Edexcel Maths Linear Topic list FOUNDATION

Edexcel GCSE Maths Linear Exam Topic List - FOUNDATION

NUMBER
Add, subtract, multiply,  Write numbers in words
divide  Write numbers from words
 Add, subtract, multiply, divide whole numbers, integers,
negatives, fractions, and decimals and numbers in index
form
 Multiply and divide any number between 0 and 1.
 Divide decimals up to 2 decimal places
 Solve a problem involving division by a decimal (up to two
decimal places)
 Know the fraction-to-decimal conversion of familiar
fractions

Order numbers  Put in order of size, integers, decimals and fractions

 Understand and use positive and negative numbers on a
number line

Factors, multiples and Understand the terms;

primes  Odd and even
 Factor
 Multiple
 Common factor
 Highest common factor
 Lowest (least) common multiple
 Prime number
 Be able to identify factors, multiples and primes from a list
of numbers
 Express a number as a product of prime factors (factor
tree)
 Find common multiples or common factors of two numbers
 Find the highest common factor (HCF) or the lowest
common multiple (LCM) of two numbers.
Edexcel Maths Linear Topic list FOUNDATION

Squares, square roots,  Know all the square numbers from 2² = 4 up to 15² = 225
cubes and cube roots  Know all the cube numbers from 2³ = 8 up to 5³ = 125
and also 10³ = 1000
 Find squares and cubes
 Find square roots and cube roots

Index notation  Use index notation for squares and cubes, eg. 5³
 Use index notation for powers of 10, eg. 106
 Understand indices in calculations

Index laws  Multiply and divide by adding or subtracting indices

 Calculate using index laws when indices are fractions or
negative

Equivalent fractions and  Find equivalent fractions

adding and subtracting  Simplify a fraction to its simplest form
fractions
 Convert between improper fractions and mixed numbers
 Add and subtract fractions

Decimals, including  Know fraction to decimal conversions for simple fractions

recurring decimals  Convert between fractions and decimals
 Understand that all recurring decimals are exact fractions,
and that some exact fractions are recurring decimals
 Convert between recurring decimals and fractions

Percentages  Understand percentages

 Convert between fractions, decimals and percentages

Using fractions, decimals  Find a fraction of a quantity

and percentages  Find a percentage of a quantity
 Use decimals to find quantities
 Use a multiplier to increase of decrease a quantity (eg. use
x 1.05 to increase by 5%, or 0.88 to decrease by 12%))
Edexcel Maths Linear Topic list FOUNDATION

Percentages  Use percentages to calculate and use

o VAT
o Simple interest
o Income tax
o Prices after an increase or decrease
o Percentage profit and loss
o Reverse percentages
o Compound interest

Fractions, decimals and  Find one number as a fraction of another number

percentages  Find one number as a percentage of another number
 Multiply using percentages or decimals as operators

Ratio  Write a ratio in its simplest form

 Divide a quantity in a given ratio
 Solve problems using ratios
 Relate ratio to linear functions

Proportion  Use direct and inverse proportion

Number operations and the  Understand multiplying and dividing, and that one is the
relationships between inverse of the other
them, including order of  Use inverse operations
operations and inverse
operations  Understand the use of brackets in calculations
 Understand the hierarchy of operations (BIDMAS)
 Solve word problems
 Understand and find reciprocals
 Understand and use 1 over a number is the inverse of
multiplying by that number

Rounding and  Round to the nearest integer (whole number)

approximation  Round numbers to any given power of 10
 Round to a number of decimal places
 Round to a number of significant figures
 Estimate the answer to a calculation by using rounding
Edexcel Maths Linear Topic list FOUNDATION

Use a calculator effectively  Simple and complex calculations, including involving time or
money
 Use the following functions
 +, -, x, ÷
 x² and √x
 x³ and ³√x
 memory functions
 brackets
 Understand that rounding too early can causes inaccuracy

Standard form  Convert numbers to and from standard form

Edexcel Maths Linear Topic list FOUNDATION

ALGEBRA
Algebraic notation  Understand notation and symbols used in algebra
 Understand the difference between “expression”, “formula”
and “equation”
 Be able to select an expression, formula or equation from a
list
 Be able to write an expression to solve a problem

Manipulate algebraic  Simplify by collecting like terms

expressions  Multiply out a single bracket
 Multiply out double brackets
 Factorise a single bracket by taking out a common factor
 Factorise a quadratic expression into double brackets
 Write expressions involving squares or cubes
 Use algebraic expressions to solve problems
 Use index laws to simplify algebraic expressions including
negative powers

Solve linear equations  Set up simple equations for a problem

 Rearrange simple equations
 Solve simple equations
 Solve equations with the unknown on either side
 Solve equations with the unknown on both sides
 Solve equations that include brackets
 Solve equations with negatives, including negative answers
 Solve equations involving fractions

