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GCSE HIGHER SCHEME OF WORK
Target
TIME Grades
Previous
Module Homework SumBooks Sheet
Module
Stage
1 Number
1
8
hours
C/B/A
2 Substitution and formulae
1
C
3 3D shape, volume and surface area
1
4 Data Handling
1
6
hours
5
hours
8
hours
5 Powers and Standard Index Form
1
C/B/A/A*
1,2
6 Pythagoras’ Theorem
1
C/B/A
1,2,5
7 Algebraic expressions, and
fractions
1
6
hours
3
hours
6
hours
C/B/A
5
8 Percentages
1
B/C
1
9 Geometry and trigonometry
1
8
hours
6
hours
C/B
6
10 Algebraic equations, and
rearranging formulae
1
7
hours
C/B
1,2,7
1
C/B/A
C/B/A
1. Estimation and Calculations
3. Rational and Irrational Numbers Ex 1
5. Prime Factors
12. Number Sequences
13. Substitution
51. Volume
53. Degree of Accuracy
62. Questionnaires
68. Histograms 1
69. Histograms 2
70. Histograms 3
75. Cumulative Frequency 1
76. Cumulative Frequency 2
91. Moving Averages
92. Box Plots
2. Standard Form
9. Indices Ex 1, 3
55. Pythagoras Theorem
8. Fractions
9. Indices Ex 2, 4
10. Simplifying Ex 1
14. Factorising Ex 1
6. Percentages
35. Regular Polygons
56. Sine, Cosine and Tangent Ratios
61. Three Dimensional Trigonometry
11. Rearranging Formulae
15. Trial and Improvement
18. Solving Equations 1 Ex 1
20. Writing Simple Equations
W Robertson
GCSE HIGHER SCHEME OF WORK
Target
TIME Grades
Previous
Module Homework SumBooks Sheet
Module
Stage
11 Transformations
1
5
hours
C/B/A
12 Handling data 2
1
6
hours
C/B
4
13 Algebraic graphs
1/2
6
hours
C/B
10
14 Ratio and proportion
1/2
C/A
1,7
15 Circles
1/2
4
hours
7
hours
C/B/A/A*
3,5,10
16 Quadratics
2
9
hours
C/B/A
7,10
17 Vectors
2
A*
18 Simultaneous equations and
inequalities
2
5
hours
6
hours
A
7,10
19 Congruence and transformations
2
4
hours
C/B/A
11,17
46. Transformations 1
47. Transformations 2
83. Enlargements with a Negative Scale Factor 1
84. Enlargements with a Negative Scale Factor 2
64. Scatter Diagrams
71. Mean
72. Mean, Median and Mode
7. Conversion Graphs
23. Straight Line Graphs
27. Recognising Graphs
32. Distance - Time Diagrams
33. Velocity - Time Diagrams
17. Direct and Inverse Proportion
52. Ratios and Scales
37. Geometry of a Circle 1
38. Geometry of a Circle 2
50. Area and Perimeter
10. Simplifying Ex 2
14. Factorising Ex 2, 3, 4
18. Solving Equations 1 Ex 2
19. Solving Equations 2
22. Writing Quadratic Equations
28. Graphs 1 (solving quadratic eqns)
39. Vectors 1
40. Vectors 2
21. Simultaneous Equations
24. Inequalities
25. Linear Inequalities
29. Graphs 2 (solving sim eqns)
36. Congruent Triangles
41. Similar Shapes
42. Similarity
W Robertson
GCSE HIGHER SCHEME OF WORK
Target
TIME Grades
Previous
Module Homework SumBooks Sheet
Module
Stage
20 Probability
2
7
hours
C/B/A/A*
21 Powers and Surds
2
B/A/A*
22 Constructions
2
23 Area and Volume
3
24 Sine rule, cosine rule and 3-D
3
8
hours
5
hours
6
hours
6
hours
25 Proportion and algebraic graphs
3
4
hours
A/A*
13,14
26 Graphical solutions of equations
3
A/A*
10,13,16,
18
27 Graphs of functions
3
28 Circle Theorems
3
29 Using a calculator
3
4
hours
4
hours
5
hours
3
hours
5
C
C/B/A/A*
3,5,11,19
A/A*
A/A*
B
15
77. Probability 1
78. Probability 2
79. Relative Probability
80. Tree Diagrams
4. Surds
31. Growth and Decay
44. Constructions
45. Loci
54. Formulae
43. Bearings
57. Sine and Cosine Rules
58. Areas of Triangles
59. Trigonometry - Mixed Exercise
89. Three Dimensional Co-ordinates 1
90. Three Dimensional Co-ordinates 2
85. Equation of a Circle
86. Simultaneous Equations 2
(with circles and straight lines)
48. Transformations of Graphs
60. Graphs of Sines, Cosines and Tangents
37. Geometry of a Circle 1
38. Geometry of a Circle 2
A/A*
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
MODULE 1 Number
TIME: 8 hours
TARGET GRADE: C/B/A
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Basic number bonds and
multiplication/division
facts.
 Awareness of position of
numbers on number
lines.
 Ability to recognise basic
number patterns.
CONTENT
Recognise triangular, square and cube
numbers NA2b (INT )
Recalling integer squares and corresponding
square roots to 15 15 NA3g
Recalling the cubes of 2, 3, 4, 5 and 10 NA3g
MAIN OBJECTIVES



Recognise the different types of
numbers, and find multiples and
factors.
Calculate squares and cubes, and
recall the relevant facts.
Find square and cube roots of
numbers.
Y10
TEXT
17-19
55-59
More
needed!
Finding multiples, factors, primes and prime
factors NA2a
Finding prime factor composition of positive
integers NA2a
Using prime factors to find HCFs and LCMs
NA2a
Rounding to the nearest integer, to decimal
places and to significant figures NA3h
Selecting and justifying appropriate degrees
of accuracy* NA4b
Checking and estimating answers to problems
NA4b

Write numbers in terms of their
prime factors and use prime factors
to find the HCF, and LCM.
71
More
needed!

Round any number to a specified
accuracy, or justify their own choice
of accuracy e.g. nearest integer,
significant figures or decimal places.
Use rounding methods to estimate
answers to complex expressions.
77-79
More
needed!
Recognising the limitations on the accuracy of
measurement* NA4b
Terminating and recurring decimals NA2c
Finding a fraction equivalent to a recurring
decimal NA2c

Calculate upper and lower bounds of
measurements or rounded numbers.
Change between fractions and
decimals, including those that recur.
Multiply and divide multiples of
powers of ten and decimals.
109-114



104-107
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Further work on indices to
include powers, with negative
and/or fractional indices.
 Trial and improvement for roots
of integers.

