1 aqa GCSE MATHS EXAMINATIoN BoARd CoVERAGE TIER ToPIC HEAdING SuB HEAdING Number Integers Ordering numbers y Number Integers Rounding numbers y Numbe...

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Randolf Alban McCormick

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Number

Integers

Ordering numbers

Both

Number

Integers

Rounding numbers

y

Both

Number

Integers

Adding and subtracting whole numbers

y

y

Both

Number

Integers

Dividing whole numbers

y

y

Both

Number

Integers

BIDMAS

y

y

Both

Number

Integers

Inverse operations

y

y

Both

Number

Negative numbers

Understanding negative numbers

y

Both

Number

Decimals

integers and decimals : the four basic operations

y

Both

Number

Decimals

Ordering decimals

Both

Number

Decimals

Using place value in calculating with decimals

Both

Number

Decimals

Order of operation : BIDMAS

Both

Number

Decimals

Rounding decimals

y

Both

Number

Decimals

Estimating decimals

y

Both

Number

Decimals

Recognising their corresponding fractions

y

Both

Number

Factors, primes and powers

Multiples, factors and prime numbers

y

Both

Number

Factors, primes and powers

Highest common factor (hcf) and lowest common multiple (lcm)

y

Both

Number

Factors, primes and powers

Squares, cubes and roots

y

Both

Number

Factors, primes and powers

Index form

y

Both

Number

Factors, primes and powers

Reciprocals

Both

Number

Fractions

Equivalent fractions

y

Both

Number

Fractions

Adding and subtracting fractions

y

y

Both

Number

Fractions

Multiplying and dividing fractions

y

y

Both

Number

Fractions

Comparing fractions

y

Both

Number

Fractions

Improper fractions and mixed numbers

y

Both

Number

Fractions

Performing calculations with mixed numbers

y

Both

Number

Fractions

Solving problems involving fractions

y

Both

Number

Fractions, decimals and percentages

Converting fractions

y

Both

Number

Fractions, decimals and percentages

Converting decimals

y

Both

Number

Fractions, decimals and percentages

Converting percentages

y

Both

Number

Fractions, decimals and percentages

Ordering decimals, fractions and percentages

y

Higher

Number

Fractions, decimals and percentages

Recurring decimals

y

Both

Number

Index notation and surds

Index form and the law of indices

y

Higher

Number

Index notation and surds

Fractional indices

Both

Number

Index notation and surds

Standard form

Higher

Number

Index notation and surds

Surds

Both

Number

Percentages

Writing one quantity as a percentage of another

y

y

y

Both

Number

Percentages

Calculating the percentage of an amount

y

y

y

Both

Number

Percentages

Increasing or decreasing an amount by a percentage

y

y

y

Both

Number

Percentages

Real-life percentage problems

y

y

Both

Number

Percentages

Percentage of a quantity

y

y

y

Both

Number

Percentages

Multiplier use in calculations

y

y

y

Both

Number

Percentages

Profit and loss

y

y

y

Both

Number

Percentages

Compound and simple interest

y

y

y

Both

Number

Percentages

Depreciation

y

y

Both

Number Ratio, proportion and rates of change Ratio, proportion and rates of change Ratio, proportion and rates of change Ratio, proportion and rates of change Ratio, proportion and rates of change Ratio, proportion and rates of change Ratio, proportion and rates of change

Percentages

Reverse percentages

y

y

y

Ratio and proportion

Simplifying a ratio

y

y

y

Ratio and proportion

Unitary form

y

y

y

Ratio and proportion

Solving ratio problems

y

y

y

Ratio and proportion

Direct and inverse proportion

y

Ratio and proportion

More complex direct and inverse proportion problems

y

Ratio and proportion

Simplifying a ratio

y

y

y

Ratio and proportion

Unitary form (1 : n)

y

y

y

Higher Higher Higher Both Higher Both Both

y

y y y

y

y y

y y

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Ratio problems

y

y

y

Dividing a quantity in a given ratio

y

y

y

HEAdING

SuB HEAdING

Ratio and proportion Ratio and proportion Ratio and proportion

Direct proportion

Algebraic expressions

Evaluating expressions

y

y

Higher

Ratio, proportion and rates of change Ratio, proportion and rates of change Ratio, proportion and rates of change Algebra

