Download Foundation – Unit 1

AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Higher – Unit 2
OVERVIEW for Higher Tier
1 hour 15 minutes non-calculator exam
66 marks – 33.3%
20 -30% Functional Elements
25 marks Number, 41 marks Algebra
ALL FOUNDATION TOPICS ARE SUBSUMED INTO HIGHER
Topic
Y10 Spring & SUMMER TERM
7. Number skills
Teaching
hours
4
8. Factors,
multiples and
powers
9. Basic rules of
algebra
10. Fractions
4
11. Decimals
3
12. Equations and
inequalities
13. Indices and
formulae
6
14. Percentages
15. Sequences
and proof
4
6
4
6
6
AQA Modular specification reference
Working with numbers and the number system: N1.2, N1.4,
N1.4h, N1.11h, N1.12h
Working with numbers and the number system: N1.6, N1.7,
N1.8, N1.9, N1.9h, N1.10h
The Language of Algebra: N4.1
Expressions and Equations: N5.1, N5.1h
Working with numbers and the number system: N1.2, N1.3,
N1.5
Fractions, Decimals and Percentages: N2.1, N2.2, N2.7
Expressions and Equations: N5.3h
Working with numbers and the number system: N1.1, N1.2
Fractions, Decimals and Percentages: N2.3, N2.4
Expressions and Equations: N5.4, N5.4h, N5.7, N5.7h
Working with numbers and the number system: N1.9
The Language of Algebra: N4.2, N4.2h
Expressions and Equations: N5.6
Fractions, Decimals and Percentages: N2.5, N2.7, N2.7h
Expressions and Equations: N5.9, N5.9h
Sequences, Functions and Graphs: N6.1, N6.2
16. Linear graphs
7
17. Ratio and
proportion
18. Quadratic
equations
4
6
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Expressions and Equations: N5.4h, N5.7h
Sequences, Functions and Graphs: N6.3, N6.4, N6.5h, N6.6h,
N6.11, N6.12
Ratio and Proportion: N3.1, N3.2, N3.3
Expressions and Equations: N5.2h, N5.5h
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 7 Number skills
Time: 4 hours
SEE FOUNDATION SCHEME OF WORK
N1.2 Add, subtract, multiply and divide any number.
N1.4 Approximate to a given power of 10, up to three decimal places and one significant figure.
ADDITIONAL HIGHER CONTENT
N1.4h Approximate to a given power of 10, up to three decimal places and one significant figure
N1.11 h Surds and π in exact calculations
N1.12h Rules of arithmetic applied to calculations and manipulations with surds
AQA
Spec
ref
N1.4h
Learning objectives
Grade
Common mistakes and misconceptions
Approximate to specified or appropriate degrees of accuracy, including a given
number of decimal places and significant figures
Check and estimate answers to problems
Estimate answers to problems involving decimals
Make estimates and approximations of calculations
B
Finding an approximate value independent
of the context in which it is set.
Working out the actual answer instead of an
approximation.
N1.11h
Simplification of surds
Rationalise a denominator
A/A*
N1.12h
Apply the rules of arithmetic to calculations and manipulations with surds
simplify expressions using the rules of surds
expand brackets where the terms may be written in surd form
solve equations which may be written in surd form
A*
Not square rooting a number when taking it
outside of the root sign
e.g √20 = √4 x 5 = 4 √ 5 instead of 2 √ 5
Not using inverse sign to rationalise a
denominator with 2 terms
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 9.1 – 9.3
AQA Modular GCSE Mathematics Higher Tier
 Place value, reading and writing numbers, non-calculator methods for addition and subtraction P1
 Non-calculator methods for multiplication and division P2
 Order of operations in a calculation P4
 Negative numbers P5
 Approximation and rounding to the nearest 10, 100, 1000 P20
 Round in real life problems P21
 Rounding using decimal places P22
 Rounding using significant figures P23
 Choosing a suitable degree of accuracy P24
 Estimation P25
 Irrational numbers P76
 Surds; manipulating and simplifying P77
 Rationalising denominators of fractions P79
HigherPractice Book sections 10.3 -10.4, 20.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Number/Teaching Resources
Lesson plans/worksheet/homework sheet
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Surds/Teaching Resources
Lesson plans/worksheets/homework sheets/powerpoints
Functional skills activities 1.1 – 1.4, 12.1 -12.2, 12.4
Notes:
Multiplication and division of integers will be limited to 3 digit by 2 digit. Decimals will be limited to multiplying or dividing by a single digit
integer or a decimal number to 1 significant figure.
