Edexcel GCSE
MATHEMATICS
Foundation
Keith Pledger
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ISBN: 978 1 4718 8246 3
© Keith Pledger 2016
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Get the most from this book
Everyone has to decide his or her own revision
strategy, but it is essential to review your work,
learn it and test your understanding. These Revision
Notes will help you to do that in a planned way,
topic by topic. Use this book as the cornerstone of
your revision and don’t hesitate to write in it —
personalise your notes and check your progress by
ticking off each section as you revise.
You can also keep track of your revision by ticking
off each topic heading in the book. You may find it
helpful to add your own notes as you work through
each topic.
Revision planner page
Tick to track your progress
Use the revision planner on pages 4 and 5 to plan
your revision, topic by topic. Tick each box when
you have:
l revised and understood a topic
l tested yourself
l checked your answers
Example page
Features to help you succeed
Rules
The key rules you need to follow when answers
questions on this topic.
Worked examples
Several worked examples are given for each topic.
Key terms
Exam-style questions
Practice exam questions are provided for each topic.
Use them to consolidate your revision and practise
your exam skills.
Answers
Check how you’ve done using the answers at the
back of the book.
Key terms are highlighted in each section.
Exam tips
Expert tips are given throughout the book to
help you polish your exam technique in order to
maximise your chances in the exam.
iii
My revision planner
Number
Number: pre-revision check
xx BIDMAS
xx Multiplying decimals
xx Dividing decimals
xx Using the number system effectively
xx Understanding standard form
xx Calculating with standard form
xx Rounding to decimal places, significance and
approximating
xx Limits of accuracy
xx Multiplying and dividing fractions
xx Adding and subtracting fractions and working with
mixed numbers
xx Converting fractions and decimals to and from
percentages
xx Applying percentage increases and decreases to
amounts
xx Finding the percentage change from one amount
to another
xx Reverse percentages
xx Repeated percentage increase/decrease
Mixed exam-style questions
xx Sharing in a given ratio
xx Working with proportional quantities
xx The constant of proportionality
xx Working with inversely proportional quantities
xx Index notation and rules of indices
xx Prime factorisation
Mixed exam-style questions
Number: summary of rules
iv
Edexcel GCSE Maths Revision Guide Foundation
Algebra
Algebra: pre-revision check
xx Working with formulae
xx Setting up and solving simple equations
xx Using brackets
xx Solving equations with the unknown on both sides
xx Solving equations with brackets
xx Simplifying harder expressions and expanding two
brackets
xx Using complex formulae and changing the subject of
a formula
xx Identities
xx Linear sequences
xx Special sequences
xx Quadratic sequences
xx Geometric progressions
Mixed exam-style questions
xx Real-life graphs
xx Plotting graphs of linear functions
xx The equation of a straight line
xx Plotting quadratic and cubic graphs
xx Finding equations of straight lines
xx Quadratic functions
xx Polynomial and reciprocal functions
xx Linear inequalities
xx Solving simultaneous equations by elimination
and substitution
xx Using graphs to solve simultaneous equations
xx Factorising quadratics of the form x2 + bx + c
xx Solve equations by factorising
Mixed exam-style questions
Algebra: summary of rules
v
Geometry
Geometry: pre-revision check
xx Bearings and scale drawings
xx Compound units
xx Working with compound units
xx Types of quadrilateral
xx Angles and parallel lines
xx Angles in a polygon
xx Congruent triangles and proof
xx Proof using similar and congruent triangles
xx Circumference
xx Pythagoras theorem
xx Arcs and sectors
Mixed exam-style questions
xx Constructions with a pair of compasses
xx Loci
xx Enlargement
xx Similarity
xx Trigonometry
xx Trigonometry for special angles
xx Finding centres of rotation
xx Understanding nets and 2D representation of
3D shapes
xx Volume and surface area of cuboids and prisms
xx Enlargement in two and three dimensions
xx Constructing plans and elevations
xx Surface area and 3D shapes
xx Vectors
Mixed exam-style questions
Geometry: summary of rules
vi
Edexcel GCSE Maths Revision Guide Foundation
Statistics and probability
Statistics and probability: pre-revision check
xx Using frequency tables
xx Using grouped frequency tables
xx Vertical line charts
xx Pie charts
xx Displaying grouped data
xx Scatter diagrams and using lines of best fit
Mixed exam-style questions
xx Single event probability
xx Combined events
xx Estimating probability
xx The multiplication rule
xx The addition rule
Statistics and probability: exam-style questions
Statistics and probability: summary of rules
Exam preparation
xx
xx
xx
xx
xx
xx
The language used in mathematics examinations
Exam technique
Key topics for revision
One week to go
Answers
Index
vii
Algebra: pre-revision check
1 This formula gives the value of p in terms of q
and r: p = 2q – 3r. Find the value of p when
q = 10 and r = 4. F S1 U4
S = ut + 1 at 2
2
a Find the value of S when u = 5, t = 4 and
a = 10.
b Make a the subject of the formula. F/H S1 U10
2 Solve the equations
a a+4=6
b b =5
3
c 5c + 4 = 6
d 15 – 3e = 24 F S1 U5
2
8 Prove that the sum of the three consecutive
numbers (n – 1), n and (n + 1) is a multiple of 3.