Higher

Algebra

Algebraic expressions

Simplifying expressions

y

y

Both

Algebra

Algebraic expressions

Multiplying out a pair of brackets

y

y

Higher

Algebra

Algebraic expressions

Introduction to factorising

y

y

Both

Algebra

Algebraic expressions

Factorising a quadratic

y

y

Higher

Algebra

Algebraic expressions

Factorising a more complex quadratic

y

y

Higher

Algebra

Algebraic expressions

Simplifying algebraic fractions

y

y

Both

Algebra

Algebraic expressions

Writing an expression

y

y

Both

Algebra

Algebraic expressions

Evaluating and simplifying an expression

y

y

Both

Algebra

Algebraic expressions

Multiplying in algebra

y

y

Both

Algebra

Algebraic expressions

Factorising

y

y

Both

Algebra

Algebraic statements

Equation, expression or formula?

y

y

Both

Algebra

Linear equations

Methods for solving equations

y

y

Both

Algebra

Linear equations

Setting up and solving equations

y

y

Both

Algebra

Linear equations

Solving equations with an unknown on both sides

y

y

Both

Algebra

Linear equations

Solving equations which contain brackets

y

y

Both

Algebra

Linear equations

Solving equations with brackets and negative numbers

y

y

Higher

Algebra

Linear equations

Solving equations

y

y

Higher

Algebra

Linear equations

Setting up equations

y

y

Higher

Algebra

Linear equations

Solving equations with an unknown on both sides

y

y

Higher

Algebra

Linear equations

Solving equations containing brackets or fractions

y

y

Higher

Algebra

Formulae

Using formulae

y

y

Higher

Algebra

Formulae

Changing the subject of a formula

y

Both

Algebra

Formulae

Formulae

y

y

Both

Algebra

Formulae

Writing an algebraic formula

y

y

Both

Algebra

Formulae

Changing the subject of a formula

y

Both

Algebra

Further graphs

Cubic functions

y

Both

Algebra

Further graphs

Reciprocal functions

y

Higher

Algebra

Further graphs

Exponential functions

y

Higher

Algebra

Further graphs

Equations and their graphs

y

Higher

Algebra

Further graphs

Trigonometric functions

y

Higher

Algebra

Further graphs

Graph of the circle

y

Higher

Algebra

Further graphs

Using graphs to solve a pair of equations

Both

Algebra

Index notation

Using index notation

y

Both

Algebra

Inequalities

Solving inequalities and showing inequalities on a number line

y

Both

Algebra

Inequalities

Finding integer solutions to an inequality

y

Both

Algebra

Inequalities

Solving linear inequalities

y

Both

Algebra

Inequalities

Inequalities with integer solutions

y

Higher

Algebra

Inequalities

Solving inequalities with two variables graphically

y

Both

Algebra

Linear graphs

Simple linear graphs

y

y

Both

Algebra

Linear graphs

Using y = mx + c

y

y

Higher

Algebra

Linear graphs

Parallel and perpendicular lines

y

Both

Algebra

Number patterns and sequences

Introduction to number sequences

y

Both

Algebra

Number patterns and sequences

The nth term

y

Both

Algebra

Quadratic equations

Factorising quadratic equations : example

y

Higher

Algebra

Quadratic equations

Solving quadratic equations by completing the square

y

Higher

Algebra

Quadratic equations

The quadratic formula

y

y

Higher

Algebra

Quadratic equations

Equations with algebraic fractions

y

y

Higher

Algebra

Quadratic equations

Problems involving quadratic equations

y

y

Both

Algebra

Quadratic graphs

Plotting quadratic graphs

y

Higher

Algebra

Quadratic graphs

Solving quadratic equations : example

y

Both

Algebra

Real-life graphs

Real-life plots and graphs

y

y

Both

Algebra

Simultaneous equations

Solving simultaneous equations using elimination

y

y

Both

Algebra

Simultaneous equations

Solving simultaneous equations using substitution

y

y

Both

Algebra

Simultaneous equations

Solving simultaneous equations graphically

Both Both Both

y

y

y y

y

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y

y

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Algebra

Simultaneous equations

Setting up and solving simultaneous equations

Higher

Algebra

Simultaneous equations

Solving a linear and quadratic equation simultaneously

Both

Algebra

Substitution

Substitution in an expression

Higher

Algebra

Transformation of functions

Types of transformations

y

Higher

Algebra

Transformation of functions

Translation

y

Both

Algebra

Trial and improvement

Trial and improvement

y

Higher

Algebra

Trial and improvement

Finding an approximate solution using trial and improvement

y

Both

Geometry and Measures

Angles and lines

Types of angles

y

Both

Geometry and Measures

Angles and lines

Estimating the size of angles

y

Both

Geometry and Measures

Angles and lines