H/W SumBooks 5
It is essential to ensure that pupils are
absolutely clear about the difference
between significant figures and
decimal places and take note of the
required degree of accuracy for
questions.
 H/W SumBooks 1

H/W SumBooks 3 Ex 1
101-3
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
MODULE 2 Substitution and formulae
TIME: 6 hours
TARGET GRADE: C
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Module 1
CONTENT
The ability to:
commutative, associative and distributive laws

Apply rules for the order
NA4a
of operations for
Four rules with negative numbers NA3a

Using the order of operations, and the
MAIN OBJECTIVES

119-120
more
Recognise descending
needed
Substituting into algebraic formulae NA5g
DIFFERENTIATION / EXTENSION /
HOMEWORK
72
numbers.
and ascending number

patterns.

Confidently use order of operations
commutative, associative and
distributive laws for positive and
negative numbers.
Y10
TEXT
68-70,
Substitute numbers into any
expression or formula.
153-4

Estimate answers before
attempting complex
substitutions.

H/W SumBooks 13

Extend finding the nth term to
expressions involving second
differences and terms in n
squared.

H/W SumBooks 12
Need an
Use the four rules for
exercise
negative numbers.
with
negative
numbers
Generating a formula NA5g

Generating common number sequences NA6a

Generating number sequences using term-toterm and position-to-term definitions NA6a
Finding the nth term (linear expressions)

Derive a formula from given
information.
Find a designated term of a
sequence given a pattern or a
formula.
Find the nth term of a linear
expression.
7-12
NA6a
Use function notation NA5a
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
MODULE 3 3D shape, volume and surface area
TIME: 5 hours
TARGET GRADE: C/B/A
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Names and properties of
2D and 3D shapes.
 Nets of simple solids.
 Experience of finding
areas of shapes from
formulae.
 Ability to give answers
to a degree of accuracy.
CONTENT
Finding areas of plane shapes using formulae
SSM4d
MAIN OBJECTIVES


Find the perimeter and area of
simple shapes, such as rectangles
squares, triangles, parallelograms,
trapezia, kites, and composites of
rectangles and triangles.
Know the formulae for area of the
shapes mentioned.
Y11
TEXT
239-257
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Fencing problems.
 Additional work using symbolic
expressions.
 Finding upper and lower bound
of areas or volumes.
Nets of simple solids SSM2k
Finding surface area of solids with triangular
and rectangular faces SSM4d
Developing, knowing and using the formula
for the volume of a cuboid SSM4d
Finding volume of solids made from cuboids
SSM4d
Finding volume of prisms SSM4d




Work confidently with 3-D shapes
and be able to calculate the volume
of cuboids, prisms, pyramids, cones,
spheres, and solids made from
cuboids.
Calculate the surface area of solids
with triangular and rectangular
faces.
Find how many boxes of a given
size fit into a larger box.
Know the formulae for area of the
shapes mentioned.
258-263

Finding upper and lower bound
of areas or volumes.


H/W SumBooks 53

H/W SumBooks 51
Investigate the different nets
that can be used to make certain
3-D shapes given a particular
area of card.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
MODULE 4 Data Handling
TIME: 8 hours
TARGET GRADE: C/B/A
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Experience of displaying
data.

An understanding of the
concept of an average.

Experience of reading
from graphs.

Some concept of a
‘running total’.
CONTENT
Designing questionnaires and criticise
methods of using questionnaires HD3a
(INT )
Understanding frequency density* HD5d
Constructing histograms for grouped
continuous data HD4a
Calculating a mean from simple data
HD4E
Calculating a moving average HD4f
Completing cumulative frequency tables
HD4a
Plotting cumulative frequency diagrams
HD4a
Using cumulative frequency to find the
median HD4e
Using cumulative frequency to find
quartiles and interquartile range HD4e
Drawing Box plots HD4a
MAIN OBJECTIVES
Y10
TEXT
213-8
DIFFERENTIATION / EXTENSION /
HOMEWORK
 H/W SumBooks 62

Use frequency density to
construct a histogram.
236-238

Extend work on histograms to unequal
intervals.
Calculate means, and moving
averages making predictions.
179


H/W SumBooks 68, 69, 70


H/W SumBooks 91

Investigate what effects, if any, to (i)
the median, (ii) the interquartile range
if you (a) + 10, (b) - 10 (c) * 10, (d) /
10, to all the data.
Collect, analyse and display own data
in a cumulative frequency diagram and
then compare the distribution with
others in the class. (E.g. the number of
minutes spent doing homework daily
during a particular month)... what
general conclusions can be made for
the subgroups within the class?
H/W SumBooks 75,76,92






Design and complete a cumulative
frequency table, identifying class
boundaries where necessary.
Plot a cumulative frequency curve
using upper class boundaries.
Solve problems using a
cumulative frequency curve (e.g.
How many____ were more
than…).
Use a cumulative frequency curve
to estimate the median, lower
quartile, upper quartile, and
interquartile
range.
Construct box plots.
224-229


Use moving averages to make
seasonal predictions.
*For 1388 this is not assessed until Stage 2.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
MODULE 5 Powers and Standard Index Form
TIME: 6 hours
TARGET GRADE: C/B/A/A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Modules 1, 2.

An ability to multiply
and divide by powers of
10.