Candidates may use any algorithm for addition, subtraction, multiplication and division.
Candidates should know that some answers need to be rounded up and some need to be rounded down. Candidates should know that when
using approximations for estimating answers, numbers should be rounded to one significant figure before the estimating is done.
Closely related - N1.1 Understand integers and place value to deal with arbitrarily large positive numbers.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 8 Factors, Multiples and Powers
Time: 4 hours
SEE FOUNDATION SCHEME OF WORK
N1.6 The concepts and vocabulary of factor (divisor), multiple, common factor, highest common factor, least common multiple, prime number and prime factor
decomposition.
N1.7 The terms square, positive and negative square root, cube and cube root.
N1.8 Index notation for squares, cubes and powers of 10.
N1.9 Index laws for multiplication and division of integer powers.
ADDITIONAL HIGHER CONTENT
N1.9h Fractional and negative powers.
N1.10h Interpret, order and calculate numbers written in standard index form.
AQA
Mod
spec ref
N1.8,
N1.9h
N1.6
N1.9,
N1.9h,
N1.10h
Learning objectives
Grade
Common mistakes and misconceptions
Understand and use index notation in calculations
Understand and use negative powers and numbers to the power of 1 or 0
Understand how to manipulate fractional powers
Write a number as a product of prime factors using index notation
Use prime factors to find HCFs and LCMs
B, A
Not being able to describe numbers written with
powers.
Working out 45 as 4 × 5.
Not identifying the prime factors that appear in
the decompositions of both numbers when
finding the HCF.
Use laws of indices to multiply and divide numbers written in index notation
Interpret, order and carry out calculations with numbers given in standard form
write an ordinary number in standard form
write a number written in standard form as an ordinary number
order numbers that may be written in standard form
simplify expressions written in standard form
solve simple equations where the numbers may be written in standard form
C, B
C, B
Not converting the answers to calculations back
into standard form
(e.g. 32 × 10–4  3.2 × 10–3).
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 10.1 – 10.6
AQA Modular GCSE Mathematics Higher Tier
 Multiples and factors, prime numbers, prime factors, products of prime factors and index notation P49
 Square numbers and cube numbers P51
 Multiplying and dividing numbers with powers, rules of indices P53
 Negative powers and reciprocals P54
 Powers and roots, harder fractional powers P58
 Very large numbers P60
 Very small numbers and Standard Form P62
 Standard Form calculations without a calculator P66
Higher Practice Book 10.1 -10.2, 15.1 – 15.3, 17.1 -17.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/HigherTier/Unit 2/Number /Teaching Resources
Lesson plans/worksheets/homework sheets
2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Indices & Standard Form/Teaching Resources
Lesson plans/homeworksheet/ /worksheet
Functional skills activities 12.3
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 9 Basic rules of Algebra
Time: 4 hours
SEE FOUNDATION SCHEME OF WORK
N4.1 Distinguish the different roles played by letter symbols in algebra, using the correct notation.
N5.1 Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.
.
ADDITIONAL HIGHER CONTENT
N5.1h Multiply two linear expressions.
