# Edexcel Foundation Maths Exam

Ratio 22-28%
Number 22-28%
Algebra 17-23%
Geometry
Statistics

## Number

#### Number 1

Number 1 Review Questions

You need be able to:

• Order positive numbers
• Order negative numbers
• Order decimal numbers
• Order fractions
• Use the symbols =, ≠, <, >, ≤, ≥

#### Number 2

You will need to be able to:

• Add, subtract, multiply and divide whole numbers
• Add, subtract, multiply and divide fractions (proper and improper)
• Add, subtract, multiply and divide mixed numbers
• Add, subtract, multiply and divide negative numbers
• Add, subtract, multiply and divide decimal numbers

#### Number 3

You will need to be able to:

• Use BIDMAS
• Use Inverse operations
• Understand reciprocals

#### Number 4

You will need to be able to:

• Identify and explain prime numbers
• Identify and explain factors
• Identify and explain multiples
• Identify and explain highest common factors
• Identify and explain lowest common multiple
• Identify and explain prime factors

#### Number 5

You will need to be able to:

• Systematic listings

#### Number 6

You will need to be able to:

• know square numbers
• know square roots
• know cube numbers
• recognise numbers to the power of 4 and 5

#### Number 7

You will need to be able to:

• Complete calculations with roots
• Complete calculations with indices

#### Number 8

You will need to be able to:

• Complete calculations with fractions
• Complete calculations with multiples of π

#### Number 9

You will need to be able to:

• Complete calculations including standard form

#### Number 10

You will need to be able to:

• Recognise and explain terminating and recurring decimals
• Convert terminating decimals to fractions and vice versa

#### Number 11

You will need to be able to:

• Identify and work with fractions in ratio problems

#### Number 12

You will need to be able to:

• Interpret fractions and percentages as operators

#### Number 13

You need to be able to:

• Use units of mass
• Use units of length
• Use units of time
• Use units of money

#### Number 14

You need to be able to:

• Use estimation and approximation

#### Number 15

You need to be able to:

• Round numbers and measures using decimal places
• Round numbers and measures using significant figures
• Identify error intervals due to truncation
• Identify error intervals due to rounding

#### Number 16

You need to be able to:

• Apply and interpret limits of accuracy

## Algebra

#### Algebra 1

You need be able to:

• Use and interpret algebraic manipulation

#### Algebra 2

You will need to be able to:

• Substitute numerical values into formulae and expressions

#### Algebra 3

You will need to be able to:

• Explain the term “expressions”
• Explain the term “equations”
• Explain the term “formulae”
• Explain the term “identities”
• Explain the term “factors”

#### Algebra 4

You will need to be able to:

• Simplify expressions
• Expand a single bracket
• Expand double brackets
• Factorise using difference of two squares
• Simply expressions using laws of indices

#### Algebra 5

You will need to be able to:

• Use mathematical formulae
• Rearrange formulae to change the subject

#### Algebra 6

You will need to be able to:

• Explain the difference between an equation and an identity
• Argue mathematically to show algebraic expressions are equivalent

#### Algebra 7

You will need to be able to:

• Interpret simple expressions as functions with inputs and outputs

#### Algebra 8

You will need to be able to:

• work with coordinates in all four quadrants

#### Algebra 9

You will need to be able to:

• Plot straight line graphs
• Identify parallel lines
• Find the equation of a line given one point and gradient
• Find the equation of the line through two given points

#### Algebra 10

You will need to be able to:

• Identify and interpret gradients and intercepts of linear functions graphically and algebraically.

#### Algebra 11

You will need to be able to:

• Identify and interpret roots of quadratic graphs
• Identify intercepts of quadratic graphs
• Identify turning points of quadratic graphs
• Deduce roots graphically

#### Algebra 12

You will need to be able to:

• Recognise, sketch and interpret quadratic graphs

#### Algebra 13

You need to be able to:

• Plot and interpret reciprocal graphs
• Plot and interpret real-life graphs

#### Algebra 14

You need to be able to:

• Solve linear equations with an unknown on one side
• Solve linear equations with the unknown on both sides
• Find approximate solutions using a graph

#### Algebra 15

You need to be able to:

• Solve quadratic equations using factorising
• Find approximate solutions using a graph

#### Algebra 16

You need to be able to:

• Solve two simultaneous equations
• Find approximate solutions using a graph

#### Algebra 17

You need to be able to:

• Form expressions and equations
• Derive simultaneous equations and solve.