CONTENT
Using index notation NA2b
Using indices in expressions NA5d
Using index laws for multiplication and
division (integer powers)* NA2b STAGE
ONE

Using standard index form NA2b
Converting between ordinary and
standard index form representations
NA3h
Using standard index form to make
estimates* NA3h
Calculating with standard index form*
NA3m
Using a calculator for standard index
form NA3r

Experience of using
powers of numbers.
MAIN OBJECTIVES





Know and use the rules of indices
(adding, subtracting and
multiplying indices).
Evaluate fractional and negative
indices.
Recognise that some numbers are
too large or too small to be
represented normally on a
calculator.
Represent standard form as a
number between 1 and 10
multiplied by a positive or
negative power of ten.
Convert between standard form
and ‘normal’ numbers.
Solve problems involving
standard form, using the correct
calculator method and making
estimates.
Interpret a calculator display
showing a number in standard
form.
Y10
61-64
(the
algebra
side is
in
Module
7 too)
81-88
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Simplify expressions involving
complex indices.
 Solve equations involving indices.
 H/W SumBooks 9

H/W SumBooks 2
NOTES
There is now a greater emphasis on manipulative algebra at Key Stage 4, particularly at this tier.
*For 1388 this is not assessed until Stage 1.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
MODULE 6 Pythagoras’ Theorem
TIME: 3 hours
TARGET GRADE: C/B/A
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Modules 1, 2, 5
 The ability to square
integers, with and
without a calculator and
use a calculator to find
square roots.
 The ability to manipulate
equations.
 Rounding an answer to a
given number of decimal
points or significant
figures.
 Plotting points given
their co-ordinates.
 Knowledge of simple
bearings.
CONTENT
Using Pythagoras’ Theorem to find the
Hypotenuse SSM2f
Using Pythagoras’ Theorem to find the
shorter sides SSM2f
Using Pythagoras’ Theorem to solve
problems SSM2f
Calculating lengths of lines on a grid
SSM3e
MAIN OBJECTIVES





Identify the hypotenuse of a rightangled triangle.
Recall Pythagoras’ theorem.
Pick out right-angled triangles
from diagrams, (e.g. circles,
isosceles triangles).
Use Pythagoras’ theorem to find
the length of any side of a right
angled triangle.
Use Pythagoras’ theorem to solve
problems such as bearings, areas
of triangles, diagonals of
rectangles etc.
Y10
287-298
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Use Pythagoras’ theorem to find the
area of isosceles and equilateral
triangles whose sides are known.
 Prove Pythagoras’ theorem for shapes
(other than squares) on the sides of
right-angled triangles.
 Investigate Pythagorean triples,
looking for a general case.
 Find a formula for the area, A cm2, of
a right-angled isosceles triangle with
hypotenuse x cm.
 Investigate how to draw a line of
exactly  5 cm.
 Further work can be developed on
applying Pythagoras’ theorem in
three-dimensional problems.
 H/W SumBooks 55
NOTES
Consult GCSE papers for types of questions, depending on the orientation of the triangle and whether or not the hypotenuse or shorter side is required.
Emphasise:-
(i) hypotenuse (opposite the right angle) is the longest side;
(ii) the length of the hypotenuse < the sum of the lengths of the other two sides.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
MODULE 7 Algebraic expressions, and fractions
TIME: 6 hours
TARGET GRADE: C/B/A
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Module 5

Four rules with negative
numbers.

Understand the concept
of a factor.

CONTENT
MAIN OBJECTIVES
Collecting like terms NA5b
Removing a single pair of brackets NA5b
Simplifying expressions using the rules of
indices NA5d

Factorising with a single pair of brackets
NA5b

Simplify expressions involving algebraic
fractions NA5b

Understanding the term ‘identity’ NA5c

Understanding the term ‘identity’.
Adding and subtracting fractions NA3c
Multiplying and dividing fractions NA3d

Use the four rules with fractions
(including mixed numbers).

Experience of the four
rules for simple
fractions.
Simplify algebra by collecting
like terms – answers may involve
negative coefficients.
Simplify algebraic expressions
using the rules of indices.
Remove and factorise a single pair
of brackets – including cases
where variables are removed as
part of the factor.
Simplify any algebraic expression
involving fractions.
Y10
128-9,
132
DIFFERENTIATION / EXTENSION /
HOMEWORK
 H/W SumBooks 10 Ex1 H/W
SumBooks 9 Ex2 and 4
161

H/W SumBooks 14 Ex1
factorising
62,63,64
Y11
208-213

More complicated expressions
which involve a combination of
brackets and fractions
Use the tools learned in this module
to prove identities.

89-100

H/W SumBooks 8 includes
algebraic fractions
NOTES
At this stage it is important to develop a logical way to set out their algebraic manipulation.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
MODULE 8 Percentages
TIME: 8 hours
TARGET GRADE: B/C
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Module 1.
 A basic understanding of
the concept of a
percentage.
 An understanding of the
ideas behind VAT,
taxation and interest.
CONTENT
Interchanging between percentages,
fractions and decimals NA3e
Finding percentages and percentage
changes NA3j
Finding VAT, a percentage profit or loss
NA3j
Using simple interest NA3j
Multiplying by a number between 0 and 1
NA3a
Understanding the multiplicative nature
of percentages as operators NA3e
Finding 100% when another amount is
known NA3e
Solving percentage problems NA3e
Solving reverse percentage problems
NA3e
Solving problems involving compound
interest NA3k
MAIN OBJECTIVES










Change between percentages,
fractions and decimals.
Find percentages of quantities
using both mental mathematics
and calculator method, and solve
percentage problems.
Increase and decrease quantities
by a percentage, including within
contexts of VAT, profit and loss.
Find one quantity as a percentage
of another, and calculate the
percentage when an actual profit
or loss is given.
Calculate simple and compound
interest.
Solve problems using percentages
e.g. taxation, bills.
Recognise that an increase of e.g.
15% leads to 115% and a decrease
of e.g. 15% leads to 85%.
Find the original amount e.g. price
before a sale, price before VAT.
Write down a decimal multiplier
that is equivalent to an increase or
decrease in percentage.
Use multipliers to solve reverse
percentage and compound interest
problems.
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Problems which lead to the necessity
of rounding to the nearest penny (eg
real-life contexts).
 Calculate original price before
compound interest.
 Combine multipliers to simplify a
series of percentage changes.
 Independent research into the many
uses made of percentages e.g. in the
media, VAT, in shops.
 H/W SumBooks 6
NOTES
Amounts of money should always be rounded to the nearest penny where necessary, except where such rounding is premature (e.g. in successive calculations like in compound
interest). Pupils typically answer compound interest questions incorrectly, either by using simple interest or by calculating over the wrong number of years.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
Module 9 Geometry and trigonometry
TIME: 6 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Module 6
 Knowledge of
Pythagoras’ theorem.
 Ability to use a
calculator to change
fractions to decimals.
 Knowledge of basic
concepts of ratio.
CONTENT
MAIN OBJECTIVES
Y10/11
Angles in polygons SSM2d (INT )