AQA
Mod
spec ref
N5.1h
Learning objectives
Grade
Common mistakes and
misconceptions
Multiply together two algebraic linear expressions with brackets
Square a linear expression
understand that the transformation of algebraic expressions obeys and generalises
the rules of generalised arithmetic
manipulate an expression by collecting like terms
multiply a single term over a bracket
write expressions using squares and cubes
factorise algebraic expressions by taking out common factors
C, B, A
Forgetting to multiply pairs of terms
multiply two linear expressions such as
Higher tier
and
at
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 11.1 – 11.6
AQA Modular GCSE Mathematics Higher Tier
 Algebra P86
 Expressions and terms, simplifying expressions P87
 Multiplying and dividing algebraic expressions with powers P89
 Brackets P91
 Factorising P92
 Brackets, more brackets P174
Higher Practice Book 12.1 – 12.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Algebraic manipulation and formulae/Teaching Resources
lesson plans/worksheets/homework sheet
Functional skills activities AQA GCSE Maths Middle sets Book P196 eBay business
Notes:
Including (x + a)(x + b) and (cx + a)(dx + b)
Closely related – N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 10 Fractions – non-calculator methods
Time: 6 hours
SEE FOUNDATION SCHEME OF WORK
N1.2 Add, subtract, multiply and divide any number.
N1.3 Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations.
N1.5 Order rational numbers.
N2.1 Understand equivalent fractions, simplifying a fraction by cancelling all common factors.
N2.2 Add and subtract fractions.
N2.7 Calculate with fractions, decimals and percentages.
ADDITIONAL HIGHER CONTENT
N5.3h Simplify rational expressions
AQA
Mod
spec ref
N5.3h
Learning objectives
Grade
Common mistakes and
misconceptions
This objective may be better left until after the teaching on quadratics
Apply the four rules to algebraic fractions, which may include quadratics and the
difference between two squares
Simplify or cancel rational expressions by looking for common factors
A/A*
Cancelling algebraic terms before
factorising
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 12.1 – 12.7
AQA Modular GCSE Mathematics Higher Tier
 Fractions, equivalent fractions, types of fractions, finding fractions of quantities P12
 How to add and subtract fractions P13
 How to multiply fractions P14
 How to divide fractions P15
 Problems involving fractions P16
 Fractions and decimals P17
 Equations with fractions P99
 Algebraic fractions; simplifying algebraic fractions P203
 Arithmetic of algebraic fractions P204
 Solving equations involving algebraic fractions P205
Higher Practice Book 10.5, 22.1, 26.1, 40.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Algebraic Manipulation and formulae/Teaching Resources
lesson plans/worksheets/homework sheets
Functional skills activities 3.1, 3.3, 14.2, 14.4
Notes:
This is part of the core number work across all units.
Closely related N2.3 Use decimal notation and recognise that each terminating decimal is a fraction.
N2.4 Recognise that recurring decimals are exact fractions and that some exact fractions are recurring decimals.
N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.
N2.6 Interpret fractions, decimals and percentages as operators.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 11 Decimals – non-calculator methods
Time: 3 hours
SEE FOUNDATION SCHEME OF WORK
N1.1 Understand integers and place value to deal with arbitrarily large positive numbers.
N1.2 Add, subtract, multiply and divide any number.
N2.3 Use decimal notation and recognise that each terminating decimal is a fraction.
N2.4 Recognise that recurring decimals are exact fractions, and that some exact fractions are recurring decimals.
ADDITIONAL HIGHER CONTENT
None
AQA
Mod
spec ref
N2.3,
N2.4
Learning objectives
Grade
Common mistakes and
misconceptions
Convert fractions to decimals
Recognise recurring decimals
Understand how recurring decimals relate to fractions
D, C, B
1
Confusing 0.3 with 3.
Not understanding that recurring
decimals are a form of exact maths and
therefore rounding answers.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 13.1 – 13.4
AQA Modular GCSE Mathematics Higher Tier
 Decimals – addition and subtraction non-calculator methods P8
 Non-calculator methods for addition and subtraction of decimals P9
 Non-calculator methods for multiplying and dividing decimals P9
 Fractions and decimals P17
 Recurring decimals P18
 Changing recurring decimals to fractions P74
Higher Practice Book 20.1
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Decimals/Teaching Resources
lesson plans/worksheets/homework sheets/powerpoints
Functional skills activities 3.4, 14.1, 14.2
Notes: This includes questions where the answer to one calculation can be used to work out the answer to a related calculation.