F/H S1 U11
3 a Expand these brackets
i 5(2a + 3)
ii h(3h – 6)
iii 3x(4x – 2y)
b Factorise fully
i 6y + 12
ii 6p2 – 9p
iii 5e2 + 10ef
iv 8x2y – 12xy2 F S1 U6
9 Here are the first 5 terms of a linear sequence.
4
10
16
22
28…
a Find the nth term of the sequence.
b Work out the 50th term in the sequence.
c Explain if 900 is a member of the sequence.
F S2 U3
F/H S1 U8
6 a Simplify
i a4 × a6
x8
ii 5
x
12e6f 7
iii
8e 9f 5
b Expand and simplify
i (t + 2)(t + 5)
ii (v – 7)(v + 5)
iii (y – 6)(y – 5) F/H S1 U9
10 a Write down the first 5 terms of the quadratic
sequence with nth term 2n2 – 3.
b Find the nth term of the quadratic sequence
that has the first 5 terms 3, 8, 15, 24, 35.
F S2 U4
11 The nth term of quadratic sequence is n2 + 5.
The nth term of a different quadratic sequence is
80 – 2n2.
Find the number that is in both sequences.
F/H S2 U5
12 Here is a geometric sequence.
5
15
45 135 …
a Find the common ratio.
b Find the 10th term of the sequence. F/H S2 U6
13 Here is the graph that shows the depth of water
in a harbour. A ship needs to enter the harbour
between 0800 and 2000. It needs a 4 metre depth
of water in the harbour. Between what times can
the ship enter the harbour? F S3 U1
10
Depth of
water (m)
4 Solve these equations
a 5x – 6 = 2x + 3
b 7 – 2p = 6p + 13
y
y
c 2 – 3 = 5 + 5 F/H S1 U7
2
4
5 Solve.
a 5(3g – 2) = 35
b 4(5h + 7) = 3(2h + 8)
c 2(5k + 8) – 6 = 4(2k – 1)
7 This formula is used to find the distance, S,
travelled by an object.
5
0
00:00 04:00 08:00 12:00 16:00 20:00 24:00
Time
Algebra
1
Algebra: pre-revision check
14 a On a coordinate grid drawn with values of x
from –3 to +3 and values of y from –6 to +8,
draw the graph of y = 2x + 1.
b Find the value of x when y = 6 F S3 U2
15 Find the equation of a straight line graph that
passes through the point (0, –2) and has a
gradient of 3. F S3 U3
22 Here is the graph of the line y + 2x = 3.
y
6
16 a On a coordinate grid drawn with values of x
from –2 to +4 and values of y from –6 to +8,
draw the graph of y = x2 – 3x – 2.
b Find the values of x when x2 – 3x – 2 = 0.
F S3 U4
17 Find the equation of a straight line graph that
passes through the point (–2, 3) and is parallel to
the line x + 2y = 8. F/H S3 U5
20 a Write down the inequality shown on this
number line.
x
1
2
3
4
2
−3
−2
−1
0
1
2
3
x
−2
Find graphically the solution to the simultaneous
equations:
y + 2x = 3
y – 2x = 1 F/H S4 U5
19 a On a coordinate grid drawn with values of
x from –3 to +3 and values of y from –10 to
+30, draw the graph of y = x3 + x2 – 3x.
b Find the values of x when x3 + x2 – 3x = 0.
F/H S3 U7
−5 −4 −3 −2 −1 0
4
−4
18 a Sketch the graph of the quadratic function
y = x2 – 4x + 3 for values of x from 0 to 5.
b Write down the roots of the equation
x2 – 4x + 3 = 0.
c Write down the line of symmetry of the
graph. F/H S3 U6
5
b Solve these inequalities
i 2x + 5 < 9
ii 24 + 2t > 30 – 3t
iii 5(y – 3)  3y – 6 F/H S4 U2
2
21 Solve this pair of simultaneous equations.
5x + 2y = 8
2x – y = 5 F/H S4 U 3 & 4
Edexcel GCSE Maths Revision Guide Foundation
23 a Expand and simplify
i (x + 4)(x – 5)
ii (y + 8)(y – 8)
iii (6 – a)(a + 6)
b Factorise
i x2 + 7x + 12
ii e2 – 3e – 10
iii b2 – 25 F/H S5 U1
24 Solve the equations
a x2 – 5x + 6 = 0
b x2 – 2x = 15
c p2 – 49 = 0 F/H S5 U2
DIFFICULTY LEVEL mID
Rules
1
2
3
You can replace words or letters in a formula with numbers.
