c
1.2: Integer powers of rational numbers
Examples 1 – 5
Ex. 1.2 Q 5
Chapter 1: Real numbers
*Chapter pre-test Q 6h-j, 12e,f
Chapter 1: Real numbers
*Chapter pre-test Q 6g, 16h,i
MathsWorld 10 Teacher edition
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1
1
Level
Number
5.0
Standard/Progression Point
Using technology they find square and cube roots
of rational numbers to a specified degree of
accuracy (for example, 3√200 = 5.848 to three
decimal places).
MathsWorld 9
MathsWorld 10
Chapter 1: Real numbers
*Chapter pre-test Q 16d-j
1.4: Irrational numbers
Example 1
Try this! p 30
Ex. 1.4 Q 3
Chapter 2: Length, area and volume
2.3: Pythagoras’ theorem
Ex. 2.3 Q 1 – 4, 9
MathsWorld 9 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 1.1, 1.2 p 161
TI 89 1.1, 1.2 p 195
5.0
5.0
Students understand ratio as both set: set
comparison (for example, number of boys :
number of girls) and subset: set comparison (for
example, number of girls : number of students),
and find integer proportions of these, including
percentages (for example, the ratio number of
girls: the number of boys is 2 : 3 = 4 : 6 = 40% :
60%).
They use ratios of number pairs to understand
constant rate of change.
Chapter 5: Ratios and rates
*Chapter pre-test Q 1, 2, 3, 4, 5
Try this! p 244
5.1: Ratio and proportion
Example 1
Ex. 5.1 Q 1, 3, 5, 11
Chapter 5: Ratios and rates
*Chapter pre-test Q 7, 8, 10
5.5: Constant and variable rates
Try this! p. 286
Example 1
Ex. 5.5 Q 1
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
2
2
Level
Number
5.0
5.0
Standard/Progression Point
They use number lines, graphs, numerical or
algebraic means to solve proportion problems and
percentage problems as proportion relative to 100.
Students use a range of strategies for
approximating the results of computations, such as
front-end estimation and rounding
(for example, 925 ÷ 34 ≈ 900 ÷ 30 = 30).
MathsWorld 9
Chapter 5: Ratios and rates
5.1: Ratio and proportion
Examples 5, 6, 7
Ex. 5.1 Q 3 – 7, 8 – 14
5.3: Percentages
Examples 1, 4, 5, 6, 7
Ex. 5.3 Q 3 – 10
Chapter 1: Real numbers
*Chapter pre-test Q 7, 16
Chapter 2: Length, area and volume
MathsWorld 10
Chapter 9: Applications of arithmetic
*Chapter pre-test Q 1 – 4, 7, 8
Chapter Warm-up Try this! p 565
9.1: Percentages and rates in retail and finance
Examples 1 – 9
Ex. 9.1 Q 1 – 10
9.2: Earning and spending
Examples 1 – 5
Ex. 9.2 Q 1 – 14
Analysis task 1: Standard drinks
Analysis task 3: LPG versus ULP
e.g. all sections in
Chapter 3: Trigonometry
Chapter 6: Measurement
Chapter 7: Similarity and trigonometry
Most questions require students to round answers
to a specified or to a sensible number of decimal
places.
5.0
Students use efficient mental and/or written
methods for arithmetic computation involving
rational numbers, including division of integers by
two-digit divisors.
Chapter 1: Real numbers
*Chapter pre-test Q 1 – 13
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
3
3
Level
Number
5.0
5.0
Standard/Progression Point
They use approximations to π in related
measurement calculations (for example,
π × 52 = 25π = 78.54 correct to two decimal
places).
They use technology for arithmetic computations
involving several operations on rational numbers
of any size.
MathsWorld 9
Chapter 2: Length, area and volume
*Chapter pre-test Q 6
2.4: Calculating perimeter
Examples 2, 3
Ex. 2.4 Q 4 – 8
2.5: Area
Examples 1d, 2b, 3, 4
Ex. 2.5 Q 1i – l, 2e – i ,
5e – j, 7
2.6: Surface area
Examples 6, 7
Ex. 2.6 Q 3 – 5, 8
2.7: Volume
Examples 3, 5
Ex. 2.7 Q 5 – 8, 13, 16, 17
Analysis task 1: Chemical storage tanks
Analysis task 2: Melbourne Central cone
Chapter 1: Real numbers
*Chapter pre-test Q 16
Also Chapters 2, 5, 7, 9, 10
MathsWorld 9 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 1.1, 1.2 p 161
TI 89 1.1, 1.2 p 195
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
4
MathsWorld 10
Chapter 3: Trigonometry
3.5: Degrees and radians
Try this! p 179
Examples 1, 2, 3, 4
Ex. 3.5 Q 1 – 5
Analysis task 3: Radians and the unit circle
Chapter 6: Measurement
*Chapter pre-test Q 7, 10
Chapter Warm-up Try this! p 369
6.2: Calculating arc length
Example 1
Ex. 6.2 Q 1, 2
6.3: Spheres and circles
Examples 1, 3, 4
Ex. 6.3 Q 1 – 10
6.4: Calculating area
Examples 2, 6
Ex. 6.4 Q 3 – 6, 11, 12, 13
6.5: Calculating surface area
Examples 5, 6, 7
Ex. 6.4 Q 3, 5 – 11
6.6: Calculating volume and capacity
Examples 2, 4, 5, 6, 9, 10
Ex. 6.6 Q 2 – 6, 12 – 20
All chapters
MathsWorld 10 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 1.1, 1.2 pp 137, 138
TI 89 1.1, 1.2 pp 171, 172
4
Level
Number
5.25
Standard/Progression Point
•
5.25
•
5.25
•
MathsWorld 9
relationships between real, rational, irrational
integers and natural numbers on a Venn
diagram
Chapter 1: Real numbers
1.1: Rational numbers
p5
1.4: Irrational numbers
Try this! p 27
determination of lowest common multiple
through investigation of prime factors
Chapter 1: Real numbers
1.3: Factors and prime factors
Examples 1, 2, 3
(See note in Teacher edition p 18 and Year 9
Cumulative test)
solution of problems involving ratio and
proportion
Chapter 5: Ratio and rates
*Chapter pre-test Q 2 – 9
5.1: Ratio and proportion
Examples 5, 6, 7
Ex. 5.1 Q 6 – 18
Chapter 7: Similarity and trigonometry
*Chapter pre-test Q 2, 3, 7, 10
7.2: Similar triangles
Example 2
Ex. 7.2 Q 2, 4, 5, 8, 11, 12, 13
5.25
•
representation and recognition of large and
small numbers in scientific notation
MathsWorld 10
Chapter 10: Irrational numbers
10.1: Irrational numbers and non-integer indices
Try this! p 613
Chapter 3: Trigonometry
*Chapter pre-test Q 1
Chapter 9: Applications of arithmetic
*Chapter pre-test Q 4, 7, 8
Chapter Warm-up Try this! p 565
9.2: Earning and spending
Examples 3, 4, 5
Ex 9.2 Q 10, 11, 12
Chapter 2: Length, area and volume
2.2: Scientific notation
Examples 1 – 7
Try this! p 69
Ex. 2.2 Q 1 – 9
Chapter 9: Applications of arithmetic
*Chapter pre-test Q 9
9.4: Scientific notation
Examples 1a, 2a, 3, 4, 5
Ex. 9.4 Q 1 – 10
MathsWorld 9 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 1.1 p 161
TI 89 1.1 p 195
MathsWorld 10 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 1.1 p 137
TI 89 1.1 p 171
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
5
5
Level
Number
5.25
5.5
Standard/Progression Point
•
•
MathsWorld 9
calculation and use of percentage change in
practical situations, for example, discounts.
Chapter 5: Ratio and rates
5.3: Percentages
Examples 4 – 12
Ex. 5.3 Q 6 – 19
Chapter 9: Applications of arithmetic
*Chapter pre-test Q 2, 3, 4, 6
9.1: Percentages and rates in retail and finance
*Chapter pre-test Q 2, 3
Examples 1 – 11
Ex. 9.1 Q 1 – 14
simplification of surds, for example,
Chapter 1: Real numbers
1.4: Irrational numbers
Examples 2, 3
Ex. Q 6, 7, 9, 10, 15
Chapter 10: Irrational numbers
*Chapter pre-test Q 8, 10, 12
10.2: Surds
Examples 1, 3, 4
Ex. 10.2 Q 4 – 7, 9
12  2 3
MathsWorld 9 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 1.1 p 161
TI 89 1.1 p 195
5.5
•
5.5
•
MathsWorld 10
MathsWorld 10 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 1.1 p 137
TI 89 1.1 p 171
calculation of the whole given the size of a
percentage; for example, if a 20% discount is
$7, what was the original value?
Chapter 5: Ratio and rates
5.3: Percentages
Examples 5, 7
Ex. 5.3 Q 7, 8
Chapter 9: Applications of arithmetic
9.1: Percentages and rates in retail and finance
Examples 5, 6
Ex. 9.1 Q 2, 3, 4
solution of proportion problems using real
numbers
Chapter 5: Ratio and rates
5.1: Ratio and proportion
Chapter Warm-up Try this! pp 243, 245
Examples 1 – 7
Ex. 5.1 Q 5 – 16
5.2: Rates
Examples 2 – 9
Ex. 5.2 Q 1 – 16
Chapter 5: Algebra toolbox 2
5.4: Real solutions to quadratic equations
Ex. 5.4 Q 13
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
6
6
Level
Number
5.5
5.5
Standard/Progression Point
•
•
calculation of approximate values for  , the
golden ratio, using measurement, definition,
and successive ratios of the Fibonacci
sequence
computation involving natural numbers,
integers, finite decimals and surds, without
the aid of technology, giving exact answers
as applicable.
MathsWorld 9
MathsWorld 10
Chapter 1: Real numbers
Analysis task 1: The golden ratio
See note in Teacher Edition
Chapter 5: Algebra toolbox 2
5.4: Real solutions to quadratic equations
Ex. 5.4 Q 13
Chapter 1: Real numbers
Chapter pre-test Q 1 – 13
1.1: Rational numbers
Examples 1, 2, 3, 4
Ex. 1.1 Q 1 – 11
1.2: Integer powers of rational numbers
Examples 1, 3, 4, 5
Ex. 1.2 Q 1 – 11
1.3: Factors and prime factors
Examples 1, 2, 3, 4, 5
Ex. 1.3 Q 1 – 11
1.4: Irrational numbers
Examples 1, 2, 3, 4
Ex. 1.4 Q 9 – 17
1.5: Adding and subtracting surds
Examples 1, 2
Ex. 1.5 Q 1, 3 – 14
1.6: Multiplying and dividing surds
Examples 1, 2, 3
Ex. 1.5 Q 1 – 10
Chapter 10: Irrational numbers
*Chapter pre-test Q 7 – 12
10.3: Adding and subtracting surds
Example 1
Ex. 10.3 Q 1 – 13
10.4: Multiplying and dividing surd
expressions
Examples 1, 2, 3, 4
Ex. 10.4 Q 1 – 13
Chapter 3: Trigonometry
3.4: Applying trigonometry
Try this! p 152
Ex. 3.4 Q 18
Chapter 6: Measurement
Analysis task 1: Honeycomb and bubbles
Chapter 2: Length, area and volume
Analysis task 3: Short shoelaces!
5.5
•
calculation of the remainder after division by
using multiplication (as needed for Euclid's
method)
Chapter 1: Real numbers
1.3: Factors and prime factors
Example 4
Ex. 1.3 Q 4, 5
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
7
7
Level
Number
5.75
5.75
Standard/Progression Point
•
•
division and multiplication of numbers in
index form, including application to scientific
notation.
Chapter 9: Applications of arithmetic
*Chapter pre-test Q 9
9.4: Scientific notation
Ex. 9.4 Q 5 – 10
MathsWorld 9 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 1.1 p 161
TI 89 1.1 p 195
MathsWorld 10 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 1.1 p 137
TI 89 1.1 p 171
Chapter 1: Real numbers
1.2: Integer powers of rational numbers
Try this! p 14
Example 4
Ex. 1.4 Q 6, 7, 8
Chapter 2: Algebra toolbox 1
2.6: Index form with pronumerals
p 128
Example 8
Ex. 2.6 Q 3, 4
Chapter 2: Length, area and volume
2.2: Scientific notation
Try this! p 69
Example 4
Chapter 9: Applications of arithmetic
9.4: Scientific notation
Examples 1, 2
application of scientific notation and recalled
approximations to squares and square roots to
approximate values for expressions.
Chapter 2: Length, area and volume
See Teacher edition p 71 for additional example
and questions
Chapter 9: Applications of arithmetic
See Teacher edition p 593 for additional example
and questions
rationalisation of expressions where division
by a square root is involved, for example,
Chapter 1: Real numbers
1.7: Rationalising the denominator
Examples 1, 2
Ex. 1.7 Q 1 – 7
Try this! p 40
Chapter 10: Irrational numbers
10.5: Rationalising the denominator
Examples 1, 2
Ex. 10.5 Q 1 – 12
knowledge of the equivalence of
3
•
5.75
•
MathsWorld 10
Chapter 2: Length, area and volume
2.2: Scientific notation
Examples 6, 7
Ex. 2.2 Q 5 – 8
 1
3
  and 10
 10 
5.75
MathsWorld 9
5
15

3
3
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
8
8
Level
Number
6.0
6.0
Standard/Progression Point
At Level 6, students comprehend the set of real
numbers containing natural, integer, rational and
irrational numbers.
They represent rational numbers in both fractional
and decimal (terminating and infinite recurring)
forms (for example, 14/ 25 = 1.16, = 47/ 99 ).
MathsWorld 9
Chapter 1: Real numbers
Chapter Warm-up Try this! p 4
1.1: Rational numbers
Ex. 1.1 Q 1
1.4: Irrational numbers
p 27 Try this!
MathsWorld 10
Chapter 10: Irrational numbers
Chapter Warm-up Try this p 611
10.1: Surds
p 612, 613
Ex. 10.1 Q 1, 2, 3
Analysis task 1: Geometry strips
Analysis task 2: The A series of paper sizes
Chapter 1: Real numbers
*Chapter pre-test Q 3, 4
Chapter Warm-up Try this! p 4
1.1: Rational numbers
Examples 1, 2, 3, 4
Ex. 1.1 Q 2 – 11
Chapter 5: Ratios and rates
5.1: Ratio and proportion
Examples 3, 4
Ex. 5.1 Q 1, 2
Chapter 9: Chance
*Chapter pre-test Q 6
9.3: Probability
Ex 9.3 Q 10
6.0
They comprehend that irrational numbers have an
infinite non-terminating decimal form.