Solve problems involving
interior/exterior angles of
polygons (regular and irregular),
and understand the concept and
limitations of tessellation.
Y11
226-9
Tangent, sine and cosine ratios. SSM2g
Uses of the three ratios. SSM2g
Angles of elevation and depression.
SSM2g
Bearings and trigonometry SSM2g

Identify appropriately the various
sides of a right-angled triangle as
the Hypotenuse, Opposite and
Adjacent.
Recall the ratios for sine, cosine,
and tangent and identify which are
required to solve a problem.
Use information given to find
angles using the appropriate ratio.
Use the appropriate ratio to find
the lengths of sides in a rightangled triangle.
Find angles of elevation and
depression using the appropriate
ratio.
Apply trigonometric ratios and
Pythagoras’ Theorem to solve
assorted problems, including
those involving bearings.
Y10
299-316
Y11 1827





DIFFERENTIATION / EXTENSION /
HOMEWORK
 H/W SumBooks 35





Further work can be developed on
applying the ratios in threedimensional problems.
Work on the sine and cosine rules
could be developed.
Given two properties of a rightangled triangle find the others.
H/W SumBooks 56
H/W SumBooks 61 3D
NOTES
For some students this work is found difficult simply because they cannot identify which sides to use or which ratio can be used. The labelling of sides can be confused when both
angles are labelled.
Emphasise the importance that a calculator is in ‘Degree mode’, and that scale drawings will score 0 marks for this type of question.
*Not assessed until Stage 3.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
Module 10 Algebraic equations, and rearranging formulae
Time: 7 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Module 1, 2, 7.
 A knowledge and
understanding of pairs of
inverse operations.
 Experience of solving
simple linear equations.
CONTENT
MAIN OBJECTIVES
Using inverse operations to solve
equations NA5e
Linear equations with integer or fractional
coefficients NA5f
Equations combining operations NA5e
Solving equations with the unknown on
both sides NA5f
Solving equations using brackets and
negative solutions NA5f
Set up simple equations NA5e
Using algebraic equations to solve
problems NA5e
Using trial and improvement to solve
non-linear equations NA5m

Use inverse operations to rearrange
formulae NA5g




Solve linear equations including
those with an unknown on both
sides, those that require prior
simplification
(e.g. brackets), fractional
equations, and those where the
answers are either negative or a
fraction.
Derive algebraic expressions from
information given and extend this
to derive equations, solving
problems.
Find square and cube roots of
numbers including decimals, and
solve non-linear equations using
trial and improvement.
Rearrange formulae, including
those where the potential subject
occurs more than once.
Y10
135-149
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Derive equations from practical
situations (such as angle
calculations).
 Solve equations where more
manipulation of fractions is
required.
 H/W SumBooks 18 Ex 1
 H/W SumBooks 20
171-2

H/W SumBooks 15
155-160

H/W SumBooks 11
NOTES
Pupils can leave their answers in fractional form where appropriate.
In ‘trial and improvement’ emphasise the need to justify the final answer by considering the half way value.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
Module 11 Transformations
Time: 5 hours
TARGET GRADE: C/B/A
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Plotting co-ordinates
 An understanding of the
concepts of congruency,
similarity and
enlargement.
CONTENT
Reflecting 2D shapes SSM2a
Rotating shapes through various angles
and about various centres of rotation
SSM2a
Using translations that are specified by a
vector SSM2a
MAIN OBJECTIVES



Enlarging assorted shapes using various
centres of enlargement and integer scale
factors SSM3c
Enlarging assorted shapes using noninteger scale factors SSM3c
Enlargement calculations SSM3d





Reflect shapes and identify
equations of mirror-lines,
including diagonal lines (y = x, y
= x).
Rotate 2-D shapes following
instruction and describe a rotation
in full.
Recognise translations as sliding
movements, and translate simple
2-D shapes within a plane using
words or vector notation.
Understand which are the
invariant properties of
enlargements.
Enlarge shapes using a variety of
positive, negative, integer and
non-integer scale factors.
Use scale factors to solve
problems involving similar
shapes.
Work on tasks involving these
transformations.
Use scale to interpret maps and
complete scale drawings.
Y11
DIFFERENTIATION / EXTENSION /
HOMEWORK
267-272
273-5





The tasks set can be extended to
include combinations of
transformations, including those
from other
modules.
Investigation into different ways of
transforming an object into a
particular image.
H/W SumBooks 46, 47
H/W SumBooks 83, 84
Negative S.F.
NOTES
Emphasis needs to be placed on ensuring that students do describe the given transformation fully.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE)
Module 12 Handling data 2
Time: 6 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Module 4
 The ability to plot points
given their co-ordinates
(in all four quadrants).
 An ability to read from
graphs.
 Knowledge of the terms
mean, median, mode and
inequality signs.
 An understanding of the
concept of a variable.
 Recognition that a
change in one variable
can affect another.
CONTENT
Identifying trends in time series HD5b
Comparing shapes of distributions HD5d
Comparing distributions using measures
of average and spread HD5d
Using a calculator for statistical
calculations HD4j
Plotting and interpreting scatter diagrams
HD4a
Describing correlation from a scatter
graph HD5f
Drawing and using a line of best fit HD4i
MAIN OBJECTIVES
Y10
DIFFERENTIATION / EXTENSION /
HOMEWORK

Make predictions based on trends
of a graph.
199-202

Use averages and range to
compare two distributions.
Evaluate mean, median, mode and
range from simple and grouped
data, justifying the choice of a
particular average. (Calculator
and non-calculator).
Plot and use a scatter graph to
describe correlation in terms of
the two variables, and as positive,
weak, negative, or strong.
Draw a line of best fit where
possible “by eye”, and use this to
make predictions.
203212, 181
239-40

H/W SumBooks 71, 72
219-223

Vary the axes required on a scatter
graph to suit the ability of the class

H/W SumBooks 64



NOTES
When plotting points or reading off where a graph crosses the x-axis, check the scale on the axes carefully.
If possible in exam questions choose an easy scale for each axis.
Students should check that their answers for mean, median and mode lie within the given range of data.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE/TWO)
Module 13 Algebraic graphs
TIME: 6 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Module 10.
 The ability to plot points
that follow a simple rule
(in four quadrants).
 The ability to substitute
positive and negative
values into a non-linear
formula.
CONTENT
Plotting graphs of functions
where y is expressed in terms
of x, leading to a straight line
NA6b
Calculating gradients of
straight lines, and exploring
gradients of parallel lines*
NA6c
Recognising the y-intercept
of a straight line* NA6c
Exploring graphs of the form
y = mx + c* NA6c
Plotting linear graphs from
real-life problems NA6d
Plotting the graph of a
quadratic function NA6e
Plotting graphs of cubic,
reciprocal and exponential
functions* NA6f
Interpret graphs representing
real-life situations NA6d
(time-distance etc)
Recognising characteristics
of graphs* NA6f
MAIN OBJECTIVES