Solving equations  Solve quadratic equations by factorising

Simultaneous equations  Solve linear simultaneous equations

Using formulae  Derive formulae

 Substitute numbers (positive or negative) into a formula,
including formulae with x² or x³ terms
 Change the subject of a simple formula
Edexcel Maths Linear Topic list FOUNDATION

Solve linear inequalities  Use inequality signs correctly (<,>,≤,≥)

 Solve a simple linear inequality with one variable
 Show the solution to a linear inequality on a number line

Error intervals  Use inequality notation to identify error intervals

Sequences  Understand odd and even numbers

 Generate number sequences from diagrams
 Describe the rule for a number sequence (eg. subtract 3)
 Find a particular term in a sequence, or explain why a
particular number is not in a sequence
 Recognise Fibonacci, geometric and quadratic sequences
and be able to continue them

Nth term of a sequence  Find the nth term expression for a sequence
 Use the nth term expression to find a particular number in
the sequence (eg. the 20th term)

Coordinates  Use axes and coordinates, both positive and negative

 Understand and plot points in four quadrants
 Find the coordinates of a point
 Plot a point given the coordinates
 Find the coordinates of the mid-point of a line
 Calculate the length of a line using coordinates

Graphs  Draw, label and add a scale to axes

 Understand that an equation of the form y = mx + c
corresponds to a straight line graph
 Plot straight line graphs from their equations
 Plot and draw a graph of an equation in the form
y = mx + c
 Find the gradient of a straight line graph

Graphs from quadratic and  Generate points for quadratic functions

other functions
 Plot graphs of quadratic functions
 Generate points for cubic and reciprocal functions
 Plot graphs of cubic and reciprocal functions
 Identify roots, turning points and lines of symmetry of
quadratic graphs
Edexcel Maths Linear Topic list FOUNDATION

Real life graphs  Plot a linear graph

 Use real life graphs, for example, for fuel bills, telephone
tariffs, currency conversion
 Use distance-time graphs
 Interpret information on linear (straight line) and non-linear
(curved) graphs
 Identify the gradient of a linear graph and interpret it in
terms of rate of change
Edexcel Maths Linear Topic list FOUNDATION

GEOMETRY
Angles on intersecting  Understand acute, obtuse, reflex and right angles
lines, in triangles and  Angles round a point add up to 360°
quadrilaterals, and on
parallel lines  Angles on a straight line add up to 180°
 Know the properties of scalene, isosceles, equilateral and
right-angled triangles
 Angles in a triangle add up to 180°
 Vertically opposite angles are equal
 Be able to mark parallel lines on a diagram
 Be able to identify perpendicular lines on a diagram
 Be able to use letters to name lines, eg. XY or AB
 Be able to use letters to name angles, eg. angle ACD
 Corresponding angles (in parallel lines)
 Alternate angles (in parallel lines)
 Calculate angles and give reasons
 Use the angles a quadrilateral add up to 360° to find
missing angles
 Use the angles in a triangle add up to 180° to find missing
angles
 Understand that the exterior angle of a triangle of a triangle
is equal to the sum of the interior angles at the other two
vertices
Edexcel Maths Linear Topic list FOUNDATION

Interior and exterior angles  Calculate the sum of interior angles in a polygon
of polygons  Understand the polygon names; pentagon, hexagon,
heptagon, octagon and decagon
 Use the angle sum of an irregular polygon in a problem
 Calculate and use the sum of the interior angles of a
regular polygon
 Understand and use fact that the exterior angles of a
polygon add up to 360°
 Understand and use the fact that an interior and exterior
angle at one vertex of a polygon add up to 180°
 Be able to calculate the exterior angle of a regular polygon
 Be able to calculate the interior angle of a regular polygon
 Be able to deduce the number of sides of a regular
polygon, given one of its angles
 Understand tessellations of regular and irregular polygons

Properties of quadrilaterals Remember the definitions and properties (including equal

sides, equal angles, parallel sides, lines of symmetry, etc.) of
special quadrilaterals, ie.
 Square
 Rectangle
 Parallelogram
 Trapezium
 Rhombus
 Kite
 Be able to sketch each type of quadrilateral
 List or classify quadrilaterals by their properties

Reflection and rotation  Recognise reflection symmetry and be able to draw lines of
symmetry in 2D shapes symmetry on a shape
 Recognise rotation symmetry of 2D shapes
 Find the order of rotational symmetry of a shape
 Complete a diagram given the line or lines of symmetry
 State a line of symmetry on a grid as a simple algebraic
equation, eg. x = 2 or y = x
 Complete diagrams with a given order of rotational
symmetry
Edexcel Maths Linear Topic list FOUNDATION