Closely related
N1.4
N1.5
N2.5
N2.6
N2.7
Approximate to a given power of 10, up to three decimal places and one significant figure.
Order rational numbers
Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.
Interpret fractions, decimals and percentages as operators.
Calculate with fractions, decimals and percentages as operators.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 12 Equations and Inequalities
Time: 6 hours
SEE FOUNDATION SCHEME OF WORK
N5.4 Set up and solve simple linear equations.
N5.7 Solve linear inequalities in one variable and represent the solution set on a number line.
ADDITIONAL HIGHER CONTENT
N5.4h Including simultaneous equations in two unknowns.
N5.7h Solve linear inequalities in two variables, and represent the solution set on a suitable diagram.
AQA Mod
spec ref
N5.4
Learning objectives
Grade
Common mistakes and misconceptions
Solve equations involving fractions
C, B
Incorrectly cancelling after multiplying by
the LCM.
Solving out of order (e.g.
N5.7,
N5.7h
Represent inequalities on a number line
Write down whole-number values for unknowns in an inequality
Solve inequalities
E, D,
C, B
N5.4h
Solve a pair of simultaneous equations by elimination or substitution or any other
valid method
solve simultaneous equations when one is linear and the other quadratic, of the form
B
where a, b and c are integers
x2
 8 : trying
4
to do −2 first).
Not reversing the sign when multiplying or
dividing by a negative.
Confusing the convention of an open circle
for a strict inequality and a closed circle for
an included boundary.
Adding equations when they should be
subtracted, and vice versa.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 14.1 – 14.7
AQA Modular GCSE Mathematics Higher Tier
 Solving equations P95
 The balance method P96
 Equations with brackets P97
 Equations with letters on both sides P98
 Writing equations P101
 Inequalities; number lines P155
 Solving inequalities P156
 Multiplying or dividing an inequality by a negative number P157
 Double inequalities P158
 Inequalities involving integers P159
 The elimination method P192
 The substitution method; solving problems using simultaneous equations P195
 Simultaneous equations in which one equation is linear and one is quadratic P197
Higher Practice Book 26.1 - 26.4, 34.1 - 34.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Linear equations and simultaneous equations/Teaching Resources
lesson plans/worksheets/homework sheets/powerpoint
Functional skills activities 9.1 -9.2, 20.1 -20.3
Notes:
Questions may have solutions that are negative or involve a fraction.
Questions may be set with or without a context in Unit 2.
Linear simultaneous equations may be set with or without a context.
Solving simultaneously one linear and one quadratic equation will not be in context or graphical on Unit 2 (but will be in context or graphical or may include
geometrical problems on Unit 3).
Closely related - N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
N5.9 Use algebra to support and construct arguments.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 13 Indices and Formulae
Time: 6 hours
SEE FOUNDATION SCHEME OF WORK
N1.9 Index laws for multiplication and division of integer powers.
N4.2 Distinguish in meaning between the words ‘equation’, ‘formula’, and ‘expression’.
N5.6 Derive a formula, substitute numbers into a formula and change the subject of a formula.
ADDITIONAL HIGHER CONTENT
N4.2h Distinguish the meaning of ‘identity’
AQA Mod
spec ref
N5.6
Learning objectives
Grade
Common mistakes and misconceptions
Rearrange a formula to make a different variable the subject of the formula.
Including where the subject appears twice.
C, B
N4.2h
Understand the word identity and the identity symbol
B
Not using brackets or a clear division (e.g.
rewriting c = 2a + 5 as a = c − 5 ÷ 2).
Not using the inverse operation (e.g. x + y =
z becomes x = z + y).