Plot a straight-line graph from a given set of
values.
Realise that an equation of the type y = mx + c
represents a straight line graph, and plot this
graph.
Understand the relevance of m and c in the
above equation.
From a given graph, find the gradient and yintercept and hence the equation of the graph.
Draw a straight-line graph without plotting
points.
Y10
251-262
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Extend to identifying regions
relating to straight line graphs.
 Having drawn the graph of type y =
ax + bx +cx, investigate how it can
be used to solve equations of the
type ax + bx + cx + k = 0, where a,
b, c and k are constants.
 Use of a graphic calculator.
 Find gradients at a point of a curve.
 H/W SumBooks 23
3
2
3
2
263


Evaluate exponential functions.
Plot curves from given quadratic, cubic,
reciprocal and exponential functions.

Interpret travel graphs, and calculate with
speed, distance and time (including decimal
divisions of an hour).
Interpret and plot real-life graphs such as
conversion graphs and distance/time graphs.
Recognise graphs e.g. filling different shaped
containers.
Understand compound measures such as
density or rate of flow, and interpret this from a
graph.



267-273
Exponen
tials in
Y11 131140
Y11 1159

H/W SumBooks 31 Growth
and Decay

H/W SumBooks 7 Conversion
Graphs
H/W SumBooks 27 Real life
graphs
H/W SumBooks 32 Distancetime
H/W SumBooks 33 Velocity
Time



NOTES
Links with the Science department could yield many experiments that would give rise to straight line relationships.
*For 1388 this is not assessed until Stage 2
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE/TWO)
Module 14 Ratio and proportion
TIME: 4 hours
TARGET GRADE: C/A
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Module 1, 7.
 Basic number skills and
ability to recognise
common factors.
 Calculator skills.
CONTENT
Simplifying ratios NA2f
Relating ratio form to
fractions NA2f
Dividing in a given ratio
NA3f
Unitary method* NA3n
(FDN )
MAIN OBJECTIVES






Using direct proportion*
NA3l & NA5h
Using inverse proportion*
NA3l & NA5h

DIFFERENTIATION / EXTENSION /
HOMEWORK
 H/W SumBooks 52 Ratios and
Recognise a ratio as a way of showing the
relationship between two numbers.
Relate a ratio to a fraction.
Simplify a ratio by dividing both its numbers
by a common factor and recognise when it is in
its lowest terms.
Recognise when two variables are in direct
proportion or inverse proportion.
Use the unitary method as a way of solving
ratio and proportion problems (e.g. recipes).
Divide a quantity into a given ratio (in two or
three parts).
Use the unitary method as a way of solving
ratio and proportion problems (e.g. recipes).

Y10 116

Scales
H/W SumBooks 17 direct and
indirect proportion
Currency calculations using current
exchange rates.
NOTES
Candidates often fall down when dividing into a 3-part ratio.
*For 1388 this is not assessed until Stage 2.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE ONE/TWO)
Module 15 Circles
Time: 7 hours
TARGET GRADE: C/B/A/A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Modules 3, 5, 10.
 Knowledge of basic
circle vocabulary, and
the ability to construct a
circle.
CONTENT
Recalling terms relating to a
circle SSM2h
Understanding and using
right angles between tangent
and radius SSM2h
Understanding and using
tangents of equal length
SSM2h
Explaining why the
perpendicular from the
centre of a chord bisects the
chord* SSM2h
Calculating circumferences*
SSM4d (INT )
Calculating lengths of arcs *
SSM4d
Calculating areas of circles*
SSM4d (INT )
Recalling formulae for areas
of circles* SSM4d (INT )
Calculating areas of
sectors* SSM4d
Using pi in exact
calculations* NA3n (INT )
MAIN OBJECTIVES






Y11
Use the vocabulary of a circle (circumference,
radius, diameter, sector, segment, chord, and
tangent).
Calculate angles within circles using rules
relating to tangents and radii.
Explain why the perpendicular from the centre
of a chord bisects the chord.
This
section is
missing
from the
text!!
See Y11
Int 208
Recall and apply the formulae for the area and
circumference of a circle given either the radius
or diameter, using various approximations to
or leaving as part of an irrational answer.
Find the length of an arc, the area and perimeter
of a sector, and the area of a segment.
Find the area of compound shapes or shaded
areas that include part of a circle.
Y11 250257
DIFFERENTIATION / EXTENSION /
HOMEWORK
 H/W SumBooks 37, 38

Find the area of an annulus, or
volume of a prism with a crosssection that is part of a circle.

H/W SumBooks 50
NOTES
can be 3 or 3.14 or 22/7 depending on accuracy or style of answer required.
Answers on a non-calculator paper can be irrational (i.e. in terms of ).
* For 1388 this is not assessed until Stage 2.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE TWO)
Module 16 Quadratics
Time: 9 hours
TARGET GRADE: C/B/A
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Modules 7, 10.
 Removing and
factorising with one pair
of brackets.
 An appreciation that if
the product of two
numbers is zero then
one of the numbers must
be zero.
 Confidence with the
four rules for directed
numbers.
 Drawing quadratic
graphs.
 Use BODMAS for
complicated examples,
and substitute values
into a complex formula.
CONTENT
Expanding brackets – the
product of two linear
expressions NA5b
Factorising of quadratic
expressions. NA5b
Finding the difference of two
squares NA5b
Solving quadratic equations
by factorising NA5k
Solving quadratic equations
by using the difference of
two squares NA5k
MAIN OBJECTIVES






Make efficient use of techniques covering
signs, products and sums.
Expand and simplify two pairs of linear
brackets, e.g. (x + 2)(x – 4), (3x + 2y)(4x + y),
(x + p)(a + g) etc.
Expand the square of a linear expression.
Factorise a trinomial
Use a factorised trinomial in one variable to
solve a quadratic equation.
Y10
129-131,
Ex C&D
133-4
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Set up quadratics from practical
situations (e.g. area of a rectangle
with both edges expressed in terms
of x).
 H/W SumBooks 10 Ex 2
162-168



Factorise using the difference of two squares
and use this to solve quadratic equations.