Measuring angles and lengths

y

Both

Geometry and Measures

Angles and lines

Parallel and perpendicular lines

y

Both

Geometry and Measures

Angles and lines

Constructing an angle

y

Both

Geometry and Measures

Angles and lines

Constructing a triangle

y

Both

Geometry and Measures

Angles and lines

Angles on a straight line and angles around a point

y

Higher

Geometry and Measures

Angles and polygons

Triangles and quadrilaterals

y

Higher

Geometry and Measures

Angles and polygons

Interior and exterior angles in a polygon

y

Higher

Geometry and Measures

Angles and polygons

Corresponding and alternate angles

y

Higher

Geometry and Measures

Angles and polygons

Proving angle facts

y

Higher

Geometry and Measures

Angles and polygons

Bearings

y

Both

Geometry and Measures

Shapes and angles

Angle facts: triangles

y

Both

Geometry and Measures

Shapes and angles

Angle facts: quadrilaterals

y

Both

Geometry and Measures

Shapes and angles

Interior and exterior angles

y

Both

Geometry and Measures

Shapes and angles

Parallel lines

y

Both

Geometry and Measures

Shapes and angles

Bearings

y

Both

Geometry and Measures

Circles

The circle

y

Both

Geometry and Measures

Circles

Circumference and area

y

Both

Geometry and Measures

Circles

Circles and arcs

y

Both

Geometry and Measures

Circles

Sectors and segments

y

Higher

Geometry and Measures

Circles

Circle theorems

y

Higher

Geometry and Measures

Circles

Circle theorem: examples

y

Both

Geometry and Measures

Construction and loci

Constructing a triangle

y

Both

Geometry and Measures

Construction and loci

Constructing other shapes

y

Both

Geometry and Measures

Construction and loci

Constructing a perpendicular bisector of a line

y

Both

Geometry and Measures

Construction and loci

Bisecting an angle

y

Both

Geometry and Measures

Construction and loci

Constructing the perpendicular from a point to a line

y

Both

Geometry and Measures

Construction and loci

Constructing the perpendicular to a line from a point on the line

y

Both

Geometry and Measures

Construction and loci

Constructing the locus of points from a fixed point

y

Both

Geometry and Measures

Construction and loci

Constructing the locus of points from a fixed line

y

Both

Geometry and Measures

Construction and loci

Constructing a region that satisfies a given set of conditions

y

Both

Geometry and Measures

Co-ordinates

Understanding co-ordinates

y

Higher

Geometry and Measures

Co-ordinates

3-D co-ordinates

y

Both

Geometry and Measures

Measure

Imperial and metric units

y

Both

Geometry and Measures

Measure

Convert metric units

y

Both

Geometry and Measures

Measure

Speed, distance and time

y

Both

Geometry and Measures

Measure

Mass, density and volume

y

Higher

Geometry and Measures

Measure

Converting metric units

y

Higher

Geometry and Measures

Measure

Converting imperial units

y

Higher

Geometry and Measures

Measure

Speed, distance and time conversion

y

Higher

Geometry and Measures

Measure

Mass, density and volume conversion

y

Higher

Geometry and Measures

Measure

Length, area or volume expressions

y

Higher

Geometry and Measures

Measure

Upper and lower bounds

y

Both

Geometry and Measures

Measuring from scales

Measurements and scales

y

Both

Geometry and Measures

Measuring from scales

Time and units

y

Both

Geometry and Measures

Measuring from scales

Timetables

y

Both

Geometry and Measures

Perimeter and area

Calculating perimeter

y

Both

Geometry and Measures

Perimeter and area

Calculating area

y

Both

Geometry and Measures

Perimeter and area

Compound shapes

y

Both

Geometry and Measures

Perimeter and area

Converting units

y

y y

y

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Higher

Geometry and Measures

Perimeter and area

Area and perimeter of 2-d shapes

y

Higher

Geometry and Measures

Perimeter and area

Area and circumference of a circle

y

Higher

Geometry and Measures

Perimeter and area

Converting between units of measure

y

Higher

Geometry and Measures

Volume and surface area

Volume of 3-D shapes

y

Higher

Geometry and Measures

Volume and surface area

Converting units of volume

y

Higher

Geometry and Measures

Volume and surface area

Surface area of a prism and a cylinder

y

Both

Geometry and Measures

Surface area and volume

Surface area of a sphere and a cone

y

Both

Geometry and Measures

3-D shapes

Names and nets of common shapes

y

Both

Geometry and Measures

3-D shapes

Front and side elevations

y

Both

Geometry and Measures

3-D shapes

Using elevations to draw shapes

y

Both

Geometry and Measures

3-D shapes

Planes of symmetry

y

Both

Geometry and Measures