#### Algebra 18

You need to be able to:

• Solve linear inequalities
• Represent and interpret inequalities on a number line

#### Algebra 19

You need to be able to:

• generate a term to term rule from a given sequence
• generate a position to term rule from a given sequence

#### Algebra 20

You need to be able to:

• Recognise and use sequences of triangular numbers
• Recognise and use sequences of square numbers
• Recognise and use sequences of cube numbers
• Recognise and use Fibonacci sequences
• Recognise and use simple geometric progressions

#### Algebra 21

You need to be able to:

• Find expressions to calculate the nth term of linear sequences

## Geometry

#### Geometry 1

You need be able to:

• Understand these terms: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons
• Label sides and angles of a triangle
• Draw diagrams from written descriptions

#### Geometry 2

You will need to be able to:

• Construct a perpendicular bisector of a line
• Construct a perpendicular bisector to a given line from a given point
• Bisect a given angle
• Solve loci problems
• Know that the perpendicular distance from a point to a line is the shortest distance to the line.

#### Geometry 3

You will need to be able to:

• Apply the properties of angles at a point
• Apply the properties of angles on a straight line
• Apply the properties of vertically opposite angles
• Understand and use corresponding angles
• Understand and use alternate angles
• Derive and use the sum of angles in a triangle
• Find the sum of angles in any polygon

#### Geometry 4

You will need to be able to:

• Derive and apply the properties and definitions of special types of quadrilaterals; including square, rectangle, parallelogram, trapezium, kite, and rhombus.
• Derive and apply the properties of all types of triangles

#### Geometry 5

You will need to be able to:

• Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)

#### Geometry 6

You will need to be able to:

• Apply angle facts
• Apply triangle congruence
• Apply similarity and properties of quadrilaterals
• Apply Pythaoras’ theorem
• Know the base angles of an isosceles triangle are equal
• Show simple proofs

#### Geometry 7

You will need to be able to:

• Identify, describe and construct congruent and similar shapes
• Identify congruent and similar shapes by considering rotation, reflection, translation, and enlargement (including fractional scale factors)

#### Geometry 8/9

You will need to be able to:

• Identify and apply circle definitions and properties; centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

#### Geometry 10/11

You will need to be able to:

• Solve geometrical problems on coordinate axes

#### Geometry 12

You will need to be able to:

• Identify properties of the faces, surfaces, edges and vertices of: cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.

#### Geometry 13

You need to be able to:

• Construct and interpret plans and elevations of 3D shapes

#### Geometry 14

You need to be able to:

• Use standard units of measures

#### Geometry 15

You need to be able to:

• Measure line segments and angles in geometric figures
• Interpret maps
• Interpret scale drawings
• Interpret use of bearings

#### Geometry 16

You need to be able to:

• Know and apply formulae to calculate areas of triangles
• Know and apply formulae to calculate areas of parallelograms
• Know and apply formulae to calculate areas of trapezium
• Know and apply formulae to calculate volume of cuboids
• Know and apply formulae to calculate volume of prisms
• Know and apply formulae to calculate volume of cylinders

#### Geometry 17

You need to be able to:

• Calculate circumference
• Calculate area of a circle
• Calculate perimeters of 2d shapes
• Calculate perimeter of composite shapes
• Calculate surface area and volume of spheres
• Calculate surface area and volume of pyramids
• Calculate surface area and volume of cones
• Calculate surface area and volume of composite solids

#### Geometry 18

You need to be able to:

• Calculate arc lengths of circles
• Calculate angles of sectors
• Calculate areas of sectors

#### Geometry 19

You need to be able to:

• Apply the concept of congruence and similarity

#### Geometry 20

You need to be able to:

• Know the Pythagoras’ theorem
• Know the trigonometric ratios
• Use trigonometry to find angles and lengths in right angled triangles