Not knowing how to interpret the symbol
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 15.1 – 15.6
AQA Modular GCSE Mathematics Higher Tier
 Writing expressions and formulae P105
 Using formulae P107
 Substitution into formulae with powers and roots P109
 Rearranging formulae P110
 Solve problems by rearranging formulae P111
 Simplifying expressions, identities P201
Higher Practice Book 24.1 - 24.5, 18.1 -18.3, 22.1
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Algebraic manipulation and formulae/Teaching Resources
lesson plans/worksheets/homework sheets
Functional skills activities 9.1 -9.2, 201.-20.3
Notes: The core algebra work across all units is N4.2
Candidates should understand the words equation, formula, expression and term but their meaning will not be tested.
Questions in Unit 2 will include formulae for generating sequences; for example, write down the first three terms of a sequence where the nth term is given by
2n + 4 (see spec. reference N6.1). Questions in Unit 2 will include formulae in words using a functional context; for example, a formula for cooking a turkey.
Questions may include formulae out of context; for example, substitute positive and negative numbers into expressions such as, 3(2 – 3y), 3x2 and 2x3
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 14 Percentages – non-calculator methods
Time: 4 hours
SEE FOUNDATION SCHEME OF WORK
N2.5 Understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions.
N2.7 Calculate with fractions, decimals and percentages.
ADDITIONAL HIGHER CONTENT
N2.7h Including reverse percentage calculations.
AQA Mod
spec ref
N2.7h
Learning objectives
Grade
Common mistakes and misconceptions
Perform calculations involving finding the original quantity
calculate a percentage of a quantity
solve percentage increase and decrease problems
use, for example, 1.12 × Q to calculate a 12% increase in the value of Q and 0.88 ×
Q to calculate a 12% decrease in the value of Q
work out one quantity as a percentage of another quantity
use percentages to calculate proportions
use reverse percentages to calculate the original amount
B
Not recognising that the problem is not a
straightforward percentage
increase/decrease question.
Not using the correct multiplier.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 16.1 – 16.5
AQA Modular GCSE Mathematics Higher Tier
 Changing fractions to decimals to percentages P28
 Expressing one quantity as a percentage of another P29
 Finding a percentage of a quantity; percentage change P30
 Percentage increase and decrease P31
 Reverse percentage problems P33
 Wages, income tax, spending, best buys, household bills, VAT, savings P34 - 39
Higher Practice Book 11.1 -11.4, 19.1 -19.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Fractions, Decimals and Percentages /Teaching Resources
lesson plans/worksheets/homework sheets/powerpoint
Functional skills activities 3.2, 14.2 – 14.3
Notes:
Percentages is part of the core number work required across all units. The core number work will be assessed so that it is linked to other
specification references within this unit. Candidates will not be required to calculate repeated percentage change or compound interest in this unit. These are
assessed in Unit 1 only. Candidates should be able to interpret percentage problems using a multiplier.
In unit 2 reverse percentage problems will be restricted to using numbers consistent with non-calculator skills.
Closely related - N2.6 Interpret fractions, decimals and percentages as operators.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 15 Sequences and Proof
Time: 6 hours
SEE FOUNDATION SCHEME OF WORK
N5.9 Use algebra to support and construct arguments.
N6.1 Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence.
N6.2 Use linear expressions to describe the nth term of an arithmetic sequence.