Chapter 1: Real numbers
1.4: Irrational numbers
Try this! p 30
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
9
Chapter 10: Irrational numbers
10.1: Irrational numbers and non-integer
indices
Ex. 10.1 Q 5, 6, 7
Try this! p 617
10.3: Adding and subtracting like surds
Ex. 10.3 Q 7, 9, 10
9
Level
Number
6.0
Standard/Progression Point
They specify decimal rational approximations for
square roots of primes, rational numbers that are
not perfect squares, the golden ratio φ, and simple
fractions of π correct to a required decimal place
accuracy.
MathsWorld 9
Chapter 1: Real numbers
1.4: Irrational numbers
Example 1
Ex. 1.4 Q 3, 6
Analysis task 1: The golden ratio
Chapter 2: Length, area and volume
2.3: Pythagoras’ theorem
Examples 2, 3, 6
Ex. 2.3 Q 1 – 5, 9 – 14
All calculations involving circles in:
2.5: Area
2.6: Surface area
2.7: Volume
Analysis task 1: Chemical storage tanks
Analysis task 2: Melbourne Central cone
Analysis task 3: Short shoelaces
MathsWorld 10
Chapter 3: Trigonometry
3.5: Degrees and radians
Examples 1, 3
Ex. 3.5 Q 2, 5, 6
Chapter 5: Algebra toolbox 2
5.4: Real solutions to quadratic equations
Ex. 5.4 Q 7
Chapter 6: Measurement
6.1: Applying Pythagoras’ theorem in two and
three dimensions
Examples 1, 2, 3, 4
Ex. 6.1 Q 1 – 11
All calculations involving circles in:
6.2: Calculating arc length
6.3: Spheres and circles
6.4: Calculating area
6.6: Calculating volume and capacity
Chapter 10: Irrational numbers
10.1: Irrational numbers and non-integer
indices
Analysis task 1: Geometry strips
Analysis task 2: The A4 series of paper sizes
6.0
Students use the Euclidean division algorithm to
find the greatest common divisor (highest
common factor) of two natural numbers 9 (for
example, the greatest common divisor of 1071 and
1029 is 21 since 1071 = 1029 × 1 + 42, 1029 = 42
× 24 + 21 and 42 = 21 × 2 + 0).
Chapter 1: Real numbers
1.3: Factors and prime factors
Examples 4, 5
Ex. 1.3 Q 4 – 8
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
10
10
Level
Number
6.0
6.0
Standard/Progression Point
Students carry out arithmetic computations
involving natural numbers, integers and finite
decimals using mental and/or written algorithms
(one- or two-digit divisors in the case of division).
They perform computations involving very large
or very small numbers in scientific notation (for
example, 0.0045 × 0.000028 = 4.5 × 10 −3 × 2.8 ×
10−5 = 1.26 × 10−7).
MathsWorld 9
MathsWorld 10
Chapter 1: Real numbers
*Chapter pre-test Q 1 – 13
(See Teacher edition for comment, and Year 9
Cumulative Revision Test)
Chapter 2: Length, area and volume
2.2: Scientific notation
Examples 3, 5, 6, 7
Ex. 2.2 Q 5 – 9
Chapter 9: Applications of arithmetic
*Chapter pre-test Q 9
9.4: Scientific notation
Examples 1, 2, 3, 4, 5
Ex. 9.4 Q 1 – 10
Chapter 10: Irrational numbers
10.1: Irrational numbers and non-integer
indices
Ex. 10.1 Q 10
6.0
They carry out exact arithmetic computations
involving fractions and irrational numbers such as
square roots
(for example, √18 = 3√2, √( 3/2 ) = (√6)/ 2) and
multiples and fractions of π (for example
π + π/ 4 = 5 / 4).
Chapter 1: Real numbers
1.4: Irrational numbers
Examples 2, 3
Ex. 1.4 Q 9 – 13
1.5: Adding and subtracting surds
Examples 1, 2
Ex. 1.5 Q 1 – 14
1.6: Multiplying and dividing surds
Examples 1, 2, 3
Ex. 1.6 Q 1 – 10
1.7: Rationalising the denominator
Examples 1, 2
Ex. 1.7 Q 1 – 7
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
11
Chapter 10: Irrational numbers
*Chapter pre-test Q 8 - 12
10.2: Surds
Examples 1, 2, 3, 4
Ex. 10.2 Q 7 – 19
10.3: Adding and subtracting surds
Example 1
Ex. 10.3 Q 1 – 13
10.4: Multiplying and dividing surd
expressions
Examples 1, 2, 3, 4
Ex. 10.4 Q 1 – 13
10.5: Rationalising the denominator
Examples 1, 2
Ex. 10.6 Q 1 – 12
Analysis task 2: The A4 series of paper sizes
11
Level
Number
6.0
Standard/Progression Point
They use appropriate estimates to evaluate the
reasonableness of the results of calculations
involving rational and irrational numbers, and the
decimal approximations for them.
MathsWorld 9
Chapter 2: Length, area and volume
2.1: Significant figures and measurement
errors
Try this! p 61
Ex. 2.3 – 2.7
Students should be encouraged in all exercises to
estimate answers and check for reasonableness
MathsWorld 10
Students should be encouraged in all exercises to
estimate answers and check for reasonableness
Most sections, particularly in
Chapter 6: Measurement
Chapter 9: Applications of arithmetic
Chapter 3: Mathematical thinking
3.2: Extended modelling tasks with technology
Practice problem 2
Try this! p 144
Try this! p 149
6.0
They carry out computations to a required
accuracy in terms of decimal places and/or
significant figures.
Chapter 2: Length, area and volume
2.1: Significant figures and measurement
errors
Examples 1, 2
Ex. 2.1 Q 1 – 4
All exercises in sections 2.4 to 2.7 include
questions that require students to round answers
to a given or sensible number of significant
figures.
Chapter 7: Similarity and trigonometry
All exercises
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
12
For example:
Chapter 3: Trigonometry
All sections
Chapter 6: Measurement
All sections
Chapter 9: Applications of arithmetic
*Chapter pre-test Q 10
9.5: Errors and significant figures
Ex. 9.5 Q 1 – 4, 7, 9
12
Level
Space
5.0
Standard/Progression Point
At Level 5, students construct two-dimensional
and simple three-dimensional shapes according to
specifications of length, angle and adjacency.
MathsWorld 9
Chapter 6: Two-dimensional space
*Chapter pre-test Q 4, 5
6.4: Angles in a circle
Example 5
Ex. 6.4 Q 4, 5
MathsWorld 10
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 5, 7, 8
1.1: Circles, chords and angles
Ex. 1.1 Q 7, 8
1.2: Representing three dimensional objects
Examples 1, 2, 3, 4
Ex. 1.2 Q 1 – 4
1.3: Polyhedra and nets
Try this! p 37
Ex. 1.3 Q 1
Chapter 3: Trigonometry
3.2: Trigonometric ratios
Try this! p 152
5.0
They use the properties of parallel lines and
transversals of these lines to calculate angles that
are supplementary, corresponding, allied (cointerior) and alternate.
Chapter 6: Two-dimensional space
*Chapter pre-test Q 1, 2d, f
Q 1, 2
6.1: Angles, parallel lines and triangles
Example 4
Ex. 6.1 Q 4a – i, 6d, f
6.2: Quadrilateral properties
Example 2b
Ex. 6.2 2a, c, d, e, f, g, i
Chapter 3: Trigonometry
3.4: Applying trigonometry
Examples 1, 2
Ex. 3.4 Q 13, 14
Chapter 6: Measurement
Chapter Warm-up Try this! p 369
6.3: Spheres and circles
p 391
Example 4
Chapter 7: Similarity and trigonometry
7.5: Applying trigonometry
Try this! p 398
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
13
13
Level
Space
5.0
Standard/Progression Point
They describe and apply the angle properties of
regular and irregular polygons, in particular,
triangles and quadrilaterals.
5.0
They use two-dimensional nets to construct a
simple three-dimensional object such as a prism or
a platonic solid.
5.0
They recognise congruence of shapes and solids.
5.0
They relate similarity to enlargement from a
common fixed point.
5.0
They use single-point perspective to make a twodimensional representation of a simple threedimensional object.
MathsWorld 9
MathsWorld 10
Chapter 6: Two-dimensional space
*Chapter pre-test Q 2, 5, 6b, 8, 9, 10
Q 2, 3
6.1: Angles, parallel lines and triangles
Examples 5, 8
Ex. 6.1 Q 3b – i, 4a – h, 6a, b, c, 7 – 11, 19 – 21
6.2: Quadrilateral properties
Example 2
Ex. 6.2 Q 2 – 8
6.3: Polygons
Examples 1, 2
Ex. 6.3 Q 1 – 7
Analysis task 1: Pascal’s angle trisector
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 2, 4
1.3: Polyhedra and nets
Try this! p 35
Example 1
Ex. 1.3 Q 4, 5
Chapter 2: Length, area and volume
2.6: Surface area
Example 3
Ex. 2.6 Q 2
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 5
1.3: Polyhedra and nets
Try this! p 37
Ex. 1.3 Q 1, 2
Chapter 6: Two-dimensional space
6.1: Angles, parallel lines and triangles
Example 1
Ex. 6.1 Q 7
Chapter 1: 2D and 3D geometry
Try this! p 15
Analysis task 2: Sylvester’s pantograph
Analysis task 3: Consul the educated monkey
Chapter 7: Similarity and trigonometry
Try this! p 360
Ex. 7.1 Q 6
Chapter 1: 2D and 3D geometry
1.6: Loci
Ex. 1.6 Q 4
MathsWorld 10 Teacher edition
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14
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 7
1.2: Representing three-dimensional objects
Example 3
Ex. 1.2 Q 1 – 5
14
Level
Space
5.0
Standard/Progression Point
They make tessellations from simple shapes.
MathsWorld 9
MathsWorld 10
Chapter 1: Real numbers
Analysis task 2: Federation Square tiles
Chapter 6: Two-dimensional space
6.3: Polygons
Ex. 6.3 Q 6
5.0
Students use coordinates to identify position in the
plane.
5.0
They use lines, grids, contours, isobars, scales and
bearings to specify location and direction on plans
and maps.
Chapter 8: Functions and modelling
*Chapter pre-test Q 1
8.2: Formulating functions
Example 1b
Ex. 8.2 Q 1 – 5
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 10
1.5: Isometric transformations
Try this! p 60, 62, 63, 65
Examples 2, 3, 5, 6
Ex. 1.5 Q 2, 3
Chapter 6: Two-dimensional space
6.1: Angles, parallel lines and triangles
Example 9
Ex. 6.1 16, 17, 19, 20
Chapter 3: Trigonometry
3.4: Applying trigonometry
Example 2
Ex. 3.4 Q 12, 13, 14, 15
Chapter 7: Similarity and trigonometry
7.5: Applying trigonometry
Example 3
Ex. 7.5 Q 9, 10, 12
5.0
They use network diagrams to specify
relationships.
5.0
They consider the connectedness of a network,
such as the ability to travel through a set of roads
between towns.
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Chapter 1: 2D and 3D geometry
1.4: Networks
Try this! p 45
Example 4
Ex. 1.4 Q 15, 16
Chapter 1: 2D and 3D geometry
1.4: Networks
Try this! p 45, 47
Examples 1, 2
Ex. 1.4 Q 2, 3, 4, 10, 11, 12, 13, 14
15
Level
Space
5.25
Standard/Progression Point
•
5.25
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5.25
•
5.25
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5.5
•
MathsWorld 9
MathsWorld 10
use of two-dimensional nets and line-segment
models to investigate regular, semi-regular
and irregular solids
Chapter 1: 2D and 3D geometry
1.3: Polyhedra and nets
Example 1
Ex. 1.3 Q 1 – 5
use of Euler’s formula for polyhedra and their
nets
Chapter 1: 2D and 3D geometry
1.4: Networks
Try this! p 51
Example 5
Ex. 1.4 Q 8, 12, 15, 16
application of the angle properties of parallel
lines and transversals to other geometrical
problems
Chapter 7: Similarity and trigonometry
7.5: Applying trigonometry
Try this! p 398
Example 3
Ex. 7.5Q 5
Chapter 6: Measurement
Chapter Warm-up Try this! p 369
knowledge of sets of conditions for pairs of
triangles to be congruent
Chapter 6: Two-dimensional space
*Chapter pre-test Q 3
6.1: Angles, parallel lines and triangles
Examples 1, 2
Ex. 6.1 Q 7
Chapter 1: 2D and 3D geometry
1.1: Circles, chords and tangents
Try this! p 15
Analysis task 2: Sylvester's pantograph
recognition of features of circles (centre,
radius, diameter, chord, arc, semi-circle,
segment, sector and tangent) and the
associated angle properties
Chapter 6: Two-dimensional space
6.4: Angles in a circle
p 335
Examples 1, 2, 3, 4
Ex. 6.4 Q 1, 2, 3
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 1
1.1: Circles, chords and angles
p. 6
Examples 1, 2, 3, 4, 5
Ex. 1.1 Q 1 – 4
MathsWorld 10 Teacher edition
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16
Level
Space
5.5
Standard/Progression Point
•
5.5
•
5.5
•
5.75
•
5.75
•
investigation of angle properties of circles and
tangents
MathsWorld 9
Chapter 6: Two-dimensional space
6.4: Angles in a circle
Try this! p 335-336
Analysis task 2: Road accident analysis
Analysis task 3: Cyclic quadrilaterals
•
Chapter 1: 2D and 3D geometry
1.1: Circles, chords and tangents
Try this! p 7, 8
Try this! p 11, 13, 15, 16
Ex. 1.1 Q 3, 4, 7, 8, 12
Analysis task 1: Tangents and intersecting
secants
representation of a point on the Earth's
surface in terms of its latitude and longitude
Chapter 6: Measurement
6.3: Spheres and circles
Try this! p 387
Examples 3, 4, 5
Ex. 6.3 Q 5, 6, 7
identification of paths and circuits in network
diagrams that illustrate connections between
objects, locations and events
Chapter 1: 2D and 3D geometry
1.4: Networks
Try this! p 45, 46, 47
Examples 1, 2, 3
location of the great circle pathway between
two points on a sphere
Chapter 6: Measurement
6.3: Spheres and circles
Try this! p 382
Example 1
Ex. 6.3 Q 1
application of geometrical transformations to
graphs
Chapter 8: Functions and modelling
8.3: Linear functions
Ex. 8.3 Q 9
Chapter 11: Algebra toolbox 2
Analysis task 1: A family of parabolas
5.75
MathsWorld 10
knowledge of latitude and longitude in
geometric terms
MathsWorld 10 Teacher edition
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Chapter 1: 2D and 3D geometry
1.5: Isometric transformations
Try this! p 60, 62, 63
Example 3
Try this! p 65
Examples 5, 6
Ex. 1.5 Q 7 – 11
Chapter 6: Measurement
6.3: Spheres and circles
Try this! p 387
17
Level
Space
6.0
6.0
Standard/Progression Point
At Level 6, students represent two- and threedimensional shapes using lines, curves, polygons
and circles.