Use BIDMAS to find the value of the missing word or letter.
Use inverses to write the formula or equation so that the missing
letter is on its own on one side of the formula or equation.
Worked examples
Look out for
a
2w means 2 × w
Here is a formula to find the perimeter of a rectangle:
P = 2l + 2w. Find the value of P when l = 6 and w = 4.
P = 2l + 2w
b
1
P=2×6+2×4
2
P = 12 + 8 = 20
Algebra: pre-revision check
Working with formulae
So if w = 5 then 2w is 2 × 5 = 10
and not 25
Cars 2U
Key terms
Tom hires a car from Cars 2U.
Formula
i How much does it cost to hire a car for
7 days?
ii Ben has £100. For how many days can he
hire a car?
Substitute
Variable
Equation
£20 plus £30 a day
You must explain your answer.
i Cost = 20 + 7 × 30
Cost = 20 + 210 2
Cost = £230
1
ii 100 = 20 + N × 30 1
100 – 20 = N × 30 3
80 = N × 30 so N = 80 ÷ 30 = 2.666… 2
Ben can hire the car for 2 days. This
costs £80. 3 days cost £110 which is
too much.
Exam tips
Always show your working
when answering algebra
questions.
Do not use trial and error
methods as you may well
lose marks.
Exam-style questions
1 Bobbie uses this number machine to work out the number of cartons of orange juice she needs for
a party.
Number
of people
÷5
+2
Number
of cartons
a How many cartons will Bobbie need for 40 people?
b How many people are in a party that uses 20 cartons?
2 This formula gives the time taken T minutes to cook a chicken of weight w kg. T = 40w + 20
a How long does it take to cook a chicken of weight 2.5 kg?
b It takes 3 hours 20 minutes to cook a different chicken. How heavy was the chicken?
[2]
[2]
[2]
[2]
Algebra
3
Algebra: pre-revision check
Setting up and solving simple equations
DIFFICULTY LEVEL mid
Rules
1
2
3
4
Always use the inverse operations to solve an equation.
+ and – are the inverse of one another.
× and ÷ are the inverse of one another.
To set up an equation a variable must be defined.
Worked examples
a
2
3
b
2
2p + 5 = 17 (–5 is the inverse operation of + 5)
2p + 5 – 5 = 17 – 5 (subtract 5 from each side
of the equation)
Key terms
2p = 12 (÷ 2 is the inverse of × 2)
Equation
p = 6 (divide each side of the equation by 2)
Inverse
operation
nn is two years younger than Ben. Clara is twice as old as
A
Ben. The total of their ages is 58. Work out their ages.
Solve
Variable
Let Ben’s age be x, Firstly, set up the equation:
Ann’s age will be x – 2, x + (x – 2) + 2x = 58
Clara’s age will be 2x Now collect like terms:
Exam tips
4x – 2 = 62
Always use algebraic
methods and show your
working to gain full marks.
4x = 60
(Add 2 to each side)
(Divide each side by 4)
x = 15
Always check your answer
to make sure it is correct.
Ann will be 13, Ben 15 and Clara 30.
Exam-style questions
1 Solve the equations
b
a a – 3 = 7 [1];
c
b
= 3 [1];
5
5d
+ 4 = 29 [2];
d
e 6 – 2e = 3 [2]
2
2 Here is a rectangle.
2x + 5
The length is 2x + 5.
The width is x – 3.
The perimeter is 46 cm.
Work out the area of the rectangle in cm2. [4]
4
Edexcel GCSE Maths Revision Guide Foundation
3c + 9 = 7 [2];
x–3
DIFFICULTY LEVEL mid
Rules
1
2
When you expand a bracket you multiply what is inside the bracket
by the number or variable outside the bracket.
When you factorise an algebraic expression you take out the
common factor from each term of the expression and put it
outside the bracket.
Worked examples
a Expand
i 4(3x + 5);
1
Look out for
ii t(3t – 4)
x × x = x2 using index laws
1
Key terms
t × (3t − 4)
t × 3t − t × 4
3t2 − 4t
4 × (3x + 5)
4 × 3x + 4 × 5
12x + 20
Brackets
Variable
Expression
b Factorise
i 4p + 6
2 × 2 × p + 2 × 3
2 is in 4 and in 6
2 2(2p + 3)
Algebra: pre-revision check
Using brackets
Expand
ii 6p2q – 9pq2
3 × p × q × 2 × p – 3 × p × q × 3 × q
3 and p and q are in both terms
2 3pq(2p – 3q)
Factorise
Exam-style questions
1 Beth is 3 years older than Amy. Cath is twice as old as Beth.
The total of their ages is 41. How old are the three girls?