Congruence and similarity  Understand what congruent means

 Identify shapes that are congruent
 Understand what similar means
 Understand that two shapes that are similar have the same
angles

Pythagoras’ theorem  Understand and use Pythagoras’ theorem in triangles

Trigonometry  Use the trigonometric ratios to find missing sides and

angles in right angled triangles
 Know the exact values or Sin and Cos 30, 45, 60 and 90
and Tan 30, 45, 60

Parts of a circle  Draw a circle with compasses, given either the diameter or
radius
Understand and remember parts of a circle:
 Centre
 Radius
 Diameter
 Chord
 Circumference
 Tangent
 Arc
 Sector
 Segment
Edexcel Maths Linear Topic list FOUNDATION

Using 2D diagrams to  Understand the words face, edge and vertex

represent 3D shapes
Identify or name these solid shapes:
 Cube
 Cuboid
 Cylinder
 Prism
 Pyramid
 Sphere
 Cone
 Draw nets and show how they fold to make a 3D solid
shape
 Understand and draw front and side elevations and plans of
simple solids
 Draw a sketch of a 3D solid shape given the front and side
elevations and plan of the solid
Edexcel Maths Linear Topic list FOUNDATION

Transformations Rotations
 Rotate a 2D shape around the origin or other point
 Understand that a rotation is defined by an angle, direction
and a centre of rotation
 Find the centre of rotation
 Understand that a rotation produces a shape congruent to
the original
Reflections
 Understand and describe reflections
 Identify the mirror line for a reflection, and find its equation
 Understand that a reflection produces a shape congruent to
the original
Translations
 Understand and use translations
 Understand that translations are defined by a distance and
a direction using a vector
 Translate a shape by a given vector
 Understand that a translation produces a shape congruent
to the original
Enlargements
 Understand that an enlargement is defined by a centre of
enlargement and a scale factor
 Understand that angles remain the same in an enlargement
 Enlarge a shape by a scale factor, using (0, 0) or any other
point as the centre
 Enlarge a shape by a fractional scale factor given a centre
 Find the centre of a given enlargement
 Identify the scale factor of a given enlargement
General transformations
 Describe a transformation
Edexcel Maths Linear Topic list FOUNDATION

Straight edge and compass  Construct a given triangle

constructions
 Construct an equilateral triangle
 Understand that SSS, SAS, ASA and RHS triangles are
unique but ASS ones are not
 Construct a perpendicular bisector of a line
 Construct a perpendicular from a point to a line
 Construct a perpendicular from a point on a line
 Bisect an angle
 Construct angles of 60°, 90°, 30° and 45°
 Construct parallel lines
 Draw circles and arcs of a given radius
 Construct a regular hexagon inside a circle
 Construct diagrams involving any of the above
 Construct diagrams from given information

Loci  Construct a region bounded by a circle and an intersecting

line
 Construct a loci of a given distance from a point and a
given distance from a line
 Construct a loci of equal distances from two points
 Construct a loci of equal distances from two lines
 Identify regions defined by “nearer to” or “greater than”
 Find or describe regions satisfying a combination of loci

Perimeter and area  Measure shapes to find perimeter or area

 Find the perimeter of a rectangle or triangle
 Use a formula to find the area of a rectangle
 Use a formula to find the area of a triangle
 Use a formula to find the area of a parallelogram
 Use a formula to find the area of a trapezium
 Calculate the perimeter and area of compound shapes
made from triangles, rectangles and other shapes
 Find the surface area of shapes such as prisms or pyramids
by using the formulae for triangles, rectangles and other
shapes
Edexcel Maths Linear Topic list FOUNDATION

Circumference and area of  Find circumference of a circle using C = πd or C = 2πr

a circle
 Find the area of a circle using A = πr²
 Use π = 3.142 or the π button on a calculator
 Find the perimeter and area of semcircles and quarter
circles
 Find the surface area of a cylinder
 Find the length of an arc
 Find the area and perimeter of a sector

Volumes of prisms  Use the formula to calculate the volume of a cuboid

 Calculate the volume of a shape made from cuboids
 Calculate volume of a prism, such as a triangular prism
 Find the volume of a cylinder

Vectors  Add, subtract, multiply and divide vectors

 Find the resultant of a vector
Edexcel Maths Linear Topic list FOUNDATION

MEASURES
Maps and scale drawings  Use, interpret and construct maps and scale drawings
 Draw lines and shapes to scale
 Estimate lengths using a scale diagram

Enlargement of shapes,  Understand the effect of enlargement on perimeter, area

including solids and volume
 Understand and use the fact that area and volume are
affected differently by an enlargement
 Understand simple enlargements when a 2D or solid shape
is an enlargement of another 2D or solid shape