#### Geometry 21

You need to be able to:

• Know the exact values of Sin 0, 30, 45, 60 and 90 degrees
• Know the exact values of Cos 0, 30, 45, 60 and 90 degrees
• Know the exact values of Tan 0, 30, 45, and 60 degrees

#### Geometry 22

You need to be able to:

• Describe translations as 2D vectors

#### Geometry 23

You need to be able to:

• Apply addition and subtraction of vectors
• Calculate multiplication of vectors by a scalar
• Apply column representations of vectors

## Ratio

#### Ratio 1

You need be able to:

• Change between units (time, length, area, volume, mass).
• Change between compound units (speed, rates of pay, prices, density, pressure).

#### Ratio 2

You will need to be able to:

• Use scale factors, scale diagrams and maps

#### Ratio 3

You will need to be able to:

• Express one quantity as a fraction of another (fraction is less than one)
• Express one quantity as a fraction of another (fraction is greater than one)

#### Ratio 4

You will need to be able to:

• Simplify ratios

#### Ratio 5

You will need to be able to:

• Divide a given quantity by a ratio

#### Ratio 6

You will need to be able to:

• Express a multiplicative relationship between two quantities as a ratio or a fraction

#### Ratio 7

You will need to be able to:

• Understand and use proportion as equality of ratios

#### Ratio 8

You will need to be able to:

• Relate ratios to fractions and to linear functions

#### Ratio 9

You will need to be able to:

• Interpret percentages and percentage changes as a fraction or a decimal
• Express one quantity as a percentage of another
• Compare two quantities using percentages
• Work with percentages greater than 100%
• Solve problems involving percentage change
• Solve problems involving percentage increase/ decrease
• Calculate simple interest

#### Ratio 10

You will need to be able to:

• Solve problems involving direct proportion
• Solve problems involving indirect proportion

#### Ratio 11

You will need to be able to:

• Calculate speed, rates of pay, unit pricing, density and pressure

#### Ratio 12

You will need to be able to:

• Compare lengths
• Compare areas and volumes using ratio notation
• Recognise and identity similarity including trigonometry ratios
• Use scale factors

#### Ratio 13

You need to be able to:

• Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y
• Interpret equations that describe direct and inverse proportion

#### Ratio 14

You need to be able to:

• Interpret the gradient of a straight line graph as a rate of change
• Recognise and interpret graphs that illustrate direct and inverse proportion

#### Ratio 15

You need to be able to:

• Solve problems involving compound interest
• Solve problems including growth and decay

## Probability

#### Probability 1

You need be able to:

• Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees

#### Probability 2

You will need to be able to:

• Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future events.

#### Probability 3

You will need to be able to:

• Express one quantity as a fraction of another (fraction is less than one)
• Express one quantity as a fraction of another (fraction is greater than one)

#### Probability 4

You will need to be able to:

#### Probability 5

You will need to be able to:

• Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size.

#### Probability 6

You will need to be able to:

• Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams.

#### Probability 7

You will need to be able to:

• Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities.

#### Probability 8

You will need to be able to:

• Calculate the probability of independent and dependent combined events
• Interpret and use tree diagrams

## Statistics

#### Statistics 1

You need be able to:

• Infer properties of populations or distributions from a sample, while knowing the limitations of sampling.

#### Statistics 2

You will need to be able to:

• Interpret and construct tables, charts and diagrams including frequency tables, bar charts, pie charts, and pictograms.
• Interpret and construct vertical line charts for ungrouped discrete numerical data.
• Interpret and construct tables and line graphs for time series data

#### Statistics 3

You will need to be able to:

• Interpret, analyse and compare the distributions of data sets involving discrete, continuous or grouped data.
• Interpret, analyse and compare median, mean, mode and modal class
• Interpret, analyse and compare range (including consideration of outliers)

#### Statistics 4

You will need to be able to:

• Apply statistics to describe a population

#### Statistics 5

You will need to be able to:

• Use and interpret scatter graphs
• Recognise correlation and know that it does not indicate causation
• Draw estimated lines of best fit
• Make predications, interpolate and extrapolate apparent trends while knowing the dangers of so doing.