H/W SumBooks 14 Ex 3, 4
Factorising
H/W SumBooks 18 Ex 2 solving
equations (including completing
square)
Apply difference of two squares to
Pythagoras’ Theorem.
Evaluation of calculations e.g. 98 –
2.
2
2

Solving quadratic equations
using the quadratic formula
NA5k

Use the formula to solve quadratic equations.
Simplify expressions by
cancelling common factors
NA5b
Finding approximate
solutions to quadratics using
graphs NA6e
Finding approximate
solutions to problems using
graphs of complex functions
NA6f

Use factorising methods to simplify algebraic
fractions.

Solve quadratic and cubic equations using a
given graph or where one has to be drawn.
Use terms like ‘minimum point’, ‘maximum
point’, ‘quadratic function’.
Use graphical methods to find the maximum or
minimum of a quadratic function.
Solve problems using cubic or exponential
graphs.





280-283
H/W SumBooks 14 Ex 2
Factorising
H/W SumBooks 22
Significance of whether
discriminant is positive, negative or
zero.

H/W SumBooks 19, 22

Use graphical calculators to enable
pupils to get through examples more
rapidly.

H/W SumBooks 28
W Robertson
GCSE HIGHER SCHEME OF WORK
DIFFERENTIATION & EXTENSION
Area of an annulus.
NOTES
There may be a need to remove the HCF (numerical) of a trinomial before factorising to make the factorisation more obvious.
Students should be reminded that factorisation should be tried before the formula is used.
In problem-solving, one of the solutions to a quadratic may not be appropriate.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE TWO)
Module 17 Vectors
Time: 5 hours
TARGET GRADE: A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 The ability to use the
four rules confidently
with fractions and
negative numbers.
CONTENT
Understanding and using
vector notation SSM3f
Calculating the sum and
difference of two vectors
SSM3f
Calculating a scalar multiple
of a vector SSM3f
Calculating the resultant of
two vectors SSM3f
Representing graphically the
sum and difference of two
vectors SSM3f
Representing graphically a
scalar multiple of a vector
SSM3f
Solving simple geometrical
problems in 2-D using vector
methods SSM3f
MAIN OBJECTIVES

Understand the content of the module
Y11
296-304
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Find the modulus of a vector, or its
angle to the horizontal
 H/W SumBooks 39, 40
NOTES
Pupils often find the pictorial representation of vectors more difficult than the manipulation of column
vectors.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE TWO)
MODULE 18 Simultaneous equations and inequalities
TIME: 6 hours
TARGET GRADE: A
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Modules 7, 10.
 The ability to solve
linear equations.
 Understanding of LCM.
 Understanding of the
concept of an inequality.
 Ability to construct
straight line graphs.
CONTENT
MAIN OBJECTIVES
Solving simultaneous
equations using elimination
NA5i

Solve linear simultaneous equations by
eliminating a variable, using them to solve
problems.
Y10 and
11
121-125
Y11 1558
Solving linear inequalities in
one variable NA5j

Solve linear inequalities through both algebraic
methods and listing possible integer values.
Solve simple inequalities involving squares.
150-152
Y11 9798

Use regions on a graph to solve inequality
problems in two variables.
Y11 99103


Solve linear simultaneous equations by
graphical methods, using them to solve
problems.
274-279


Solving linear inequalities in
two variables and finding the
solution set NA5j
Solving simultaneous
equations using a graphical
method NA5i
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Simultaneous equations that need
rearranging before one of the
methods can be used.
 Most able: Solve simultaneous
equations in 3 variables.
 H/W SumBooks 21
 H/W SumBooks 24


Use graphical calculators to enable
pupils to get through examples more
rapidly.
Use gradient and intercept to draw
lines.
H/W SumBooks 25 Graphical
Inequalities
H/W SumBooks 29 Sim.Eqns
graphically
NOTES
Inaccurate graphs could lead to incorrect solutions.
Could lead to investigations such as Car hire, Mobile Phones.
Many pupils find locating regions difficult – it is often useful to choose a particular point on one side of the line to check if it fits the inequality.
All working should be clearly presented and show how coefficients are matched and eliminated.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE TWO)
MODULE 19 Congruence and transformations
TIME: 4 hours
TARGET GRADE: C/B/A
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Modules 11, 17.
 Understanding of
reflection, rotation,
translation and
enlargement and an
ability to describe each
transformation in full.
CONTENT
MAIN OBJECTIVES
Understand similarity and
congruence SSM2e
Prove the congruence of
triangles using formal
arguments SSM2e

Transforming 2-D shapes
using a combination of
transformations SSM3b
Recognising properties
which are preserved under
transformations SSM3b

Recognise combinations of transformations and
describe them in full.

Recognise properties that are preserved, and
those that are changed under transformations.

Calculate missing sides of triangles and other
shapes (e.g. regular polygons) using similarity.
Prove the congruence of triangles using formal
arguments.
Y11
278-287
288These
pages
missing
from the
book!!
276-7
DIFFERENTIATION / EXTENSION /
HOMEWORK
 H/W SumBooks 41, 42

H/W SumBooks 36
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE TWO)
MODULE 20 Probability
TIME: 7 hours
TARGET GRADE: C/B/A/A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Writing probabilities as
fractions, decimals or
percentages.
 Probability of an event
happening or not
happening.
CONTENT
MAIN OBJECTIVES
Estimating probability from
theoretical models HD4b
Using relative frequency
HD4b
Using the vocabulary of
probability to interpret
results HD5g
Using probability estimates
to compare results HD5h
(INT )
Selecting and justifying a
method of sampling* HD2d
Understanding the effect of
sample size on probability
estimates HD5i (INT)

Understanding the concepts
of mutual exclusivity and
independent events HD4g
Knowing when to add or
multiply probabilities HD4g


Know when to use the P(A) + P(B) ‘OR’ rule,
and the P(A) (B) ‘AND’ rule.
Using tree diagrams to
represent outcomes of
compound events HD4h

Probability of an event happening or not
happening.
Use the result P(not n) = 1 – P(n) for
consecutive events.
Complete tree diagrams as a means of showing
outcomes for two successive events and related
probabilities, and use them to solve probability
problems.