Interpretation and accuracy  Read and interpret scales on measuring equipment

 Know the relationships between seconds, minutes, hours,
days, weeks, months and years
 Use 12 and 24 hour clock times correctly
 Work out the difference between two times
 Understand that choice of unit affects accuracy
 Understand that measurements given to a whole unit may
be up to half a unit inaccurate in either direction

Converting measurements  Know conversion factors between different metric units

 Convert between metric units
 Convert between metric measurements of area
 Convert between metric measurements of volume
 Convert between different metric units of speed, eg. metres
per second and km per hour
 Convert between metric units of volume and metric units of
capacity, eg. 1 cm³ = 1 ml

Estimation of measures  Make estimates of measurements

 Choose appropriate units for estimates of measurements

Bearings  Use 3 figure bearings to describe a direction

 Mark a point on a diagram, given a bearing and distance
from another point
 Measure a bearing on a map or scale plan
 Given a bearing of one point from another, find the bearing
of the first point from the second
Edexcel Maths Linear Topic list FOUNDATION

Compound measures  Understand and use compound measures, including speed

and density

Measure and draw lines  Measure and draw straight lines to the nearest mm
and angles  Measure and draw angles to the nearest degree

Drawing using a ruler and  Make accurate drawings of triangles and other 2D shapes
protractor using ruler and protractor
 Make an accurate scale drawing from a diagram
 Use accurate drawing to solve bearings problems
Edexcel Maths Linear Topic list FOUNDATION

STATISTICS
Data handling  Decide on what data and analysis may be required for a
problem
 Data collection
 Presenting data
 Discuss data

Bias  Understand how sources of data might be biased

Designing a survey  Identify what data is needed

 Consider fairness of a survey
 Understand sample and population

Design data collection  Design and use a data collection sheet, including one for
methods continuous data
 Sort and classify data, and put data into a table
 Group data into class intervals with equal width

Tables and lists  Take data from tables and lists

Two-way tables  Design two-way tables

 Use information to complete a two-way table

Charts and diagrams Draw the following charts or diagrams

 Pictogram
 Bar chart or dual bar chart
 Pie chart
 Histogram (with equal class intervals)
 Frequency diagram for grouped data
 Frequency polygon
 Line graph
 Scatter graph
 Frequency polygon for grouped data
 Stem and leaf diagram
Edexcel Maths Linear Topic list FOUNDATION

Types of average and Calculate the following

range
 Mean
 Mode
 Median
 Range
 Modal class
 Interval containing the median
 Estimate the mean of grouped data in a frequency table
using mid-points
 Find the median for grouped data
 Estimate the mean for grouped data

Interpreting graphs and Understand and find information from

diagrams  bar charts and dual bar charts
 pie charts
 stem and leaf diagrams
 scatter graphs
 frequency polygons
 Find information from pictograms, bar charts, line graphs,
frequency polygons, frequency diagrams and histograms
(with equal intervals)
 Find information from pie charts
 Find median, mode, and range from stem and leaf
diagrams

Patterns in data  Find patterns in data

 Find exceptions in data

Lines of best fit  Draw a line of best fit

 Understand positive, negative and no correlation
 Understand what correlation means for the data shown
 Understand that correlation doesn’t necessarily mean one
variable is the cause of the other one
 Predict values using a line of best fit
 Understand that “no correlation” does not necessarily mean
no relationship between the values, just no linear
relationship
Edexcel Maths Linear Topic list FOUNDATION

Comparing data  Compare two sets of data using mean and range
 Compare two pie charts, and understand that the sizes
represented in each depend on the total represented by
each
 Compare data from dual bar charts
 Understand the advantages and disadvantages of different
types of average

Using calculators  Calculate mean using the correct key on a scientific

calculator
Edexcel Maths Linear Topic list FOUNDATION

PROBABILITY
Probability language and  Impossible, unlikely, even chance, likely and certain events
the probability scale  Mark events or probabilities on a 0 to 1 probability scale
 Write probabilities as fractions, decimals or percentages

Estimates of probability and  Find probabilities of events using dice, spinners, coins
relative frequency  Understand and use relative frequency as estimates of
probability
 Calculate an estimate of how many times an event will
occur, given its probability and the number of trials

Listing events  List the outcomes for one or two events

 Use and draw diagrams to show all possibilities

Mutually exclusive  Add simple probabilities

outcomes  Understand that the sum of all the mutually exclusive
outcomes is 1
 Know that if P is a probability of an outcome occurring,
then 1 - P is the probability of the same outcome not
occurring
 Fill in a missing probability in a table

Experimental data and  Compare experimental data with theoretical probability

theoretical probability  Understand that the same experiment repeated can have
different results, and that increasing sample size increases
accuracy
 Compare results from different sample sizes

Tree diagrams  Draw a tree diagram to represent 2 events

 Calculate the probability of 2 events