MathsWorld 9
Chapter 7: Similarity and trigonometry
7.5: Applications of trigonometry
Examples 1, 2, 3
Ex. 7.5 All questions
They make representations using perspective,
isometric drawings, nets and computer-generated
images.
MathsWorld 10 Teacher edition
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MathsWorld 10
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 5, 6, 7
1.2: Representing three-dimensional objects
Examples 1, 2, 3, 4
Ex. 1.2 Q 1 – 5
1.3: Polyhedra and nets
Try this! p 37
Ex. 1.3 Q 1, 2
1.4: Networks
Try this! p 45
Example 4
Ex. 1.4 Q 15, 16
1.5: Isometric transformations
Examples 1, 2, 4
Try this! p 60
Ex. 1.5 Q 1, 4, 5, 6
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 7, 8
1.2: Representing three-dimensional objects
Examples 1, 2, 3, 4
Ex. 1.2 Q 1 – 5
1.3: Polyhedra and nets
Try this! p 37
Ex. 1.3 Q 1, 2
1.5: Isometric transformations
Examples 1, 2, 4
Try this! p 60
Ex. 1.5 Q 1, 4, 5, 6
18
Level
Space
6.0
Standard/Progression Point
They recognise and describe boundaries, surfaces
and interiors of common plane and threedimensional shapes, including cylinders, spheres,
cones, prisms and polyhedra.
MathsWorld 9
Chapter 2: Length, area and volume
2.4: Calculating perimeter
2.5: Area
2.6: Surface area
2.7: Volume
MathsWorld 10
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 3, 4, 5, 6
1.3: Polyhedra and nets
Try this! p 35, 37
Ex. 1.3 Q 1, 2, 4, 5
Chapter 6: Measurement
6.2: Calculating arc length
6.3 Spheres and circles
Try this! p 383
6.4: Calculating area
6.5: Calculating surface area
6:6: Calculating volume and capacity
6.0
They recognise the features of circles (centre,
radius, diameter, chord, arc, semi-circle,
circumference, segment, sector and tangent) and
use associated angle properties.
Chapter 2: Length, area and volume
2.4: Calculating perimeter
p 87
Example 3
2.5: Area
p 93
Example 4
Chapter 6: Two-dimensional space
6.4: Angles in a circle
Try this! p 335-6
Examples 1, 2, 3, 4, 5
Ex. 6.4 Q 1 – 5
Analysis task 2: Road accident analysis
MathsWorld 10 Teacher edition
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19
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 1
Chapter Warm-up Try this! p 5
1.1: Circles, chords and tangents
Try this! 7, 8, 11, 12, 13, 15
Examples 1, 2, 3, 4, 5
Ex. 1.1 Q 1 – 13
Analysis task 1: Tangents and intersecting
secants
19
Level
Space
6.0
Standard/Progression Point
MathsWorld 9
Students explore the properties of spheres.
MathsWorld 10
Chapter 1: 2D and 3D geometry
*Chapter pre-test Q 1
Chapter Warm-up Try this! p 5
1.1: Circles, chords and tangents
Try this! 7, 8, 11, 12, 13, 15
Examples 1, 2, 3, 4, 5
Ex. 1.1 Q 1 – 13
Analysis task 1: Tangents and intersecting
secants
Chapter 6: Measurement
6.3: Spheres and circles
Try this! p 383
6.0
Students use the conditions for shapes to be
congruent or similar.
Chapter 7: Similarity and trigonometry
7.1: Similarity and scale
Examples 1, 2
Ex. 7.1 Q 1, 2
7.2: Similar triangles
Examples 1, 2
Ex. 7.2 Q 1, 3, 5, 6, 7, 9, 10, 11
Chapter 1: 2D and 3D geometry
1.1: Circles, chords and tangents
Try this! p 15, 16
Ex. 1.1
1:6: Loci
Ex. 1.6 Q 4
Analysis task 2: Sylvester's pantograph
Analysis task 3: Consul the educated monkey
Chapter 6: Measurement
6.6: Calculating volume and capacity
Try this! p 430, 434
Examples 7, 8, 9, 10
Ex. 6.6 Q 7, 12
6.0
They apply isometric and similarity
transformations of geometric shapes in the plane.
Chapter 7: Similarity and trigonometry
7.1: Similarity and scale
Try this! p 360
Ex. 7.1 Q 6, 9
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Chapter 1: 2D and 3D geometry
1.5: Isometric transformations
Examples 1, 2, 4
Ex. 1.5 Q 1, 2, 4, 5, 6
20
Level
Space
6.0
6.0
Standard/Progression Point
MathsWorld 9
They identify points that are invariant under a
given transformation (for example, the point (2, 0)
is invariant under reflection in the x-axis, so the x
axis intercept of the graph of y = 2x – 4 is also
invariant under this transformation).
They determine the effect of changing the scale of
one characteristic of two- and three-dimensional
shapes (for example, side length, area, volume and
angle measure) on related characteristics.
Chapter 1: 2D and 3D geometry
1.5: Isometric transformations
Try this! p 62, 63, 65
Example 3, 5, 6
Ex. 1.5 7, 8, 10, 11
Chapter 5: Ratios and rates
5.1: Ratio and proportion
Ex. 5.1 Q 15, 16, 17
Chapter 7: Similarity and trigonometry
Chapter Warm-up p 358
7.1: Similarity and scale
Try this! p 361
Ex. 7.1 Q 3, 4, 5, 7, 8, 10, 11, 12
6.0
They use latitude and longitude to locate places on
the Earth’s surface and measure distances between
places using great circles.
6.0
Students describe and use the connections
between objects/location/events according to
defined relationships (networks)
MathsWorld 10
MathsWorld 10 Teacher edition
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21
Chapter 6: Measurement
6.5: Calculating surface area
Ex. 6.5 Q 6
6.6: Calculating volume and capacity
Try this! p 437
Ex. 6.6 Q 17
Analysis task : A limit to size
Chapter 6: Measurement
6.3: Spheres and circles
Try this! p 382
Examples 1, 3, 5
Ex. 6.3 Q 1, 2, 3, 4, 10
Chapter 1: 2D and 3D geometry
1.4: Networks
Try this! p 45, 46, 47, 49
Examples 1,2, 3, 4
Ex. 1.4 Q 1 – 16
21
Level
Measurement,
Chance and Data
5.0
5.0
Standard/Progression Point
At Level 5, students measure length, perimeter,
area, surface area, mass, volume, capacity, angle,
time and temperature using suitable units for these
measurements in context.
They interpret and use measurement formulas for
the area and perimeter of circles, triangles and
parallelograms and simple composite shapes.
MathsWorld 9
MathsWorld 10
Chapter 2: Length, area and volume
*Chapter pre-test
Q 4 – 10
2.4: Calculating perimeter
2.5: Area
2.6: Surface area
2.7: Volume
Chapter 3: Trigonometry
All sections
Chapter 2: Length, area and volume
*Chapter pre-test Q 4–8
2.4: Calculating perimeter
2.5: Area
Chapter 6: Measurement
*Chapter pre-test Q 3 – 10
6.2: Calculating arc length
6.4: Calculating area
Chapter 6: Measurement
*Chapter pre-test Q 3 – 10
All sections
Chapter 4: Algebra toolbox 1
Analysis task 3: Garden paths
5.0
They calculate the surface area and volume of
prisms and cylinders.
5.0
Students estimate the accuracy of measurements
and give suitable lower and upper bounds for
measurement values.
Chapter 2: Length, area and volume
*Chapter pre-test Q 9, 10
2.6: Surface area
Examples 1, 2, 3, 6, 7
Ex. 2.6 Q 1 – 6, 8
2.7: Volume
Examples 1, 2, 3
Ex. 2.7 Q 1 – 11
Analysis task 1: Chemical storage tanks
Chapter 6: Measurement
*Chapter pre-test Q 8, 9, 10
6.5: Calculating surface area
Examples 1, 2, 3, 5
Ex. 6.5 Q 1, 2, 3
6.6: Calculating volume and capacity
Examples 1, 2
Ex. 6.6 Q 1 – 6, 23, 24
Chapter 2: Length, area and volume
*Chapter pre-test Q 3
2.1: Significant figures and measurement
errors
Ex. 2.1 Q 6 – 8
Chapter 9: Applications of arithmetic
9.5: Errors and significant figures
Example 2
Ex. 9.5 Q 5, 6, 9, 10
MathsWorld 10 Teacher edition
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22
Level
Measurement,
Chance and Data
5.0
5.0
5.0
Standard/Progression Point
They calculate absolute percentage error of
estimated values.
Students use appropriate technology to generate
random numbers in the conduct of simple
simulations.
Students identify empirical probability as long-run
relative frequency.
MathsWorld 9
MathsWorld 10
Chapter 2: Length, area and volume
2.1 Significant figures and measurement
errors
Try this! p 63
Example 2
Ex. 2.1 Q 9, 11
Chapter 9: Applications of arithmetic
9.5: Errors and significant figures
Try this! p 597
Example 1
Ex. 9.5 Q 5, 6, 8
Chapter 10: Analysing data
10.1: Sampling and questionnaires
Examples 1, 2
Try this! p 565
Ex. 10.1 Q 4
Chapter 4: Statistical variables and
relationships
4.6: Populations, samples and randomness
Examples 2, 3
Ex. 4.6 Q 2, 3, 4
MathsWorld 9 Practice and Enrichment
Workbook (and CD): Technology toolkit
TI 83/84 1.8 p 165
TI 89 1.8 p 199
MathsWorld 10 Practice and Enrichment
Workbook (and CD): Technology toolkit
TI 83/84 1.8 p 141
TI 89 1.8 p 176
Chapter 9: Chance
*Chapter pre-test Q 6
9.3: Probability
Try this! p 536
Example 3
Ex. 9.3 Q 8 – 12
Chapter 7: Chance
*Chapter pre-test Q 3, 4, 10
Chapter Warm-up Try this! p 462
7.1: Probability
Example 2
Try this! p 464
Ex. 7.1 Q 8
7.2: Tables and Venn diagrams
Examples 1, 3
Ex. 7.2 Q 9
Analysis task 3: The ace race
MathsWorld 10 Teacher edition
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23
Level
Measurement,
Chance and Data
5.0
Standard/Progression Point
They calculate theoretical probabilities by
dividing the number of possible successful
outcomes by the total number of possible
outcomes.
5.0
They use tree diagrams to investigate the
probability of outcomes in simple multiple event
trials.
5.0
Students organise, tabulate and display discrete
and continuous data (grouped and ungrouped)
using technology for larger data sets.
MathsWorld 9
MathsWorld 10
Chapter 9: Chance
*Chapter pre-test Q 4, 5
9.3: Probability
Try this! p 536
Example 3
Ex. 9.3 Q 8 – 12
Chapter 7: Chance
*Chapter pre-test Q 2, 4
7.1: Probability
Try this! p 463
Examples 3, 4
Ex. 7.1 Q 2 – 7, 9 – 14
Chapter 9: Chance
9.4: Diagrams and tables
Examples 1, 2
Ex. 9.4 Q 1, 2, 6
Chapter 7: Chance
7.4: Tree diagrams and compound events
Examples 1, 2, 3
Try this! p 487
Ex. 7.4 Q 1 – 15
Analysis task 1: Tram’s game of chance
Analysis task 2: Pascal’s triangle and
probabilities
Chapter 10: Analysing data
*Chapter pre-test
Q 1, 2, 3, 7, 8, 9, 10
10.3: Representing data
Examples 1, 2, 3, 4
Ex. 10.3 Q 1 – 11
Chapter 4: Statistical variables and
relationships
4.2: Displaying statistical variables
Examples 1, 2
Ex. 4.1 Q 1 – 10
MathsWorld 9 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 6.1– 6.6 p 183–190
TI 89 6.1– 6.5 p 218–224
MathsWorld 10 Teacher edition
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24
24
Level
Measurement,
Chance and Data
5.0
Standard/Progression Point
They represent uni-variate data in appropriate
graphical forms including dot plots, stem and leaf
plots, column graphs, bar charts and histograms.
5.0
They calculate summary statistics for measures of
centre (mean, median, mode) and spread (range,
and mean absolute difference), and make simple
inferences based on this data.
5.25
•
conversion between units and between
derived units
MathsWorld 9
MathsWorld 10
Chapter 10: Analysing data
*Chapter pre-test Q 1, 2, 3, 9, 10
10.3: Representing data
Examples 1, 2, 3, 4
Ex.10.3 Q 1 – 11
Chapter 4: Statistical variables and
relationships
4.2: Displaying statistical variables
Examples 1, 2
Ex. 4.1 Q 1 – 10
4.5: Boxplots: A visual summary
Examples 1, 2
Ex. 4.5 Q 1 – 11
Chapter 10: Analysing data
*Chapter pre-test Q 3, 4, 5, 6
10.4: Summarising data
Examples 1, 2, 3, 4
Ex. 10.4 Q 1 – 15
Chapter 4: Statistical variables and
relationships
4.3: Summarising data: measures of centre
Examples 1, 2, 3
Ex. 4.3 Q 1 – 8
4.4: Summarising data: measures of spread
Try this! p 237
Example 1 – 5
Ex. 4.4 Q 1 – 8
Chapter 2: Length, area and volume
*Chapter pre-test Q 2e, f
2.6: Surface area
Example 6
2.7: Volume
Example 3
Ex. 2.7 Q 4, 5, 7, 8, 11, 15, 16
Chapter 6: Measurement
*Chapter pre-test Q 1
6.4: Calculating area
Example 2
6.6: Calculating volume and capacity
Example 1
MathsWorld 10 Teacher edition
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25
Level
Measurement,
Chance and Data
5.25
Standard/Progression Point
•
use of Pythagoras’ theorem to calculate the
length of the hypotenuse
MathsWorld 9
Chapter 2: Length, area and volume
2.3: Pythagoras’ theorem
Examples 1, 2, 3, 5
Ex. 2.3 Q 1, 2, 3, 4, 5, 6, 12, 14
Analysis task 3: Short shoelaces!