ADDITIONAL HIGHER CONTENT
N5.9h Use algebra to construct simple proofs
AQA Mod
spec ref
N5.9h
Learning objectives
Grade
Common mistakes and misconceptions
Use algebra to construct simple proofs
use algebraic expressions to support an argument or verify a statement
construct rigorous proofs to validate a given result
A, A*
Not recognising that the proof cannot be
given with numerical examples. Failure to
relate to simple properties of numbers (eg
even (2n) odd (2n + 1)
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 17.1 – 17.8
AQA Modular GCSE Mathematics Higher Tier
 Continuing a sequence, using rules P124
 Number sequences P126
 Sequences of numbers from shape patterns P128
 Special sequences of numbers P129
 London GCSE – using and applying mathematics Chapter 11 (leads to proof)
 Pure Mathematics 1 – Proof Chapter 7 P173
Higher Practice Book 28.1 - 28.2, 22.1
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Algebraic Proof/Teaching Resources
lesson plans and starter/homework sheets/worksheets
2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Sequences/Teaching Resources
lesson plans/homework sheets/worksheets
Functional skills activities
Notes: Candidates should be able to describe how a sequence continues and will need to be familiar with the idea of a non-linear sequence, such as the
triangular numbers or a sequence where the nth term is given by n2 + 4. Candidates should know that the nth term of the square number sequence is given by
n2.
At Higher tier, candidates will be expected to use skills of expanding and factorising when constructing a proof.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 16 Linear Graphs
Time: 7 hours
SEE FOUNDATION SCHEME OF WORK
N6.3 Use the conventions for coordinates in the plane and plot points in all four quadrants, including using geometric information.
N6.4 Recognise and plot equations that correspond to straight-line graphs in the coordinate plane, including finding their gradients.
N6.11 Construct linear functions from real-life problems and plot their corresponding graphs.
N6.12 Discuss, plot and interpret graphs (which may be non-linear) modelling real situations.
ADDITIONAL HIGHER CONTENT
N5.4h Including simultaneous equations in two unknowns.
N5.7h Solve linear inequalities in two variables, and represent the solution set on a suitable diagram.
N6.5h Understand that the form y = mx + c represents a straight line and that m is the gradient of the line and c is the value of the y-intercept.
N6.6h Understand the gradients of parallel lines.
AQA Mod
spec ref
N6.5h,
N6.6h
N5.4h
N5.7h
Learning objectives
Grade
Common mistakes and misconceptions
Plot straight-line graphs
recognise that equations of the form
correspond to straight line graphs in
the coordinate plane
Find the gradient of a straight-line graph
Understand the meaning of m and c in the equation y = mx + c
Find the equation of a line
Understand the gradient of parallel lines
manipulate the equations of straight lines so that it is possible to tell whether lines
are parallel or not
plot graphs of functions in which y is given explicitly in terms of x or implicitly
complete partially completed tables of values for straight line graphs
calculate the gradient of a given straight line using the y-step method
Use a graphical method to solve simultaneous equations
D, C, B
Forgetting the negative on the gradient.
B
Solve inequalities graphically
Draw or identify regions on a coordinate grid, using the convention of a dashed line
for strict inequalities and solid line for an included inequality.
know the difference between
solve simple linear inequalities in one variable
B
Forgetting to ensure that the individual lines
are drawn accurately.
Not appreciating that the graphical solutions
to simultaneous equations are only
approximate.
Mixing up whether the lines should be
dotted or solid.
Shading the incorrect area.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 18.1 – 18.7
AQA Modular GCSE Mathematics Higher Tier
 Straight line graphs, drawing a graph from a rule P134
 Special graphs P135
 Gradient and intercept P136
 Perpendicular lines P139
 Rearranging equations P140
 Using graphs to solve simultaneous equations P189
 Simultaneous equations with no solution P191
 Graphs of inequalities P159
 Regions P160
 Inequalities involving sloping lines P161
 Real-life situations P145
 Distance-time graphs P147
 Speed-time graphs P150
Higher Practice Book 29.1, 32.1 – 32.3, 34.1
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Coordinates and graphs/Teaching Resources
lesson plans/worksheets/homework sheets/powerpoints
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Linear Equations and Simultaneous equations/Teaching Resources
lesson plans/worksheets/powerpoints
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Inequalities in 1 and 2 variables/Teaching Resources
lesson plans/worksheets/homework sheets
Functional skills activities – any real-life graphs
Notes: In unit 2 candidates will be required to identify points with given coordinates and identify coordinates of given points.