Writing probabilities as fractions, decimals or
percentages.
Estimate probabilities and use relative
frequencies to make predictions or test for bias.
Probability of an event happening or not
happening.
Use the result P(not n) = 1 – P(n) for
consecutive events.
Understand sampling techniques, and justify
their choice.
Appreciate that a larger sample size will give a
more accurate estimate, and question the
reliability of results.
Analyse experimental data and compare this to
theoretical results.
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Use the fraction button of a
calculator to work with harder
fractions.
 Use Venn diagrams to solve
probability questions.
 Make predictions of outcomes for
probability games and then test the
predictions.
 Consider the rules of a probability
game where the first player is
favourite to win and change the
rules to make the game fair.
 Use spreadsheets to generate
random dice throws etc. to consider
large numbers of trials – look at
effects as n becomes large, plot
graphs …. This could lead to
asymptotes.
 H/W SumBooks 77
 H/W SumBooks 78
 H/W SumBooks 79 Relative

Prob
H/W SumBooks 80 Tree
diagrams
OBJECTIVES
Use the ideas of conditional probability to solve problems.
NOTES
Pupils can often lose marks at probability due to inability to manipulate fractions.
Pupils do not always appreciate that some descriptions of probabilities cover more than one outcome e.g. tossing 2 coins and obtaining ‘one of each’.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE TWO)
MODULE 21 Powers and Surds
TIME: 8 hours
TARGET GRADE: B/A/A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Module 5.
 Evaluating powers, and
the rules of indices.
 Some understanding that
a surd is more accurate
than a rounded answer.
CONTENT
Understanding and using
reciprocals NA3a
Fractional and negative
powers NA3a
Recognising the
relationships between
fractional powers and roots
NA3g
Recalling the zero power
NA3g
Using index laws for
multiplication and division
of integer, fractional and
negative powers NA3a
Using surds and in exact
calculations NA3n
Rationalising a denominator
– simple cases only* NA3n
Using powers to explore
exponential growth and
decay NA3t
MAIN OBJECTIVES







Evaluate integer, fractional negative and zero
powers with or without a calculator.
Understand the term reciprocal, and use this in
calculations involving powers.
Use the rules of indices on all types of powers
of numeric and algebraic terms.
Understand the concept of a root being an
irrational number, and leave answers to
problems in surd form.
Simplify numeric calculations by manipulating
surds.
Rationalise a denominator.
Understand exponential growth and decay, and
use it to make predictions.
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Investigate the constant e.
 Estimating answers of complex
calculations involving surds, or
powers.
 H/W SumBooks 4 Surds
 H/W SumBooks 31 Growth
and Decay
NOTES
Where appropriate, pupils will need to be able to move between power and surd or power and reciprocal forms.
* For 1388 this is not assessed until Stage 3.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE TWO)
MODULE 22 Constructions
TIME: 5 hours
TARGET GRADE: C
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 An ability to use a pair
of compasses.
 Understanding of the
term’s perpendicular,
bisecting and parallel.
CONTENT
Constructing triangles
SSM4c
Constructing a perpendicular
bisector and finding the midpoint of a line segment
SSM4c
Construct perpendiculars to a
line SSM4c
Bisecting an angle SSM4c
Finding Loci SSM4e
Constructing graphs of
simple loci NA6h (INT )
MAIN OBJECTIVES




Construct shapes from given information using
only compasses and a ruler.
Construct perpendicular bisectors, and angle
bisectors using only compasses and a ruler.
Construct LOCI in terms of distance from a
point, equidistance from two points, distance
from a line, equidistance from two lines and
line of sight.
Shade regions using LOCI to solve problems
e.g. vicinity to lighthouse/ port.
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Solve LOCI problems that require a
combination of LOCI.
 Past GCSE questions.
 H/W SumBooks 44

Constructions
H/W SumBooks 45 Loci
NOTES
All working should be presented clearly, and accurately. A sturdy pair of compasses is essential.
Work on LOCI particularly lends itself to practical activities.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE THREE)
MODULE 23 Area and Volume
TIME: 6 hours
TARGET GRADE: C/B/A/A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Modules 3, 5, 11, 19.
 Formulae for finding
areas of plane shapes,
and volumes of cuboids
and prisms.
CONTENT
Solving problems involving
surface areas of more
complex solids* SSM2i
Solving problems involving
volumes of more complex
solids * SSM2i
Solving problems involving
more complex shapes and
solids SSM2i
Understanding the
dimensions of formulae for
perimeter, area and volume
SSM3d
Understanding the effect of
enlargement on areas and
volumes SSM3d
Converting between area and
volume measures SSM4d
MAIN OBJECTIVES






Solve problems involving surface areas of
prisms, cylinders, pyramids, and spheres.
Find the surface area of a cone from a given
net.
Solve problems involving volumes of prisms,
cylinders, pyramids, cones and spheres.
Recognise whether a formula represents a
length, area or volume by considering its
dimensions.
Understand the effect an enlargement has on
the area and volume of a shape, by considering
scale factors.
Convert between units of area and volume e.g.
square metres to square centimetres.
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Use trigonometry calculations to
solve problems of volume and
surface area.
 The scale factor for mass/weights of
similar solids.
 H/W SumBooks 54 Dimensions
of Formulae
NOTES
The notion of approximate similarity can be discussed, for example between infants and adults.
For 1388 this is assessed in Stage 2.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE THREE)
MODULE 24 Sine rule, cosine rule and 3-D
TIME: 6 hours
TARGET GRADE: A/A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Names and properties of
3-D shapes.
 The three trigonometric
ratios.
 Pythagoras’ theorem.
 Ability to substitute and
rearrange complex
formulae.
CONTENT
MAIN OBJECTIVES
Y11
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Find a side using the cosine rule,
when the quadratic formula is
required.
 The ambiguous case for sine rule.
 H/W SumBooks 57 Cosine and
Using the cosine rule SSM2g

Use the cosine rule to find the size of an angle
or side in a non-right-angled triangle.
49-50
Using the sine rule SSM2g

Use the sine rule to find the size of an angle or
side in a non-right-angled triangle.
51-53
Area of a triangle using sin C
* SSM2g STAGE TWO
Using Pythagoras’ theorem
in 3-D problems SSM2f
Using trigonometric
relationships in 3-D
problems SSM2g

Find the area of a triangle using sin C.