MathsWorld 10
Chapter 6: Measurement
6.1: Applying Pythagoras’ theorem in two and
three dimensions
Examples 1, 3
Ex. 6.1 Q 1a, c, f, g, h, 2a – i
Chapter 3: Mathematical thinking
3.1: Mathematical modelling
Example problem 1 p 134 – 136
3.2: Extended modelling tasks with technology
Try this! p 151, 159
Problem set 3.2 Q 1, 2
5.25
•
5.25
•
use of similarity and scale to calculate side
lengths in triangles
Chapter 7: Similarity and trigonometry
7.2: Similar triangles
Example 2
Ex. 7.2 Q 2, 4, 5, 7, 8, 11, 12, 13
7.3: Trigonometric ratios
Try this! p 374, 375
representation of compound events involving
two categories and the logical connectives
and, or and not using lists, grids (lattice
diagrams), tree diagrams, Venn diagrams and
Karnaugh maps (two-way tables) and the
calculation of associated probabilities
Chapter 9: Chance
9.4: Diagrams and tables
Examples 1, 2, 3, 4, 5, 6
Ex. 9.4 Q 1 – 13
Analysis task 1: At the fair
MathsWorld 10 Teacher edition
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26
Chapter 7: Chance
*Chapter pre-test Q 6, 7, 8, 9, 10
7.1: Probability
Try this! p 463
Examples 1, 4
Ex. 7.1 Q 10 – 14
7.4: Tree diagrams and compound events
Try this! p 487
Examples 1, 2, 3
Ex. 7.4 Q 1 – 15
Analysis task 1: Tram’s game of chance
Analysis task 2: Pascal’s triangle and
probabilities
26
Level
Measurement,
Chance and Data
5.25
Standard/Progression Point
•
representation of statistical data using
technology
MathsWorld 9
Chapter 10: Analysing data
10.3: Representing data
Ex. 10.3 Q 6 – 9
10.4: Summarising data
p. 604
Ex. 10.4 Q 1 – 14
MathsWorld 9 Practice and Enrichment
Workbook (and CD): Technology toolkit
TI 83/84 6.1– 6.6 p 183–190
TI 89 6.1– 6.5 p 218–224
5.5
•
5.5
•
MathsWorld 10
Chapter 4: Statistical variables and
relationships
4.2: Displaying statistical variables
Example 1
Ex. 4.2 Q 4
MathsWorld 10 Practice and Enrichment
Workbook (and CD): Technology toolkit
TI 83/84 6.1– 6.7 pp 159–168
TI 89 6.1– 6.7 pp 194 – 203
calculation and application of ratio,
proportion and rate of change such as
concentration, density, and the rate of filling
a container
Chapter 5: Ratio and rates
*Chapter pre-test Q 7, 8, 9
5.2: Rates
Examples 1 – 9
Ex. 5.2 Q 1 – 16
5.5 Constant and variable rates
Try this! p 286, 287-288
Example 1
Ex. 5.5 Q 1 – 12
Analysis task 1: How much water do we use?
Analysis task 2: Grand Prix
Analysis task 3: Compound interest
Chapter 9: Applications of arithmetic
*Chapter pre-test Q 7, 8
9.1: Percentages and rates in retail and finance
Analysis task 1: Standard drinks
Analysis task 3: LPG versus ULP
use of Pythagoras’ theorem to calculate the
length of a side other than the hypotenuse
Chapter 2: Length, area and volume
2.3: Pythagoras’ theorem
Example 6
Ex. 2.3 Q 8, 9, 10, 11, 13
Chapter 6: Measurement
6.1: Applying Pythagoras’ theorem in two and
three dimensions
Example 2
Ex. 6.1 Q b, d, e, i, j, k, l, 4
MathsWorld 10 Teacher edition
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27
27
Level
Measurement,
Chance and Data
5.5
Standard/Progression Point
•
5.5
•
5.5
•
MathsWorld 9
MathsWorld 10
use of trigonometric ratios to calculate
unknown sides in a right-angled triangle
Chapter 7: Similarity and trigonometry
7.3: Trigonometric ratios
Try this! pp 374, 375
Examples 1 – 3
Ex. 7.3 Q 5 – 17
Analysis task 2: Boom angles
Chapter 3: Trigonometry
*Chapter pre-test Q 5 – 6, 8, 9
3.3: Calculating side lengths and angles in
right-angled triangles
Examples 1, 2
Ex. 3.3 Q 1
3.4: Applying trigonometry
Examples 1, 2, 3, 4
Ex. 3.4 Q 1 – 5, 7 – 14, 17, 18
Analysis task 1: GPS and dead reckoning
display of data as a box plot including
calculation of quartiles and inter-quartile
range and the identification of outliers
Chapter 10: Analysing data
10.4: Summarising data
Example 4
Ex. 10.4 Q 5 – 8, 12
10.5: Boxplots
Examples 1, 2
Ex. 10.5 Q 1 – 10
Chapter 4: Statistical variables and
relationships
4.4: Summarising data: measures of spread
Try this! p 237, 238
Example 1
Ex. 4.4 Q 1 – 4
4.5: Boxplots: a visual summary
Examples 1, 2
Ex. 4.5 Q 1 – 11
qualitative judgement of positive or negative
correlation and strength of relationship and, if
appropriate, application of gradient to find a
line of good fit by eye.
Chapter 8: Functions and modelling
8.7: Mathematical models
Try this! p 487, 489
Ex. 8.7 Q 6, 7, 14
Chapter 4: Statistical variables and
relationships
4.9: Relationships between two numerical
variables
Examples 1, 2, 3
Ex. 4.9 Q 1 – 9
MathsWorld 10 Teacher edition
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28
Level
Measurement,
Chance and Data
5.75
Standard/Progression Point
•
MathsWorld 9
conversion between degrees and radians, and
use of radians when calculating arc length
and area of sectors
MathsWorld 10
Chapter 3: Trigonometry
3.5: Degrees and radians
Try this! p 179
Examples 1, 2, 3
Ex. 3.5 Q 1 – 6
Chapter 6: Measurement
Chapter Warm-up Try this! p 369
6.2: Calculating arc length
Examples 1, 2, 3
Ex. 6.2 Q 1 – 3
6.4: Calculating area
Try this! p 407
Example 6
Ex. 6.4 Q 11, 12
5.75
•
use of Pythagoras’ theorem in threedimensional applications
MathsWorld 10 Teacher edition
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Chapter 6: Measurement
6.1: Applying Pythagoras’ theorem in two and
three dimensions
Try this! p 372
Example 4
Ex. 6.1 Q 7, 8, 9, 10
6.5: Calculating surface area
Examples 4, 9
Ex. 6.5 Q 2, 3
6.6: Calculating volume and capacity
Example 3b
Ex. 6.6 Q 6
Analysis task 3: Arts Centre spire
29
Level
Measurement,
Chance and Data
5.75
Standard/Progression Point
•
5.75
•
5.75
•
MathsWorld 9
MathsWorld 10
calculation of unknown angle in a rightangled triangle using trigonometric ratios
Chapter 7: Similarity and trigonometry
7.4: Calculating angles
Examples 1, 2
Ex. 7.4 Q 3 – 9
Chapter 3: Trigonometry
*Chapter pre-test Q 7, 10
3.3: Calculating side lengths and angles in
right-angled triangles
Examples 3, 4
Ex. 3.3 Q 3, 4
3.4: Applying trigonometry
Examples 2, 3
Ex. 3.4 Q 2, 6, 13, 14, 15, 16, 18, 19
use of surveys as a means of obtaining
information about a population, including
awareness that sample results will not always
provide a reasonable estimate of population
parameters.
Chapter 10: Analysing data
10.1: Sampling and questionnaires
Example 4
Ex. 10.1 Q 1, 2, 3, 7, 8, 9, 10, 11, 12
Chapter 4: Statistical variables and
relationships
4.6: Populations, samples and randomness
Example 3
Try this! p 254
Ex. 4.6 Q 1, 2, 4, 5
placement of a line of best fit on a scatter plot
using technology and, where appropriate, use
of a line of best fit to make predictions.
Chapter 8: Functions and modelling
8.7: Mathematical modelling
Try this! p 485
Example 1
Try this! p 489
Ex. 8.7 Q 6, 7, 14
Chapter 4: Statistical variables and
relationships
4.9: Relationships between two numerical
variables
Example 3
Ex. 4.9 Q 8, 9
Analysis task 2: Cricket problem
Analysis task 3: Forensic formulas
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30
Level
Measurement,
Chance and Data
6.0
Standard/Progression Point
At Level 6, students estimate and measure length,
area, surface area, mass, volume, capacity and
angle.
MathsWorld 9
Chapter 2: Length, area and volume
*Chapter pre-test
Q 4 – 10
2.4: Calculating perimeter
Examples 1, 2, 3
Ex. 2.4 Q 1 – 8
2.5: Area
Examples 1, 2, 3, 4
Ex. 2.5 Q 1 – 10
2.6: Surface area
Examples 1 – 7
Ex. 2.6 Q 1 – 8
2.7: Volume
Examples 1, 2, 3, 4
Ex. 2.7 Q 1 – 17
Analysis task 1: Chemical storage tanks
Analysis task 2: Melbourne Central cone
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31
MathsWorld 10
Chapter 3: Trigonometry
*Chapter pre-test Q 5 – 10
3.3: Calculating side lengths and angles in
right-angled triangles
Examples 1, 2, 3, 4
Ex. 3.3 Q 1 – 3
3.4: Applying trigonometry
Examples 1, 2, 3, 4
Ex. 3.4 Q 1 – 19
Analysis task 1: GPS and dead reckoning
Chapter 6: Measurement
6.2: Calculating arc length
Examples 1, 2, 3
Ex. 6.2 Q 1 – 3
6.4: Calculating area
Try this! p 407
Examples 1 – 6
Ex. 6.4 Q 1 – 13
6.5: Calculating surface area
Examples 1 – 9
Ex. 6.5 Q 1 – 11
6.6: Calculating volume and capacity
Examples 2 – 10
– 24
31
Level
Measurement,
Chance and Data
6.0
Standard/Progression Point
They select and use appropriate units, converting
between units as required.
6.0
They calculate constant rates such as the density
of substances (that is, mass in relation to volume),
concentration of fluids, average speed and
pollution levels in the atmosphere.
6.0
Students decide on acceptable or tolerable levels
of error in a given situation.
MathsWorld 9
MathsWorld 10
Chapter 2: Length, area and volume
*Chapter pre-test Q 1, 2
2.5: Area
Ex. 2.5 Q 4
2.6: Surface area
Example 6
2.7: Volume
Example 3
Ex. 2.7 Q 8, 14, 15, 16
Chapter 3: Trigonometry
Chapter 5: Ratio and rates
5.2: Rates
Examples 1 – 9
Ex. 5.2 Q 1 – 16
Chapter 9: Applications of arithmetic
Analysis task 1: Standard drinks
Analysis task 3: LPG versus ULP
Chapter 2: Length, area and volume
2.1 Significant figures and measurement
errors
Ex. 2.1 Q 6 – 11
Chapter 3: Trigonometry
3.4: Applying trigonometry
Ex. 3.4 Q 9, 10
Chapter 3: Mathematical thinking
Try this! p 136
Chapter 7: Similarity and trigonometry
Analysis task 3: Angle errors
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32
Chapter 6: Measurement
All sections
Chapter 9: Applications of arithmetic
Try this! p 597, 598
9.5: Errors and significant figures
Examples 1, 2
Ex. 9.5 Q 5 – 10
32
Level
Measurement,
Chance and Data
6.0
Standard/Progression Point
They interpret and use mensuration formulas for
calculating the perimeter, surface area and volume
of familiar two- and three-dimensional shapes and
simple composites of these shapes.
MathsWorld 9
Chapter 2: Length, area and volume
2.4: Calculating perimeter
2.5: Area
2.6: Surface area
2.7: Volume
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MathsWorld 10
Chapter 6: Measurement
6.2: Calculating arc length
Examples 1, 2, 3
Ex. 6.2 Q 1 – 3
6.4: Calculating area
Try this! p 407
Examples 1 – 6
Ex. 6.4 Q 1 – 13
6.5: Calculating surface area
Examples 1 – 9
Ex. 6.5 Q 1 – 11
6.6: Calculating volume and capacity
Examples 2 – 10
– 24
33
Level
Measurement,
Chance and Data
6.0
Standard/Progression Point
Students use Pythagoras’ theorem and
trigonometric ratios (sine, cosine and tangent) to
obtain lengths of sides, angles and the area of
right-angled triangles.
MathsWorld 9
Chapter 2: Length, area and volume
2.3: Pythagoras’ theorem
Examples 1, 2, 3, 4, 5, 6
Ex. 2.3 Q 1 – 18
2.4: Calculating perimeter
Try this! p 85
Ex. 2.4 Q 3
2.6: Surface area
Example 5
Ex. 2.6 Q 6
Analysis task 3: Short shoe laces
Chapter 3: Mathematical thinking
3.1: Mathematical modelling
Example problem 1Try this! p 136
3.2: Extended modelling tasks with technology
Extended example problem 1 Try this! p 151
Problem set 3.2 Q1, 2
MathsWorld 10
Chapter 3: Trigonometry
*Chapter pre-test Q 5 – 10
3.3: Calculating side lengths and angles in
right-angled triangles
Examples 1, 2, 3, 4
Ex. 3.3 Q 1 – 3
3.4: Applying trigonometry
Examples 1, 2, 3, 4
Ex. 3.4 Q 1 – 19
Analysis task 1: GPS and dead reckoning
Chapter 6: Measurement
6.1: Applying Pythagoras’ theorem in two and
three dimensions
Analysis task 3: Arts Centre spire
Chapter 6: Two dimensional space
Analysis task 2: Road accident analysis
Chapter 7: Similarity and trigonometry
7.3: Trigonometric ratios
Ex. 7.3 Q 15, 16
Analysis task 2: Boom angles part b
6.0
They use degrees and radians as units of
measurement for angles and convert between units
of measurement as appropriate.
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34
Chapter 3: Trigonometry
3.5: Degrees and radians
Try this! p 179
Examples 1, 2, 3, 4
Ex. 3.5 Q 1 – 5
Analysis task 3: Radians and the unit circle
34
Level
Measurement,
Chance and Data
6.0
Standard/Progression Point
Students estimate probabilities based on data
(experiments, surveys, samples, simulations) and
assign and justify subjective probabilities in
familiar situations.
6.0
They list event spaces (for combinations of up to
three events) by lists, grids, tree diagrams, Venn
diagrams and Karnaugh maps (two-way tables).
6.0
They calculate probabilities for complementary,
mutually exclusive, and compound events
(defined using and, or and not).
6.0
They classify events as dependent or independent.
MathsWorld 9
MathsWorld 10
Chapter 9: Chance
9.3: Probability
Try this! p 536
Example 3
Ex. 9.3 Q 8 – 12
Chapter 7: Chance
7.1: Probability
Try this! p 464
Ex. 7.1 Q 8, 9
Chapter 9: Chance
9.4: Diagrams and tables
Examples 1, 2, 6
Ex. 9.4 Q 1, 2, 6, 7, 8, 12
Chapter 7: Chance
7.2: Tables and Venn diagrams
7.3: Independent and mutually exclusive
events
7.4: Tree diagrams and compound events
Examples 1, 2, 3
Try this! p 487
Ex. 7.4 Q 1 – 15
Analysis task 1: Tram’s game of chance
Analysis task 2: Pascal’s triangle and
probabilities
Chapter 9: Chance
9.4: Diagrams and tables
Example 3
Ex. 9.4 Q 3, 5, 69, 10, 11, 13
Chapter 7: Chance
7.3: Independent and mutually exclusive
events
Examples 1, 2, 3, 4
Try this! p 48
Ex. 7.3 Q 1 – 15
7.4: Tree diagrams and compound events
Examples 1, 2, 3
Ex. 7.4 Q 1 – 15
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35
Chapter 7: Chance
7.3: Independent and mutually exclusive
events
Try this! p 480
Examples 1, 2, 3
Ex. 7.3 Q 8, 13, 14
35
Level
Measurement,
Chance and Data
6.0
Standard/Progression Point
Students comprehend the difference between a
population and a sample.