In unit 2 candidates will be expected to use graphs that model real situations where a calculator is not required.
In unit 2 candidates will not be expected to answer questions related to shapes and other geometrical applications. This will be assessed in unit 3.
Candidates should note that distance-time graphs will be assessed in Unit 2 only.
Gradients of perpendicular lines will not be assessed as a negative reciprocal but candidates should understand the meaning of perpendicular and be able to
draw a line perpendicular to another line.
Solving simultaneously one linear and one quadratic equation will not be in context or graphical on Unit 2 (but will be in context or graphical or may include
geometrical problems on Unit 3).
Candidates may be asked to represent given linear inequalities graphically or identify inequalities that satisfy a given region in the x-y plane.
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 17 Ratio and proportion – non-calculator methods
SEE FOUNDATION SCHEME OF WORK
N3.1 Use ratio notation, including reduction to its simplest form and its various links to fraction notation.
N3.2 Divide a quantity in a given ratio
N3.3 Solve problems involving ratio and proportion, including the unitary method of solution.
ADDITIONAL HIGHER CONTENT
None
Resources:
AQA GCSE Maths Middle sets Book Sections 7.1 to 7.8 (7.8 higher)
AQA Modular GCSE Mathematics Higher Tier
 Ratio P43
 Sharing in a given ratio P44
 Proportion; direct and inverse proportion P46
 Direct proportion P114
 Inverse proportion P117
Higher Practice Book 13.1 -13.2, 21.1 – 21.2
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Ratio/Teaching Resources
lesson plans & starters/sorting activity/problem sheets/homework sheets
Functional skills activities 4.1, 4.2, 15.1 – 15.3
Notes: This is part of the core number work required across all units. Division in a given ratio is only tested in Unit 2.
Candidates should be able to use informal strategies, use the unitary method of solution, multiply by a fraction or other valid method.
Time: 4 hours
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Topic 18 Quadratic equations
Time: 6 hours
N5.2h Factorise quadratic expressions, including the difference of two squares
N5.5h Solve quadratic equations.
AQA Mod
spec ref
N5.2h
Learning objectives
Grade
Common mistakes and misconceptions
Factorise a quadratic expression that is the difference of two squares
B
Incorrectly expanding brackets (e.g.
expanding (x – 3)2 as x2 – 9
N5.2h
Factorise a quadratic of the form x²+ bx + c
factorise quadratic expressions using the sum and product method or by inspection
(FOIL)
Solve quadratic equations by rearranging
Solve quadratic equations by factorising or completing the square
Equations may be derived from rational expressions
Write quadratic equations for problems and then solve them
B
Looking for numbers whose sum is c and
product b.
B
Forgetting that there are two solutions to a
quadratic equation.
B
Not identifying which is the unknown value,
or using two variables.
N5.2h,
N5.5h
N5.2h,
N5.5h
AQA Modular GCSE Two Year Scheme of Work 2010
4360 Specification
Resources:
AQA GCSE Maths Middle sets Book Sections 19.1 – 19.4
AQA Modular GCSE Mathematics Higher Tier
 Factorising; factorising quadratic expressions P175
 Further factorising P178
 Solving quadratic equations P179
 Using the quadratic formula P180
 Completing the square; rearranging quadratics P182
 Solving quadratics by completing the square P184
 Problems solved using quadratic equations P185
Higher Practice Book 40.1 - 40.3
www.aqa.org.uk/ 2010 ready/GCSE Maths/Free online resources/Higher Tier/Unit 2/Quadratic Equations/teaching Resources
lesson plans/worksheets/homework sheets
Functional skills activities
Notes: This is part of the core number work required across all units. Division in a given ratio is only tested in Unit 2.
Candidates should be able to use informal strategies, use the unitary method of solution, multiply by a fraction or other valid method.
Use of the quadratic formula will not be specifically tested on Unit 2 but candidates may use it to solve a quadratic equation, leaving the answers in surd form
where appropriate.