Sine
H/W SumBooks 58

Solve problems (including those involving
bearings) using the sine and cosine rules.
Use Pythagoras’ theorem, trigonometric ratios,
sine rule and cosine rule to solve problems in 3D.

H/W SumBooks 43

H/W SumBooks 89, 90 3D
problems
H/W SumBooks 61 3D problems
H/W SumBooks 59 Mixed trig
exercise

Angle between a line and a
plane SSM2g
35-36


37-9
NOTES
Pupils may need to be reminded that the sine rule and cosine rule should not be used on right-angled triangles.
Reminders of simple geometrical facts may be helpful, e.g. angle sum of a triangle, the smallest side is opposite the smallest angle.
Pupils find the cosine rule more difficult for obtuse angles.
* For 1388 this is assessed in Stage 2.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE THREE)
MODULE 25 Proportion and algebraic graphs
TIME 4 hours
TARGET GRADE: A/A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Modules 13, 14.
 The concept of
proportion.
 Ability to plot curves.
 Pythagoras’ theorem.
CONTENT
Setting up equations
involving proportion NA5h
Graphical representations of
equations involving
proportion NA5h
Constructing the graphs of
simple loci, including the
circle x2 + y2 = r2 NA6h
MAIN OBJECTIVES

Define inverse or direct proportion in terms of a
formula, finding the constant using given
information.
Y11
175-180
DIFFERENTIATION / EXTENSION /
HOMEWORK
 Use of three variables in proportion
questions e.g. y is directly
proportional to the square of x and x
is directly proportional to the cube
of z; write a statement to show the
proportionality between y and z.
 For the most able: Investigation
based on the cylinder e.g. A closed
cylinder, half filled with water, is
placed with its curved surface in
contact with a horizontal table.
Mark on the circular end of the
cylinder the position of the water
level. Repeat the problem for when
the cylinder is a quarter full.
Generalise for any fraction.
181-185

Express a circle of radius r, and centre (0,0) in
algebraic form.

H/W SumBooks 85, 86
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE THREE)
MODULE 26 Graphical solutions of equations
TIME: 4 hours
TARGET GRADE: A/A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Modules 10, 13, 16, 18.
 The ability to solve
linear simultaneous
equations algebraically
and graphically.
 The ability to draw
straight-line graphs,
quadratics graphs and
the graphical
representation of a
circle.
 The ability to
manipulate algebraic
expressions confidently.
CONTENT
Solving by substitution a pair
of simultaneous equations
(one non-linear) NA5l
Use simultaneous equations
to calculate where a straightline graph meets a circle
NA5l
Using graphs to solve a pair
of simultaneous equations
(one non-linear) NA6e
Using graphs to show where
a straight-line graph
intersects a circle NA6h
MAIN OBJECTIVES

Solve by substitution a pair of simultaneous
equations (one non-linear).

Use simultaneous equations to calculate where
a straight-line graph meets a circle.

Use graphs to solve a pair of simultaneous
equations (one non-linear).

Use graphs to show where a straight-line graph
intersects a circle.
DIFFERENTIATION / EXTENSION /
HOMEWORK

Circles with a centre other than the
origin.

H/W SumBooks 86

Circles with a centre other than the
origin.
Intersections of two curves.

W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE THREE)
MODULE 27 Graphs of functions
TIME: 4 hours
TARGET GRADE: A/A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Knowledge of sin, cos
and tan.
 Experience of
substituting values into a
function.
CONTENT
Drawing, sketching and
describing the graphs of
trigonometric functions
SSM2g
Applying transformations to
the function y = f(x) :
y = f(x) + a
y = f(ax)
y = f(x + a) NA6g
y = af(x)
(for linear, quadratic, sine
and cosine functions)
MAIN OBJECTIVES
Y10/11

Sketch the curves y = sin x, y = cos x and y =
tan x.
40-44


Draw such graphs as y = a + b sin x.
Use graphs to aid the solution of equations such
as a + b cos x = 1, for angles between 0 and
360.
Given the graph of y = f(x), be able to sketch
the graphs of y = f(x) + a, y = f(ax), y = f(x + a),
and y = af(x) by applying transformations.
Investiga
tive task
141-4

DIFFERENTIATION / EXTENSION /
HOMEWORK






Use a graphical calculator to
investigate the effects the above
factors have on the graph of a
function.
The study of such curves as y = a +
b sin (cx + d).
Quadratic graphs and completing
the square.
Investigation of curves which are
unaffected by particular
transformations.
H/W SumBooks 48 functions
with x2 and x3
H/W SumBooks 60
NOTES
Investigation of simple relationships such as sin (180 – x) = sin x, and sin (90 – x) = cos x can help.
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE THREE)
MODULE 28 Circle Theorems
TIME: 5 hours
TARGET GRADE: B
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
 Module 15.
 Angle facts for triangles,
quadrilaterals,
interior/exterior angles
of polygons, parallel
lines, angles on a
straight line, and angles
at a point.
 Nomenclature of a
circle.
CONTENT
Prove and use circle
theorems SSM2h
The angle subtended by an
arc at the centre of a circle is
twice the angle subtended
at any point on the
circumference SSM2h
Angles in the same segment
are equal SSM2h
The angle subtended at the
circumference by a semicircle is a right angle.
SSM2h
Opposite angles of a cyclic
quadrilateral add up to 180
degrees SSM2h
Explain why the
perpendicular from the
centre of a chord bisects the
chord SSM2h
Prove and use the alternate
segment theorem SSM2h
MAIN OBJECTIVES

Y11 Int
text
DIFFERENTIATION / EXTENSION /
HOMEWORK
Theorem
1 205-6
H/W SumBooks 60
Understand and use the properties to solve
problems.
Theorem
2 205-6
Theorem
4 207
Theorem
3 207
NOTES
LOCI questions may be used to introduce circle theorems, e.g. page 137 of Edexcel GCSE Higher (old edition).
W Robertson
GCSE HIGHER SCHEME OF WORK
1387/1388 (STAGE THREE)
MODULE 29 Using a calculator
TIME: 3 hours
TARGET GRADE: A/A*
PRIOR KNOWLEDGE/
STARTER OBJECTIVES
CONTENT
Using a calculator effectively
and efficiently for complex
calculations NA3o
Using an extended range of
calculator function keys
NA3o
MAIN OBJECTIVES

DIFFERENTIATION / EXTENSION /
HOMEWORK
Understand the content of the module.
W Robertson