6.0
They generate data using surveys, experiments
and sampling procedures.
6.0
They calculate summary statistics for centrality
(mode, median and mean), spread (box plot, interquartile range, outliers) and association (by-eye
estimation of the line of best fit from a scatter
plot).
MathsWorld 9
Chapter 10: Analysing data
10.1: Sampling and questionnaires
Analysis task 3: Investigating sample size
MathsWorld 10
Chapter 4: Statistical variables and
relationships
4.6: Populations, samples and randomness
Examples 1, 3
Ex. 4.6 Q 1, 2, 5
Chapter 4: Statistical variables and
relationships
4.6: Populations, samples and randomness
Ex. 4.6 Q 4
Chapter 10: Analysing data
*Chapter pre-test
Q3–6
10.4: Summarising data
Examples 1 – 4
Ex. 10.4 Q 1 – 15
10.5: Boxplots
Examples 1, 2
Ex. 10.5 Q 1 – 10
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36
Chapter 4: Statistical variables and
relationships
4.3: Summarising data: measures of centre
Examples 1, 2, 3
Ex. 4.3 Q 1 – 8
4.4: Summarising data: measures of spread
Try this! p 237, 238
Example 1
Ex. 4.4 Q 1 – 4
4.5: Boxplots: a visual summary
Examples 1, 2
Ex. 4.5 Q 1 – 11
4.9: Relationships between two numerical
variables
Examples 1, 2, 3
Ex. 4.9 Q 1 – 4
36
Level
Measurement,
Chance and Data
6.0
Standard/Progression Point
They distinguish informally between association
and causal relationship in bi-variate data, and
make predictions based on an estimated line of
best fit for scatter-plot data with strong association
between two variables.
MathsWorld 9
Chapter 8: Functions and modelling
Try this! p 489
8.7: Mathematical models
Example 1
Ex. 8.7 Q 5, 6, 7, 8, 12, 14
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37
MathsWorld 10
Chapter 4: Statistical variables and
relationships
4.9: Relationships between two numerical
variables
Examples 1, 2, 3
Ex. 4.9 Q 1 – 9
Analysis task 2: Cricket problem
Analysis task 3: Forensic formulas
37
Level
Structure
5.0
Standard/Progression Point
At Level 5 students identify collections of
numbers as subsets of natural numbers, integers,
rational numbers and real numbers.
5.0
They use Venn diagrams and tree diagrams to
show the relationships of intersection, union,
inclusion (subset) and complement between the
sets.
5.0
They list the elements of the set of all subsets
(power set) of a given finite set and comprehend
the partial-order relationship between these
subsets with respect to inclusion (for example,
given the set {a, b, c} the corresponding power set
is {Ø, {a}, {b}, {c}, {a, b}, {b, c}, {a, c}, {a, b,
c}}.)
They test the validity of statements formed by the
use of the connectives and, or, not, and the
quantifiers none, some and all, (for example,
‘some natural numbers can be expressed as the
sum of two squares’).
5.0
5.0
They apply these to the specification of sets
defined in terms of one or two attributes, and to
searches in data-bases.
MathsWorld 9
MathsWorld 10
Chapter 1: Real numbers
Chapter Warm-up Try this!
p4
1.1: Real numbers
Ex. 1.1 Q 1
Chapter 10: Irrational numbers
10.1: Irrational numbers and non-integer
indices
p 613
Chapter 9: Chance
9.2: Venn diagrams
Examples 1, 2
Ex. 9.2: Q 1 – 4
Chapter 7: Chance
*Chapter pre-test Q 7, 8
7.2: Tables and Venn diagrams
Chapter 9: Chance
9.1: The language of sets
Examples 4, 5
Ex. 9.1 Q 7, 8
Chapter 1: Real numbers
1.5: Adding and subtracting surds
Ex. 1.5 Q 6
Chapter 9: Chance
9.2: Venn diagrams
Try this! p 522, 524
Examples 1, 2, 3, 4
Ex. 9.2 Q 1 – 17
Chapter 9: Chance
9.2: Venn diagrams
Try this! p 522, 524
Examples 1, 2, 3, 4
Ex. 9.2 Q 1 – 17
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38
38
Level
Structure
5.0
Standard/Progression Point
Students apply the commutative, associative, and
distributive properties in mental and written
computation (for example, 24 × 60 can be
calculated as 20 × 60 + 4 × 60 or as 12 × 12 × 10).
5.0
They use exponent laws for multiplication and
division of power terms (for example 23 × 25 =
28, 20 = 1, 23 ÷ 25 = 2−2, (5 2)3 = 56 and (3 × 4)2 =
32 × 42).
5.0
Students generalise from perfect square and
difference of two square number patterns
(for example, 252 = (20 + 5)2 = 400 + 2 × (100) +
25 = 625. And 35 × 25 = (30 + 5) (30 – 5) = 900 −
25 = 875)
5.0
Students recognise and apply simple geometric
transformations of the plane such as translation,
reflection, rotation and dilation and combinations
of the above, including their inverses.
5.0
They identify the identity element and inverse of
rational numbers for the operations of addition
and multiplication
(for example, ½ + − ½ = 0 and 2/3 × 3/2 = 1).
Students use inverses to rearrange simple
mensuration formulas, and to find equivalent
algebraic expressions
(for example, if P = 2L + 2W, then W = P/2 − L. If
A = πr2 then r = √A/π).
5.0
MathsWorld 9
MathsWorld 10
Chapter 4: Algebra toolbox 1
Number examples regularly used before
generalising, particularly in conjunction with use
of a geometric model (e.g., p 203). See further
note and examples in Teacher edition.
Chapter 1: Real numbers
1.2: Integer powers of rational numbers
Examples 3, 4, 5
Ex. 1.2 Q 1 – 10
Chapter 10: Irrational numbers
*Chapter pre-test Q 1 – 6
Chapter 4: Algebra toolbox 1
Number examples regularly used before
generalising, particularly in conjunction with use
of a geometric model. See further note and
examples in Teacher edition p 214
Chapter 1: 2D and 3D geometry
1.5: Isometric transformations
Examples 1, 4
Ex. 1.5 Q 1, 4, 5, 6
See MathsWorld 8 Chapter 1 Integers and
Chapter 5 Analysis Task 3: Generalising the
number laws. (in part a). Extend this to a  b  1
b a
Chapter 4: Algebra toolbox 1
4.2: What does solving mean?
Example 7
Ex. 4.2 Q 27
MathsWorld 10 Teacher edition
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39
39
Level
Structure
5.0
5.0
Standard/Progression Point
They solve simple equations (for example, 5x+ 7
= 23, 1.4x − 1.6 = 8.3, and 4x2 − 3 = 13) using
tables, graphs and inverse operations.
They recognise and use inequality symbols.
MathsWorld 9
MathsWorld 10
Chapter 4: Algebra toolbox 1
*Chapter pre-test
Q 10
4.2: What does solving mean?
Examples 1, 2, 3, 4, 5
Ex. 4.2 Q 1 – 17
Chapter 5: Algebra toolbox 2
*Chapter pre-test Q 3
Chapter 4: Algebra toolbox 1
4.2: What does solving mean?
Example 6
Ex. 4.2 Q 20, 21, 24, 25, 26
Chapter 5: Algebra toolbox 2
*Chapter pre-test Q 5
Chapter 8: Functions and modelling
8.1: What is a function?
Examples 3, 4
Ex. 8.1 Q 9, 10
Chapter 8: Functions and modelling
*Chapter pre-test Q 4, 6
8.1 Identifying and representing functions
Examples 1, 2
Chapter 11: Algebra toolbox 2
*Chapter pre-test
Q5
5.0
They solve simple inequalities such as y ≤ 2x+ 4
and decide whether inequalities such as x2 > 2y are
satisfied or not for specific values of x and y.
5.0
Students identify a function as a one-to-one
correspondence or a many-to-one correspondence
between two sets.
Chapter 4: Algebra toolbox 1
4.2: What does solving mean?
Example 6
Ex. 4.2 Q 20, 21, 24-26
(See note and further examples in Teacher
edition p 184)
Chapter 5: Algebra toolbox 2
*Chapter pre-test Q 8
Chapter 8: Functions and modelling
*Chapter pre-test Q 4, 5
8.1: What is a function?
Try this! p 424
Ex. 8.1 Q 7
Chapter 8: Functions and modelling
*Chapter-pre-test Q 3
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40
40
Level
Structure
5.0
5.0
Standard/Progression Point
They represent a function by a table of values, a
graph, and by a rule.
They describe and specify the independent
variable of a function and its domain, and the
dependent variable and its range.
MathsWorld 9
MathsWorld 10
Chapter 8: Functions and modelling
*Chapter pre-test Q 1, 2, 3, 6, 8
8.1: What is a function?
Try this! p 427
Examples 1, 2
Ex. 8.1 Q 5 – 8
Chapter 8: Functions and modelling
*Chapter-pre-test Q 1, 7, 8, 9, 10
Chapter Warm-up p 509
8.2: Comparing linear and quadratic functions
Try this! p 519
Examples 1, 2
Ex. 8.2 Q 1 – 5
8.3: Fitting rules to quadratic graphs
Examples 1, 2
Ex. 8.3 Q 1 – 11
8.4: Exponential functions
Try this! p 536
Example 1
Ex. 8.4 Q 1 – 6
8.5 Reciprocal functions
Try this1 p 543
Example 1
Ex. 8.5 Q 1 – 7
Chapter 8: Functions and modelling
*Chapter pre-test Q 8
8.1: What is a function?
Examples 2, 3
Ex. 8.1 Q 7, 8
8.2: Formulating functions
Example 1
Ex. 8.2 Q 2, 3, 4, 5
Chapter 8: Functions and modelling
8.1: Identifying and representing functions
Example 2
In Exercises 8.2 to 8.7, students will need to
consider the independent variable of a function
and its domain, and the dependent variable and its
range
MathsWorld 10 Teacher edition
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41
41
Level
Structure
5.0
5.0
Standard/Progression Point
They construct tables of values and graphs for
linear functions.
They use linear and other functions such as f(x) =
2x − 4, xy = 24, y = 2x and y = x2 − 3 to model
various situations.
MathsWorld 9
MathsWorld 10
Chapter 8: Functions and modelling
8.2: Formulating functions
Example 1
Ex. 8.2 Q 1, 3, 5
8.3: Linear functions
Try this! p 443
Examples 3, 4, 5, 6, 7, 8
4, 5, 6
Chapter 8: Functions and modelling
*Chapter-pre-test Q 7
8.2: Comparing linear and quadratic functions
Ex. 8.2 Q 4
Chapter 8: Functions and modelling
Chapter Warm-up Try this!
8.2: Formulating functions
Example 1
Ex. 8.2 Q 1 – 5
8.3: Linear functions
Ex. 8.3 Q 17 – 21
8.4: Reciprocal functions
Try this! p 463
Example 1
Ex. 8.4 Q 1 – 5
8.5: Exponential functions
Try this! p 469
Example 1
Ex. 8.5 Q 1, 3, 4, 5
8.6: Quadratic functions
Try this! p 476
Examples 1, 2
Ex. 8.6 Q 1, 2, 3
Chapter 8: Functions and modelling
*Chapter pre-test Q 7, 8, 9
Chapter Warm-up Try this! p 509
8.3: Reciprocal functions
Try this! p 541
Example 1
Ex. 8.3 Q 4 – 7
8.6: Modelling with functions
Ex. 8.6 Q 1 – 8
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42
42
Level
Structure
5.25
Standard/Progression Point
•
5.25
•
5.25
•
MathsWorld 9
MathsWorld 10
relationships between two sets using a Venn
diagram, tree diagram and Karnaugh map
Chapter 9: Chance
9.2: Venn diagrams
Example 4
Ex. 9.2 Q 1g – 15
9.4: Diagrams and tables
Examples 3, 4, 5
Ex. 9.4 Q 3, 4, 5, 10, 11
Chapter 7: Chance
7.2: Tables and Venn diagrams
Examples 1, 2, 3, 4
Ex. 7.2 Q 1 – 14
factorisation of algebraic expressions by
extracting a common factor
Chapter 4: Algebra toolbox 1
4.4: Factorising algebraic expressions
Try this! p 197, 198, 199
Examples 1, 2
Ex. 4.4 Q 1 – 12
Chapter 2: Algebra toolbox 1
2.1: Algebraic expressions: substitution,
expansion and common factors
Example 5
Ex. 2.1 Q 7, 8
2.2: Factorisation involving binomial factors
Examples 1, 2, 3, 4
Try this! p 99
Ex. 2.2 Q 1 – 6
solution of equations by graphical methods
Chapter 8: Functions and modelling
8.3: Linear functions
Example 9
Ex. 8.3 Q 22
Chapter 2: Algebra toolbox 1
Analysis task 1: Numerical methods
Chapter 11: Algebra toolbox 2
11.2: Other techniques for solving equations
Examples 1, 2
Try this! p 662, 665
Ex. 11.2 Q 1 – 12
Analysis task 2: Simba’s SMS costs
MathsWorld 9 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 2.2 p 167; 2.4 p 169
TI 89 2.2 p 204; 2.4 p 206
MathsWorld 10 Teacher edition
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43
Chapter 5: Algebra toolbox 2
Chapter Warm-up Try this! p 291
5.7: Other techniques for solving equations
Examples 1, 2
Ex. 5.7 Q 1 – 8
MathsWorld 10 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 2.2 – 2.4 pp. 142 – 144
TI 89 2.2 – 2.4 pp. 180 – 182
43
Level
Structure
5.25
Standard/Progression Point
•
5.25
•
5.5
•
MathsWorld 9
MathsWorld 10
identification of linear, quadratic and
exponential functions by table, rule and graph
in the first quadrant
Chapter 8: Functions and modelling
8.3: Linear functions
Examples 1 – 9
Ex. 8.3 Q 1 – 25
8.5: Exponential functions
Example 1
Ex. 8.5 Q 1 – 6
8.6: Quadratic functions
Examples 1, 2
Ex. 8.6 Q 1 – 4
Chapter 8: Functions and modelling
Chapter Warm-up Try this! p 509
8.2: Comparing linear and quadratic functions
Try this! p 519
Example 2
Ex. 8.2 Q 1 – 5
8.3: Fitting rules to quadratic graphs
Examples 1, 2
Ex. 8.3 Q 1 – 11
8.4: Exponential functions
Try this! p 536
p. 537, 538
Example 1
Ex. 8.4 Q 1 – 6
Analysis task 3: Hammer throw
knowledge of the quantities represented by
the constants m and c in the equation
y = mx + c
Chapter 8: Functions and modelling
*Chapter pre-test
Q 2, 3, 7, 8
8.3: Linear functions
Try this! p 443
Examples 1, 2, 3
Ex. 8.3 Q 1, 6, 7, 12, 17, 18, 19, 20
Chapter 8: Functions and modelling
8.2: Comparing linear and quadratic functions
p 520
Example 1
Ex. 8.2 Q 4
expression of the relationship between sets
using membership,  , complement, ′,
intersection,  , union,  , and subset,  ,
for up to two sets.