Pythagoras' theorem

Finding the hypotenuse using Pythagoras' theorem

y

Both

Geometry and Measures

Pythagoras' theorem

Finding a shorter side using Pythagoras' theorem

y

Both

Geometry and Measures

Pythagoras' theorem

Calculating the distance between two points

y

Both

Geometry and Measures

Pythagoras' theorem

Pythagoras' theorem and real-life problems

y

Higher

Geometry and Measures

Pythagoras' theorem

3-dimensional shapes

y

Both

Geometry and Measures

Similarity and congruence

Calculating sides and areas of similar shapes

y

Higher

Geometry and Measures

Similarity and congruence

Calculating volumes of similar 3-d shapes

y

Higher

Geometry and Measures

Similarity and congruence

Volume and area of similar solids: example

y

Higher

Geometry and Measures

Similarity and congruence

Congruence

y

Both

Geometry and Measures

Similarity, congruence and symmetry

Similarity and congruence

y

Both

Geometry and Measures

Similarity, congruence and symmetry

Line symmetry

y

Both

Geometry and Measures

Similarity, congruence and symmetry

Rotational symmetry

y

Both

Geometry and Measures

Similarity, congruence and symmetry

Tessellation

y

Both

Geometry and Measures

Surface area and volume

Calculating volume of 3-d shapes

y

Both

Geometry and Measures

Surface area and volume

Converting units of volume

y

Both

Geometry and Measures

Surface area and volume

Calculating the surface area of a prism

y

Higher

Geometry and Measures

Transformations

Rotation

y

Higher

Geometry and Measures

Transformations

Reflection

y

Higher

Geometry and Measures

Transformations

Translation

y

Higher

Geometry and Measures

Transformations

Enlargement

y

Higher

Geometry and Measures

Transformations

Multiple transformations and describing these as a single transformation

y

Both

Geometry and Measures

Transformations

Rotation

y

Both

Geometry and Measures

Transformations

Reflection

y

Both

Geometry and Measures

Transformations

Translation

y

Both

Geometry and Measures

Transformations

Enlargement

y

Both

Geometry and Measures

Transformations

Multiple transformations

y

Both

Geometry and Measures

Trigonometry

The three trigonometric ratios

y

Both

Geometry and Measures

Trigonometry

Using trigonometry to find a length

y

Both

Geometry and Measures

Trigonometry

Using trigonometry to find angles

y

Both

Geometry and Measures

Trigonometry

Using trigonometry to solve problems

y

Higher

Geometry and Measures

Trigonometry

Using trigonometry in 3-d shapes

y

Higher

Geometry and Measures

Trigonometry

The area of a triangle

y

Higher

Geometry and Measures

Trigonometry

The sine rule

y

Higher

Geometry and Measures

Trigonometry

The cosine rule

y

Both

Geometry and Measures

Vectors

Vector quantities

y

Both

Geometry and Measures

Vectors

The laws of vector addition

y

Both

Geometry and Measures

Vectors

Parallel vectors

y

Higher

Geometry and Measures

Vectors

Solving geometric problems involving vectors

Both

Statistics

Averages

Comparing distributions

y

Both

Statistics

Averages

Mean, median, mode and range

y

Both

Statistics

Averages

Stem and leaf diagrams

y

Both

Statistics

Averages

Ungrouped frequency tables

y

Both

Statistics

Averages

Grouped frequency tables

y

Higher

Statistics

Averages

Inter-quartile range and stem and leaf diagrams

y

Higher

Statistics

Averages

Moving averages

y

Both

Statistics

Collecting data

Collecting and recording data

y

Both

Statistics

Collecting data

Two-way tables

y

y

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Statistics

Collecting data

Questionnaires

y

Higher

Statistics

Collecting data

Sampling

y

Both

Statistics

Presenting data

Bar charts, pie charts, line graphs, frequency diagrams, histograms and frequency polygons

y

Both

Statistics

Presenting data

Pictograms

y

Higher

Statistics

Presenting data

Cumulative frequency graphs

y

Higher

Statistics

Presenting data

Box plots, data comparison and histograms with unequal widths

y

Both

Statistics

Presenting data

Scatter graphs and correlations

y

Both

Probability

Probability

The probability scale and writing probabilities

y

Both

Probability

Probability

Two-way probability tables

y

Both

Probability

Probability

Mutually exclusive events

y

Both

Probability

Probability

Relative frequency

y

Both

Probability

Probability

Probability and sample spaces

y

Higher

Probability

Probability

Mutually exclusive events

y

Both

Probability

Probability

Independent events

y

Both

Probability

Probability

Probability trees

y

Higher

Probability

Probability

Relative frequency

y

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