Chapter 9: Chance
9.1: The language of sets
Examples 1 – 9
Ex. 9.1 Q 1 – 17
Chapter 7: Chance
7.2: Tables and Venn diagrams
Examples 2, 3, 4
Ex. 7.2 Q 1 – 14
MathsWorld 10 Teacher edition
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44
Level
Structure
5.5
5.5
Standard/Progression Point
•
•
MathsWorld 9
representation of numbers in a geometric
sequence (constant multiple, constant
percentage change) as an exponential
function
Chapter 8: Functions and modelling
8.2: Formulating functions
Ex. 8.2 Q 2
8.5: Exponential functions
Try this! p 470
Ex. 8.5 Q 1, 2, 3
Chapter 8: Functions and modelling
8.4: Exponential functions
pp. 537, 538
Ex. 8.4 Q 1
knowledge of the relationship between
geometrical and algebraic forms for
transformations
Chapter 8: Functions and modelling
8.3: Linear functions
Ex. 8.3 Q 9, 10
Chapter 1: 2D and 3D geometry
1.5: Isometric transformations
Try this! p 60, 62, 63, 65
Examples 3, 5, 6
Ex. 1.5 Q 7 – 11
Chapter 11: Algebra toolbox 2
11.1: Solving quadratic equations
Try this! p 649, 651
Ex. 11.1 Q 5, 6, 11
5.5
•
MathsWorld 10
expansion of products of algebraic factors, for
example,  2 x  1 x  5  2 x2  9 x  5
Chapter 4: Algebra toolbox 1
4.3: Expanding algebraic expressions
Try this! p 192, 193
Examples 1, 2, 3
Ex. 4.3 Q 1 – 6
4.5: Expanding binomials
Try this! p 204, 205
Examples 1, 2
Ex. 4.5 Q 1 – 13
4.7: Perfect squares and difference of squares
Try this! p 214, 216, 218
Examples 1, 2, 3, 4, 5
Ex. 4.7 Q 1 – 14
MathsWorld 10 Teacher edition
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45
Chapter 5: Algebra toolbox 2
5.6: Graphing quadratic functions
Try this! p 333, 334
Chapter 2: Algebra toolbox 1
*Chapter pre-test Q 3, 4, 5
2.1: Algebraic expressions: substitution,
expansion and common factors
Examples 3, 4
Ex. 2.1 Q 4, 5, 6, 8, 9, 10
2.3: Perfect squares and differences of squares
Try this! p 102, 103
Examples 1, 2, 4, 8
45
Level
Structure
5.5
5.5
Standard/Progression Point
•
•
equivalence between algebraic forms; for
example, polynomial, factorised and turning
point form of quadratics
use of inverse operations to re-arrange
formulas to change the subject of a formula
MathsWorld 9
MathsWorld 10
Chapter 4: Algebra toolbox 1
4.3: Expanding algebraic expressions
Try this! p 192, 193
Examples 1, 2, 3
Ex. 4.3 Q 1 – 6
4.4: Factorising algebraic expressions
Try this! p 197
Examples 1, 2
Ex. 4.4 Q 1 – 3, 5 – 12
4.5: Expanding binomials
Try this! p 204, 205
Examples 1, 2
Ex. 4.5 Q 1 – 13
4.6: Factorising quadratic trinomials
Try this! p 210, 211
Examples 2, 3
Ex. 4.6 Q 2 – 9
4.7: Perfect squares and differences of squares
Try this! p 214, 218
Examples 1, 2, 3, 4, 5
Ex. 4.7 Q 1 – 14
4.8: Index form with pronumerals
Examples 3 – 9
Ex. 4.8 Q 3 – 13
Analysis task 1: Pascal’s triangle and binomial
expansions
Analysis task 2: Completing the square
Chapter 2: Algebra toolbox 1
2.1: Algebraic expressions: substitution,
expansion and common factors
Try this! p 93
Ex. 2.1 Q 6
2.3: Perfect squares and differences of squares
Try this! p 102
Ex. 2.3 Q 1 – 9
2.4: Factorising quadratic trinomials
Try this! p 109, 112
Examples 1, 2, 3, 4
Ex. 2.4 Q 1 – 7
2.5: Completing the square
Try this! p 117, 119, 120
Examples 1, 2
Ex. 2.5 Q 1, 2, 3
2.6: Index form with pronumerals
Examples 1 – 8
Ex. 2.6 Q 1 – 4
Chapter 5: Algebra toolbox 2
5.6: Graphing quadratic equations
Try this! p 332
Chapter 8: Functions and modelling
8.3: Fitting rules to quadratic graphs
Try this! p 528
Chapter 4: Algebra toolbox 1
4.2: What does solving mean?
Try this! p 185
Example 7
Ex. 4.2 Q 22a – r
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46
Level
Structure
5.75
Standard/Progression Point
•
expression of irrational numbers in both exact
and approximate form
MathsWorld 9
MathsWorld 10
Chapter 1: Real numbers
1.4: Irrational numbers
Example 1
1.5: Adding and subtracting surds
Ex. 1.5 Q 11
Analysis task 1: The golden ratio
Chapter 3: Trigonometry
3.5: Degrees and radians
Examples 1, 2, 3
Ex. 3.5 Q 1 – 6
Analysis task 3: Radians and the unit circle
(Challenge)
Chapter 2: Length, area and volume
Questions involving Pythagoras’ theorem and
Chapter 6: Measurement
Questions involving Pythagoras’ theorem and


Chapter 10: Irrational numbers
10.2: Surds
Ex. 10.2 e.g., Q 15
5.75
•
factorisation of simple quadratic expressions
and use of the null factor law for solution of
equations
Chapter 4: Algebra toolbox 1
4.6 Factorising quadratic trinomials
Examples 2, 3
Ex. 4.6 Q 2 – 9
4.7: Perfect squares and difference of squares
Examples 2, 3, 5
Ex. 4.7 Q 4, 6, 9, 10, 11, 13
Chapter 2: Algebra toolbox 1
2.3: Perfect squares and differences of squares
Examples 2, 4
Ex. 2.3 Q 3, 5, 6
2.4 Factorising quadratic trinomials
Examples 1, 2, 3
Ex. 2.4 Q 1 – 5
Chapter 11: Algebra toolbox 2
11.1: Solving quadratic equations
Examples 2, 3
Ex. 11.1 Q 4, 7, 14
Chapter 5: Algebra toolbox 2
5.3: Rational solutions of quadratic equations
Examples 1, 2
Ex. 5.3 Q 1, 2, 3, 4, 6, 8, 9
5.4: Real solutions to quadratic equations
Try this! p 320
Example 1
Ex. 5.4 Q 1 – 5
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47
Level
Structure
5.75
5.75
Standard/Progression Point
•
•
MathsWorld 9
MathsWorld 10
testing of sequences by calculating first
difference, second difference or ratio
between consecutive terms to determine
existence of linear, quadratic and exponential
functions
Chapter 8: Functions and modelling
8.3: Linear functions
p 445
Example 3
Ex. 8.3 Q 2
8.5: Exponential functions
Try this! p 470
p 472
Ex. 8.5 Q 1
8.7: Mathematical models
Example 2
Ex. 8.7 Q 1 – 3
Analysis tasks 1: Water hyacinth
Analysis task 2: Video and DVD sales
Chapter 8: Functions and modelling
8.2: Comparing linear and quadratic functions
pp 52- - 524
Example 2
Ex. 8.2 Q 1 – 5
8.4: Exponential functions
pp 537, 538
Example 1
Ex. 8.4 Q 1, 3, 4, 5
8.6: Modelling with functions
pp 548, 549
Ex. 8.6 Q 1 – 4
Analysis task 2: Russet-tipped and bronze-spotted
butterflies
Analysis task 3: Hammer throw
formulation of pairs of simultaneous
equations and their graphical solution
Chapter 11: Algebra toolbox 2
11.2: Other techniques for solving equations
Ex. 11.2 Q 2, 3, 5, 7
Analysis task 2: Simba’s SMS costs
Chapter 5: Algebra toolbox 2
5.2: Using graphs to solve simultaneous linear
equations
Try this! 292, 295, 296
Examples 1 – 5
Ex. 5.2 Q 1 – 15
Analysis task 1: Using matrices to solve
simultaneous linear equations
Analysis task 3: Jemima helps Mr Workalot!
MathsWorld 9 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 2.2 p 167; 2.4 p 169
TI 89 2.2 p 204; 2.4 p 206
MathsWorld 10 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 2.2 – 2.4 pp. 142 – 144
TI 89 2.2 – 2.4 pp. 178 – 182
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48
48
Level
Structure
5.75
Standard/Progression Point
•
representation of algebraic models for sets of
data using technology
6.0
At Level 6, students classify and describe the
properties of the real number system and the
subsets of rational and irrational numbers.
6.0
They identify subsets of these as discrete or
continuous, finite or infinite and provide examples
of their elements and apply these to functions and
relations and the solution of related equations.
MathsWorld 9
MathsWorld 10
Chapter 8: Functions and modelling
8.5: Exponential functions
Try this! p 469
Example1
Ex. 8.5 Q 3 – 5
8.6: Quadratic functions
Try this! p 476, 479
Ex. 8.6 Q 3
8.7: Mathematical models
Try this! p 485, 489
Example 2
Ex. 8.7 Q 4, 6, 8, 11, 12, 13, 14, 15
Analysis task 1: Water hyacinth
Analysis task 3: Water tank costs
Chapter 4: Statistical variables and
relationships
4.9: Relationships between two numerical
variables
Examples 1, 2, 3
Ex. 4.9 Q 1, 4, 7, 8, 9
Analysis task 2: Cricket problem
Analysis task 3: Forensic formulas
Chapter 1: Real numbers
Try this! p 27
1.4: Irrational numbers
Ex. 1.4 Q 1, 2
Chapter 10: Irrational numbers
10.1: Irrational numbers and non-integer
indices
p 613
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Chapter 8: Functions and modelling
8.3: Fitting rules to quadratic graphs
Ex. 8.3 Q 9
8.4: Exponential functions
Ex. 8.4 Q 3, 4, 5
8.6: Modelling with functions
Ex. 8.6 Q 6, 7, 8
Analysis task 1: Braking distance
Analysis task 2: Russet-tipped and bronze-spotted
butterflies
Analysis task 3: Hammer throw
Chapter 5: Algebra toolbox 2
5.5: The nature of solutions
Try this! p 327
Examples 1, 2
Ex. 5.5 Q 1 – 13
49
Level
Structure
6.0
Standard/Progression Point
Student express relations between sets using
membership,  , complement, ′, intersection,  ,
union,  , and subset,  , for up to three sets.
6.0
They represent a universal set as the disjoint union
of intersections of up to three sets and their
complements, and illustrate this using a tree
diagram, Venn diagram or Karnaugh map.
6.0
Students form and test mathematical conjectures;
for example, ‘What relationship holds between the
lengths of the three sides of a triangle?’
MathsWorld 9
MathsWorld 10
Chapter 9: Chance
9.1: The language of sets
Examples 1, 4, 6, 7, 8, 9
Ex. 9.1 Q 1 – 15
Chapter 7: Chance
*Chapter pre-test Q 6, 7
7.1: Probability
Try this! p 463
7.2: Tables and Venn diagrams
Examples 1, 2, 3, 4
Ex. 7.2 Q 1 – 14
7.4: Tree diagrams and compound events
Example 3
Ex. 7.4 Q 1 – 12
Chapter 9: Chance
9.2: Venn diagrams
Examples 1, 2
Ex. 9.2
9.4: Diagrams and tables
Examples 1, 2, 3, 4, 5
Ex. 9.4
Chapter 7: Chance
7.2: Tables and Venn diagrams
Examples 1, 2, 3, 4
Ex. 7.2 Q 1 – 14
Chapter 2: Length, area and volume
2.7: Volume
Try this! p 113 – 115
Chapter 1: 2D and 3D geometry
1.1: Circles, chords and angles
Try this! p 7, 11, 13, 16
Ex. 1.1 Q 12
1.4: Networks
Try this! p 45
Chapter 6: Two-dimensional space
6.4: Angles in a circle
Try this! p 336
Analysis task 3: Cyclic quadrilaterals
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Chapter 2: Algebra toolbox 1
Chapter Warm-up Try this! p 89
2.4: Factorising quadratic trinomials
Try this! p 109
50
Level
Structure
6.0
Standard/Progression Point
They use irrational numbers such as π ,  and
common surds in calculations in both exact and
approximate form.
MathsWorld 9
MathsWorld 10
Chapter 1: Real numbers
1.4: Irrational numbers
Examples 1, 2, 3
Ex. 1.4 Q 12, 13
1.5: Adding and subtracting surds
Examples 1, 2
Ex. 1.5 Q 3 – 12
1.6: Multiplying and dividing surds
Examples 1, 2, 3
Ex. 1.6 Q 1 – 10
Analysis task 1: The golden ratio
Analysis task 2: Federation Square tiles
Chapter 2: Length, area and volume
Questions involving Pythagoras’ theorem and
Chapter 3: Trigonometry
3.5: Degrees and radians
Try this! p 179
Examples 1, 2, 3, 4
Ex. 3.5 Q 1 – 6
Analysis task 3: Radians and the unit circle
Chapter 5: Algebra toolbox 2
5.4: Real solutions of quadratic equations
Try this! p 320
Examples 1, 2
Ex. 5.4 Q 1 – 13

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Chapter 10: Irrational numbers
10.1: Irrational numbers
Try this! p 614
Ex. 10.1 Q 5, 6, 7
51
Level
Structure
6.0
Standard/Progression Point
Students apply the algebraic properties (closure,
associative, commutative, identity, inverse and
distributive) to computation with number, to
rearrange formulas, rearrange and simplify
algebraic expressions involving real variables.
MathsWorld 9
Chapter 4: Algebra toolbox 1
*Chapter pre-test
Q5–9
4.3: Expanding algebraic expressions
Try this! p 192, 193
Examples 1, 2, 3
Ex. 4.3 Q 1 – 6
4.4: Factorising algebraic expressions
Try this! p 197, 198
Examples 1, 2
Ex. 4.4 Q 1 – 12
4.5: Expanding binomials
Try this! p 204, 205
Examples 1, 2
Ex. 4.5 Q 1 – 13
4.6: Factorising quadratic trinomials
Try this! p 210, 212
Examples 1, 2
Ex. 4.6 Q 1 – 9
4.7: Perfect squares and difference of squares
Try this! p 214, 216, 218
Examples 1, 2, 3, 4, 5
Ex. 4.7 Q 1 – 14
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MathsWorld 10
Chapter 2: Algebra toolbox 1
*Chapter pre-test Q 3 – 9
2.1: Algebraic expressions: substitution,
expansion and common factors
Examples 3, 4, 5
Try this! p 93, 95
Ex. 2.1 Q 4 – 11
2.2: Factorisation involving binomial factors
Examples 1, 2, 3, 4
Try this! p 91
Ex. 2.2 Q 1 – 6
2.3: Perfect squares and differences of squares
Examples 1 – 6
Try this! p 102, 103
Ex. 2.3 Q 1 – 9
2.4: Factorising quadratic trinomials
Try this! 109, 111, 112
Ex. 2.4 Q 1 – 7
52
Level
Structure
6.0
Standard/Progression Point
They verify the equivalence or otherwise of
algebraic expressions (linear, square, cube,
exponent, and reciprocal,
(for example,
4 x − 8 = 2(2x − 4) = 4(x − 2);
(2a − 3)2 = 4a2 − 12a + 9;
(3w)3 = 27w3 ;
4 2 2
x3 y
 
 x 2 y 1 ;
3
xy x y
xy
MathsWorld 9
Chapter 4: Algebra toolbox 1
4.3: Expanding algebraic expressions
Try this! p 192, 193
Examples 1, 2, 3
Ex. 4.3 Q 1 – 6
4.4: Factorising algebraic expressions
Try this! p 197, 198
Examples 1, 2
Ex. 4.4 Q 1 – 12
4.5: Expanding binomials
Try this! p 204, 205
Examples 1, 2
Ex. 4.5 Q 1 – 13
4.6: Factorising quadratic trinomials
Try this! p 210, 212
Examples 1, 2
Ex. 4.6 Q 1 – 9
4.7: Perfect squares and difference of squares
Try this! p 214, 216, 218
Examples 1, 2, 3, 4, 5
Ex. 4.7 Q 1 – 14
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MathsWorld 10
Chapter 2: Algebra toolbox 1
*Chapter pre-test Q 3 – 9
Chapter Warm-up Try this! p 89
2.1: Algebraic expressions: substitution,
expansion and common factors
Examples 3, 4, 5
Try this! p 93
Ex. 2.1 Q 4 – 11
2.2: Factorisation involving binomial factors
Examples 1, 2, 3, 4
Try this! p 99
Ex. 2.2 Q 1 – 6
2.3: Perfect squares and differences of squares
Try this! p 102, 103
Examples 1, 2, 3, 4, 5, 6
Ex. 2.3 Q 1 – 9
2.4: Factorising quadratic trinomials
Try this! p 109, 111, 112
Examples 1, 2, 3, 4
Ex. 2.4 Q 1 – 7
53
Level
Structure
6.0
6.0
Standard/Progression Point
Students identify and represent linear, quadratic
and exponential functions by table, rule and graph
(all four quadrants of the Cartesian coordinate
system) with consideration of independent and
dependent variables, domain and range.
They distinguish between these types of functions
by testing for constant first difference, constant
second difference or constant ratio between
consecutive terms (for example, to distinguish
between the functions described by the sets of
ordered pairs
{(1, 2), (2, 4), (3, 6), (4, 8) …}; {(1, 2), (2, 4), (3,
8), (4, 14) …}; and {(1, 2), (2, 4), (3, 8), (4, 16)
…}).
MathsWorld 9
MathsWorld 10
Chapter 8: Functions and modelling
*Chapter pre-test
Q1–8
8.3: Linear functions
Try this! p 443
Examples 1 – 9
Ex. 8.3 Q 1 – 25
8.5: Exponential functions
Try this! p 470
Example 1
Ex. 8.5 Q 1 – 6
8.6: Quadratic functions
Try this! p 476
Examples 1, 2
Ex. 8.6 Q 1 – 4
Chapter 8: Functions and modelling
8.2: Comparing linear and quadratic functions
Try this! p 519
Examples 1, 2
Ex. 8.2 Q 1 – 5
8.3: Fitting rules to quadratic graphs
Examples 1, 2
Ex. 8.3 Q 1 – 11
8.4: Exponential functions
Try this! p 536
Example 1 p 539
Ex. 8.4 Q 1 – 6
8.6: Modelling with functions
Ex. 8.6 Q 1 – 8
Analysis task 2: Russet-tipped and bronze-spotted
butterflies
Analysis task 3: Hammer throw
Chapter 8: Functions and modelling
8.3: Linear functions
Examples 3, 4
Ex. 8.3 Q 2
8.5: Exponential functions
Try this! p 470
Example 1
Ex. 8.5 Q 1 – 6
8.7: Functions and modelling
Example 2
Ex. 8.7 Q 1, 3, 13
Analysis task 1: Water hyacinth
Chapter 8: Functions and modelling
8.2: Comparing linear and quadratic functions
Try this! p 519
Examples 1, 2
Ex. 8.2 Q 1 – 5
8.4: Exponential functions
Try this! p 536
Example 1 p 539
Ex. 8.4 Q 1 – 6
8.6: Modelling with functions
Ex. 8.6 Q 1 – 6
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54
6.0
6.0
They use and interpret the functions in modelling
a range of contexts.
They recognise and explain the roles of the
relevant constants in the relationships f(x ) = a x +
c, with reference to gradient and y axis intercept,
f( x) = a (x + b)2 + c and
f( x) = cax.
Chapter 8: Functions and modelling
8.2: Formulating functions
Example 1
Ex. 8.2 Q 1 – 5
8.3: Linear functions
Try this! p 443
Examples 3, 7, 9
Ex. 8.3 Q 11 – 22
8.4: Reciprocal functions
Try this! p 463
Example 1
Ex. 8.4 Q 4
8.5: Exponential functions
Try this! p 469
Example 1
Ex. 8.5 Q 3, 4, 5, 6
8.6: Quadratic functions
Try this! p 476
Examples 1, 2
Ex. 8.6 Q 1, 2, 3
8.7: Functions and modelling
Examples 1, 2
Ex. 8.7 Q 2 – 13, 15
Analysis task 1: Water hyacinth
Analysis task 2L Video and DVD sales
Analysis task 3: Water tank costs
Chapter 8: Functions and modelling
8.2: Comparing linear and quadratic
functions
Try this! p 519
Examples 1, 2
Ex. 8.2 Q 1 – 5
8.3: Fitting rules to quadratic graphs
Examples 1, 2
Ex. 8.3 Q 1 – 11
8.4: Exponential functions
Try this! p 536
Example 1 p 539
Ex. 8.4 Q 1 – 6
8.6: Modelling with functions
Ex. 8.6 Q 1 – 8
Analysis task 1: Braking distance
Analysis task 2: Russet-tipped and bronzespotted butterflies
Analysis task 3: Hammer throw
Chapter 8: Functions and modelling
Chapter pre-test Q 6, 7, 8
8.3: Linear functions
Examples 1, 2, 3, 4, 6, 7, 9
Ex. 8.3 Q 1, 3, 7, 10, 12, 17, 18, 19, 20, 21, 22,
23, 24
Chapter 8: Functions and modelling
8.2: Comparing linear and quadratic
functions
Try this! p 519
Examples 1, 2
Ex. 8.2 Q 1 – 5
8.4: Exponential functions
Try this! p 536
Example 1
Ex. 8.4 Q 1 – 6
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55
6.0
They solve equations of the form f(x) = k, where k
is a real constant (for example, x( x + 5) = 100)
and simultaneous linear equations in two
variables (for example, {2x − 3y = −4 and 5x + 6y
= 27} using algebraic, numerical (systematic
guess, check and refine or bisection) and
graphical methods.
Chapter 11: Algebra toolbox 2
11.1: Solving quadratic equations
Examples 1, 2, 3, 4
Ex. 11.1 Q 4, 7
11.2: Other techniques for solving equations
Examples 1, 2, 3
Try this! p 662
Ex. 11.2 Q 1 – 19
Analysis task 2: Simba’s SMS costs
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Chapter 2: Algebra toolbox 1
Analysis task 1: Numerical methods
Chapter 5: Algebra toolbox 2
5.3: Rational solutions of quadratic equations
Ex. 5.3 Q 5, 7
5.7: Other techniques for solving equations
Examples 1, 2, 3
Ex. 5.7 Q 1 – 9, 12, 13
56
Level
Working
mathematically
5.0
5.0
Standard/Progression Point
At Level 5, students formulate conjectures and
follow simple mathematical deductions (for
example, if the side length of a cube is doubled,
then the surface area increases by a factor of four,
and the volume increases by a factor of eight).
Students use variables in general mathematical
statements.
MathsWorld 9
Chapter 1: Real numbers
1.6: Multiplying and dividing surds
Try this! p 40
MathsWorld 10
Chapter 2: Algebra toolbox 1
Chapter Warm-up Try this! p 89
Chapter 4: Algebra toolbox 1
4.6: Factorising quadratic trinomials
Try this! p 210
4.7: Perfect squares and difference of squares
Try this! p 214
Chapter 2: Length, area and volume
Formulae used in all sections
e.g., measurement formulae in
Chapter 6: Measurement
Chapter 5: Ratio and rates
5.3: Percentages
Examples 9, 10, 11, 12
Ex. 5.3 Q 12 – 16
Chapter 8: Functions and modelling
Variables used in all sections
Chapter 10: Analysing data
10.4: Summarising data
Examples 1, 2
5.0
They substitute numbers for variables (for
example, in equations, inequalities, identities and
formulas).
Chapter 4: Algebra toolbox 1
*Chapter pre-test Q 2 – 4
Chapter Warm-up Try this! p 169
4.1: Formulas and substitution
Examples 1, 2, 3, 4 , 5
Try this! p 172
Ex. 4.1 Q 1 – 10
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57
Chapter 2: Algebra toolbox 1
*Chapter pre-test Q 2
Chapter Warm-up Try this! p 89
2.1: Algebraic expressions: substitution,
expansion and common factors
Examples 1, 2
Try this! p 92
Ex. 2.1 Q 1, 2, 3
57
Level
Working
mathematically
5.0
Standard/Progression Point
Students explain geometric propositions (for
example, by varying the location of key points
and/or lines in a construction).
5.0
Students develop simple mathematical models for
real situations (for example, using constant rates
of change for linear models).
5.0
They develop generalisations by abstracting the
features from situations and expressing these in
words and symbols.
MathsWorld 9
Chapter 6: Two dimensional space
6.1: Angles, parallel lines and triangles
Try this! p 310
Ex. 6.1 Q 9
6.2: Quadrilateral properties
Example 1
Ex. 6.2 Q 1, 4
6.4: Angles in a circle
Try this! p 336, 338
MathsWorld 10
Chapter 1: 2D and 3D geometry
1.1: Circles, chords and tangents
Try this! p 8, 12, 15, 16
Chapter 8: Functions and modelling
8.2: Formulating functions
Example 1
Ex. 8.2 Q 1 – 5
Chapter 8: Functions and modelling
Chapter Warm-up Try this! p 420
Chapter 3: Trigonometry
Chapter Warm-up Try this! p 142
Chapter 8: Functions and modelling
8.2: Comparing linear and quadratic
functions
Try this! p 519
5.0
They predict using interpolation (working with
what is already known) and extrapolation
(working beyond what is already known).
Chapter 8: Functions and modelling
8.7: Mathematical models
Try this! p 485
Examples 1, 2
Ex. 8.7 Q 5, 6, 7, 8, 9
Chapter 4: Statistical variables and
relationships
4.9: Relationships between two numerical
variables
Examples 1, 2, 3
Ex. 4.9 Q 1 – 9
Analysis task 2: Cricket problem
Analysis task 3: Forensic formulas
Chapter 8: Functions and modelling
Chapter Warm-up Try this! p 509
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58
Level
Working
mathematically
5.25
5.25
5.25
5.50
Standard/Progression Point
•
•
•
•
MathsWorld 9
development of alternative algebraic models
for a set of data and evaluation of their
relative merits
Chapter 8: Functions and modelling
8.7: Mathematical models
Ex. 8.7 Q 15
presentation of algebraic arguments using
appropriate mathematical symbols and
conventions
Chapter 2: Length, area and volume
2.3: Pythagoras’ theorem
Ex. 2.3 Q 19
See also MathsWorld 8
evaluation of the appropriateness of the
results of their own calculations
justification or proof of generalisations made
from specific cases
MathsWorld 10
Chapter 5: Algebra toolbox 2
5.5: The nature of solutions
Try this! p 327
Chapter 5 Algebra toolbox
Analysis task 2: Odds and evens
All chapters, but particularly
All chapters, but particularly
Chapter 2: Length, area and volume
Chapter 3: Trigonometry
Chapter 7: Similarity and trigonometry
Chapter 6: Measurement
Chapter 2: Length, area and volume
2.3: Pythagoras’ theorem
Try this! p 74
Chapter 5: Algebra toolbox 2
5.4: Real solutions to quadratic equations
p. 321, 322
Chapter 6: Two-dimensional space
6.1: Angles, parallel lines and triangles
Try this! p 307
Ex. 6.1 Q 1, 2, 9, 19
6.2: Quadrilateral properties
Try this! p 310
Example 1
Ex. 6.2 Q 1, 6, 7
Chapter 6: Measurement
6.4: Calculating area
Heron’s formula: Example 3
6.6: Calculating volume and capacity
Volume of truncated pyramid
Try this! p 430, 431
Volume of truncated cone
Try this! p 434, 435
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59
Level
Working
mathematically
5.50
Standard/Progression Point
•
selection and use of technology to explore
geometric and algebraic relationships and
data trends
MathsWorld 9
Chapter 2: Length, area and volume
Analysis task 1: Chemical storage tanks
Analysis task 3: Short shoelaces!
Chapter 3: Mathematical thinking
3.2: Extended modelling tasks with
technology
Try this! p 154
Chapter 5: Ratios and rates
Analysis task 1: How much water do we use?
Analysis task 2: Grand Prix
Analysis task 3: Compound interest
Chapter 6: Two-dimensional space
6.4: Angles in a circle
Try this! pp 335-336
Analysis task 1: Pascal’s angle trisector
Chapter 7: Similarity and trigonometry
Calculators are used in sections 7.3 to 7.5 for
angles and trigonometric calculations.
Chapter 8: Functions and modelling
8.5: Exponential functions
Ex. 8.5 Q 3, 4
8.7: Mathematical models
Example 2
Ex. 8.7 Q 4, 6, 8, 14, 15
Analysis task 1: Water hyacinths
Analysis task 2: Video and DVD sales
Analysis task 3: Water tank costs
Chapter 10: Analysing data
10.4: Summarising data
Exercise 10.4 Q 1 - 11
MathsWorld 10 Teacher edition
Chapter 11:
Algebra toolbox
Copyright © Macmillan Education Australia.
Unauthorised
copying2prohibited.
Chapter
60 Warm-up Try this! p 641
Analysis task 2: Simba’s SMS costs
MathsWorld 9 Practice and Enrichment
MathsWorld 10
Chapter 1: 2D and 3D geometry
1.1: Circles, chords and tangents
Try this! p 7, 8, 11, 12, 13, 15, 16
Ex. 1.1 Q 7, 8, 12
Analysis task 1: Tangents and intersecting
secants
Chapter 3: Trigonometry
3.6: The unit circle
Try this! p 187, 189, 193
Chapter 4: Statistical variables and
relationships
4.2: Displaying statistical variables
Ex. 4.2 Q 4
4.4: Summarising data: Measures of spread
Ex. 4.4 Q 5
4.9: Relationships between two numerical
variables
Ex. 4.9 Q 1, 7, 8, 9
Chapter 5: Algebra toolbox 2
5.1: Solving linear simultaneous equations
Try this! p 292
Analysis task 3: Jemima helps Mr Workalot
Chapter 8: Functions and modelling
8.4: Exponential functions
Ex. 8.4 Q 3, 4
8.6: Modelling with functions
Ex. 8.6 Q 7, 8
Analysis task 1: Braking distance
Chapter 9: Applications of arithmetic
9.1: Percentages and rates in retail and
60
finance
Ex. 9.1 Q 12, 14
Analysis task 3: LPG versus ULP
MathsWorld 10 Practice and Enrichment
Workbook (and CD) Technology toolkit
Level
Working
mathematically
5.75
5.75
Standard/Progression Point
•
•
use of an 'equations editor' to insert
mathematical material in a text document
simulation of events using technology
MathsWorld 9
MathsWorld 10
Equation editor is a standard installable add-in
for Microsoft Word. Students could be asked to
prepare a solution to an analysis task using this
software
Equation editor is a standard installable add-in
for Microsoft Word. Students could be asked to
prepare a solution to an analysis task using this
software
Chapter 9: Chance
Analysis task 3: A day at the races
Chapter 4: Statistical variables and
relationships
4.6 Populations, samples and randomness
Ex. 4.6 Q 3, 4
Chapter 7: Chance
Analysis task 1: Tram's game of chance
See note in Teacher edition (re use of ProbChart
spreadsheet)
MathsWorld 10 Teacher edition
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61
Level
Working
mathematically
5.75
Standard/Progression Point
•
representation and manipulation of symbolic
expressions using technology
MathsWorld 9
Chapter 4: Algebra toolbox 1
4.2: What does solving mean?
Example 3
Ex. 4.2 Q 12, 13, 15 – 19
4.3: Expanding algebraic expressions
Try this! p 192
4.4: Factorising algebraic expressions
Try this! p 199
4.6: Factorising quadratic trinomials
Try this! p 210
4.7: Perfect squares and differences of
squares
Try this! p 214, 218
MathsWorld 10 Teacher edition
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MathsWorld 10
Chapter 2: Algebra toolbox 1
2.1: Algebraic expressions, substitution,
expansion and common factors
Try this! p 92
2.3: perfect squares and differences of
squares
Try this! p 102
2.4: Factorising quadratic trinomials
Try this! p 109, 112
Chapter 5: Algebra toolbox 2
5.3: Rational solutions of quadratic equations
Ex. 5.3 Q 5, 6, 7
5.4: Real solutions to quadratic equations
Ex. 5.4 Q 10
5.5 The nature of solutions
Try this! p 327
Ex. 5.5 Q 7, 13
5.6: Graphing quadratic functions
Example 3, 4
Ex. 5.6 Q 8
5.7: Other techniques for solving equations
Examples 1, 2, 3
Ex. 5.7 Q 12
Analysis task 1: Using matrices to solve
simultaneous linear equations
Analysis task 3: Jemima helps Mr Workalot!
62
Level
Working
mathematically
5.75
Standard/Progression Point
•
recognition of functionality of technology
and its limitations, such as image resolution,
discontinuities in graphs and systematic error
in computation through rounding
MathsWorld 9
MathsWorld 10
Chapter 3: Mathematical thinking
3.2: Extended modelling tasks with
technology
Extended example problems 1, 2
Chapter 4: Statistical variables and
relationships 4.2: Displaying statistical
variables
Example 1
Chapter 8: Functions and modelling
Tip: What viewing window is that? p 454
8.6: Quadratic functions
Try this! p 476
8.7: Mathematical models
Ex. 8.7 Q 4, 11
Chapter 5: Algebra toolbox 2
5.1: Solving simultaneous linear equations
Try this! p 292
Ex. 5.1 Q 5, 6
5.2: Using graphs to solve simultaneous linear
equations
Ex. 5.2 Q 4, 9, 10, 11
5.3: Rational solutions of quadratic equations
Ex. 5.3 Q 5, 7
5.4: Real solutions to quadratic equations
Ex. 5.4 Q 10
5.7: Other techniques for solving equations
Examples 1, 2, 3
Tip p 347
Chapter 11: Algebra toolbox 2
11.2: Other techniques for solving equations
Examples 1, 2, 3
Try this! p 662
Ex. 11.2 Q 12, 13, 14
Analysis task 3: Scale issues
MathsWorld 9 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 3.1, 3.2 p 171, 172
TI 89 3.1, 3.2 p 208, 209
Chapter 8: Functions and modelling
8.3: Fitting rules to quadratic graphs
Ex. 8.3 Q 9
8.4: Exponential functions
Try this! p 536
Ex. 8.4 Q 5
8.6: Modelling with functions
Ex. 8.6 Q 8
MathsWorld 10 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 3.1, 3.2 p 147, 148
TI 89 3.1, 3.2 p 184, 185
MathsWorld 10 Teacher edition
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63
63
Level
Working
mathematically
6.0
Standard/Progression Point
At Level 6, students formulate and test
conjectures, generalisations and arguments in
natural language and symbolic form (for example,
‘if m2 is even then m is even, and if m2 is odd then
m is odd’).
MathsWorld 9
Chapter 4: Algebra toolbox 1
4.5: Expanding binomials
Try this! p 204, 205
4.7: Perfect squares and difference of squares
Try this! p 214
Analysis task 1: Pascal’s triangle and binomial
expansions
Analysis task 2: Completing the square
Chapter 6: Two-dimensional space
6.1: Angles, parallel lines and triangles
Try this! p 307, 310
Example 2
Ex. 6.1 Q 1, 2, 8, 9, 19
6.2: Quadrilateral properties
Example 1
Ex. 6.2 Q 1, 3, 4, 6, 7
6.3: Polygons
Try this! p 331
6.4: Angles in a circle
Try this! pp 335-336
Analysis task 3: Cyclic quadrilaterals
MathsWorld 10
Chapter 1: 2D and 3D geometry
1.1: Circles, chords and tangents
Ex. 1.1 Q 12
1.6: Loci
Ex. 1.6 Q 2
Analysis task 1: Tangents and intersecting
secants
Analysis task 2: Sylvester’s pantograph
Analysis task 3: Consul the educated monkey
Chapter 2: Algebra toolbox 1
Chapter Warm-up Try this! p 89
Chapter 5: Algebra toolbox 2
5.5: The nature of solutions
Try this! p 327
Chapter 7: Similarity and trigonometry
7.2: Similar triangles
Ex. 7.2 Q 6, 9, 11
Analysis task 1: Quadrilateral midpoints
Chapter 11: Algebra toolbox 2
Analysis task 1: A family of parabolas
MathsWorld 10 Teacher edition
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64
Level
Working
mathematically
6.0
Standard/Progression Point
They follow formal mathematical arguments for
the truth of propositions.
MathsWorld 9
MathsWorld 10
Chapter 2: Length, area and volume
2.3: Pythagoras’ theorem
Try this! p 74
Chapter 5: Algebra toolbox 2
5.4: Real solutions to quadratic equations
p. 321, 322
Chapter 6: Two-dimensional space
6.1: Angles , parallel lines and triangles
Try this! p 307, 310
Example 2
6.2: Quadrilateral properties
Example 1
Chapter 6: Measurement
6.4: Calculating area
Heron’s formula: Example 3
6.6: Calculating volume and capacity
Volume of truncated pyramid
Try this! p 430, 431
Volume of truncated cone
Try this! p 434, 435
MathsWorld 10 Teacher edition
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65
65
Level
Working
mathematically
6.0
Standard/Progression Point
Students choose, use and develop mathematical
models and procedures to investigate and solve
problems set in a wide range of practical,
theoretical and historical contexts (for example,
exact and approximate measurement formulas for
the volumes of various three dimensional objects
such as truncated pyramids).
MathsWorld 9
MathsWorld 10
Chapter 2: Length, area and volume
Analysis task 1: Chemical storage tanks
Analysis task 3: Short shoelaces!
Chapter 2: Algebra toolbox 1
2.6: Index form with pronumerals
Ex. 2.6 Q 6
Chapter 3: Mathematical thinking
Chapter Warm-up Try this! p 132
3.1 Mathematical modelling
Example problem 1Try this! p 136
Practice problems 1, 2
Example problems 2, 3
Problem set 3.1
3.2: Extended modelling with technology
Extended example problem 1 Try this! pp 149,
150, 151, 159, 161, 162, 163
Problem set 3.2
Chapter 3: Trigonometry
Analysis task 1: GPS and dead reckoning
Chapter 5: Algebra toolbox 2
Chapter Warm-up Try this! p 291
Analysis task 2: Tourist town ratings
Chapter 6: Measurement
6.4: Calculating area
Heron’s formula: Example 3
6.6: Calculating volume and capacity
Volume of truncated pyramid
Try this! p 430
Volume of truncated cone
Try this! p 434
Analysis task 1: Honeycombs and bubbles
Chapter 7: Chance
Analysis task 2: Pascal’s triangle and
probabilities
6.0
They generalise from one situation to another, and
investigate it further by changing the initial
constraints or other boundary conditions.
Chapter 6: Two-dimensional space
6.4: Polygons
Try this! p 331
Chapter 1: 2D and 3D geometry
1.1: Circles, chords and tangents
Try this! p 11, 13
Chapter 10: Analysing data
Analysis task 3: Investigating sample size
Chapter 2: Algebra toolbox 1
2.1: Algebraic expressions, substitution,
expansion and common factors
Try this! p 92
Chapter 11: Algebra toolbox 2
Analysis task 1: A family of parabolas
MathsWorld 10 Teacher edition
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66
66
Level
Working
mathematically
6.0
Standard/Progression Point
They judge the reasonableness of their results
based on the context under consideration.
MathsWorld 9
MathsWorld 10
For example,
For example,
Chapter 2: Length, area and volume
Sections 2.3 – 2.7
All exercises
Chapter 3: Trigonometry
Sections 3.1 – 3.4
All exercises
Chapter 7: Similarity and trigonometry
Sections 7.2 – 7.5
Chapter 6: Measurement
Sections 6.1 – 6.6
MathsWorld 10 Teacher edition
Copyright © Macmillan Education Australia. Unauthorised copying prohibited.
67
67
Level
Working
mathematically
6.0
Standard/Progression Point
They select and use technology in various
combinations to assist in mathematical inquiry, to
manipulate and represent data, to analyse
functions and carry out symbolic manipulation.
MathsWorld 9
MathsWorld 10
Chapter 1: Real numbers
1.4: Irrational numbers
Ex. 1.4 Q 5, 6, 7
1.5: Adding and subtracting surds
Ex. 1.5 Q 2
1.6: Multiplying and dividing surds
Try this! p 40
1.7: Rationalising the denominator
Try this! p 45
Chapter 2: Algebra toolbox 1
2.1: Algebraic expressions, substitution,
expansion and common factors
Try this! p 91, 92
2.3: Perfect squares and differences of perfect
squares
Try this! p 102
2.4: Factorising quadratic trinomials
Try this! p 109, 112
MathsWorld 9 Practice and Enrichment
Workbook (and CD) Technology toolkit
TI 83/84 1.1 p 161
TI 89 1.1 p 195
Chapter 3: Trigonometry
Analysis task 2: The sine function
Chapter 2: Length, area and volume
Analysis task 1: Chemical storage tanks
Chapter 3: Mathematical thinking
3.2: Extended modelling tasks with
technology
Extended example problems 1, 2
Chapter 4: Algebra toolbox 1
4.1: Formulas and substitution
Try this! p 172
4.2: What does solving mean?
Try this! p 179
Example 3
Ex. 4.2 Q 12 – 19
4.3: Expanding algebraic expressions
Try this! p 192
4.4: Factorising algebraic expressions
Try this! p 199
MathsWorld 10 Teacher edition
4.6: Factorising
quadratic
trinomials
Copyright © Macmillan Education Australia.
Unauthorised
copying
prohibited.
Try68
this! p 210
4.7: Perfect squares and difference
Chapter 5: Ratios and rates
Chapter 4: Statistical variables and
relationships
4.9: Relationships between two numerical
variables
Ex. 4.9 Q 1, 4, 7, 8, 9
Chapter 5: Algebra toolbox 2
5.1: Solving linear simultaneous equations
Try this! p 292
Ex. 5.1 Q 5, 6
5.5: The nature of solutions
Try this! p 327
5.6: Graphing quadratic functions
Try this! p 333
5.7: Other techniques for solving equations
Examples 1, 2
Ex. 5.7 Q 1, 2, 3, 9
Analysis task 1: Using matrices to solve
simultaneous linear equations
Analysis task 3: Jemima helps Mr Workalot!
Chapter 8: Functions and modelling
68
8.6: Modelling with functions
Ex. 8.6 Q 8
Analysis task 1: Braking distance
Chapter 9: Applications of arithmetic
Level
Working
mathematically
6.0
Standard/Progression Point
They use geometry software or graphics
calculators to create geometric objects and
transform them, taking into account invariance
under transformation.
MathsWorld 9
Chapter 1: Real numbers
Analysis task 1: The golden ratio
Chapter 3: Mathematical thinking
3.2: Extended modelling tasks with
technology
Extended example problem 1
Try this! p 149
Problem set 3.2 Q 1, 2
Chapter 6: Two-dimensional space
6.4: Angles in a circle
Try this! p 335-336,
Analysis task 3: Cyclic quadrilaterals
MathsWorld 10
Chapter 1: 2D and 3D geometry
1.1: Circles, chords and tangents
Try this! p 7, 8, 11, 12, 13, 15, 16
Ex. 1.1 Q 7, 8, 12
Analysis task 1: Tangents and intersecting
secants
Chapter 3: Trigonometry
3.6: The unit circle
Try this! p 187, 189, 193
Chapter 7: Similarity and trigonometry
Analysis task 1: Quadrilateral midpoints
MathsWorld 10 Teacher edition
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69