[3]
2 PQRS is a rectangle.
The length of the rectangle is
(2x – 5) cm
(2x – 5) cm.
P
Q
The width of the rectangle
6 cm
is 6 cm.
The area of the rectangle
R
S
is 72 cm2.
Work out the perimeter of the rectangle.
[4]
Exam tips
Always check your answer
by multiplying out the
brackets.
Always define your variable
e.g. let Amy’s age be x.
Then set up your equation.
Algebra
5
Mixed exam-style questions
(Strands 1, 2 and 3)
1 The diagram show the position of two villages.
N
Redford
Redford is on a bearing of 050° from Brownhills.
Karen walks from Brownhills to Redford.
She walks at an average speed of 6 km/h.
Brownhills
She takes 1 h 30 mins to cover the distance.
a Work out the distance between Brownhills and Redford.
[2]
b Using a scale of 1 cm to 4 km, make an accurate scale drawing showing the position of the two villages. [3]
2 The diagram shows a square attached to four similar regular polygons.
Calculate the number of sides on the polygons.
[3]
3 ABC is an isosceles triangle.
D and E are points on BC.
AB = AC, BD = EC
Prove that triangle ADE is isosceles.
[3]
A
B
D
E
C
4 The wheel on a bicycle has a diameter of 70 cm. John cycles 15 km on the bicycle.
a How many revolutions will the wheel make during the journey?
b The journey takes John 1 h 20 mins. Calculate John’s average speed.
5 In the diagram PQ is parallel to ST.
QX = XS
Prove that triangles PQX and STX are congruent.
[4]
[2]
P
S
X
6 The diagram shows a plan of a garden design.
Q
T
A circular pond with a diameter of 1.5 m is dug in the lawn.
The centre of the pond is in the centre of the lawn.
a Make an accurate scale drawing of the plan using a scale of 2 cm: 1 m.[4]
b Calculate the area of the lawn.
[4]
2m
4m
patio
pond
lawn
8m
6
Edexcel GCSE Maths Revision Guide Foundation
[3]
[4]
A
B
3 cm
C
8 A paper cone is made from a folding a piece of paper in the shape of sector of a circle. The angle at the
centre of the sector is 100°. The radius of the sector is 6 cm.
a Calculate the length of the arc of the sector.
[2]
b Calculate the diameter of the base of the finished cone
[2]
6 cm
100°
9 The diagram shows a trapezium PQRS.
PQ is parallel to SR.
PS = QR.
Show that triangles PXS and QXR are similar.
P
Mixed exam-style questions
7 The diagram shows a right-angled triangle drawn inside a quarter circle. The chord AC is 3 cm.
a Calculate the radius of the circle.
b Calculate the area of the segment ABC.
[3]
Q
X
S
R
10 ABCD is a rhombus.
AC = 10.8 cm, BD = 15.6 cm.
Calculate the length of the sides of the rhombus.
A
[4]
B
10.8 cm
15.6 cm
D
C
Geometry
7
Exam technique
●
Be prepared and know what to expect.
●
Read each question carefully.
●
Don’t just learn key points.
●
Show stages in your working.
●
Work through past papers. Start from the back
and work towards the easier questions. Your
teacher will be able to help you.
●
Check your answer has the units.
●
Work steadily through the paper.
●
Practice is the key, it won’t just happen.
●
Skip questions you cannot do and then go back to
them if time allows.
●
Read the question thoroughly.
●
Use marks as a guide for time 1 mark = 1 min.
●
Present clear answers at the bottom of the space
provided.
●
Go back to questions you did not do.
●
Read the information below the diagram – this is
accurate.
●
Use mnemonics to help remember formula you
will need, for example:
SOH
sin = opposite/hypotenuse
CAH
cos = adjacent/hypotenuse
TOA
tan = opposite/adjacent
or ‘silly old hens cackle and hale, till old age’.
for the order of operations, BIDMAS: Brackets,
Indices, Division, Multiply, Add, Subtract
formula triangles for the relationship between
three parameters e.g. speed, distance and time
●
Cross out answers if you change them, only
give one answer.
●
Underline the key facts in the question.
●
Estimate the answer.
●
Is the answer right/realistic?
●
Have the right equipment.
Calculator
Pens
Pencils
Ruler, compass, protractor
Eraser
Tracing paper
Spares
●
Never give two different answers to a question.
●
Never just give just an answer if there is more
than 1 mark.
●
●
Never measure diagrams; most diagrams are not
drawn accurately.
D
S
D
S
Never just give the rounded answer; always show
the full answer in the working space.
Edexcel GCSE Maths Revision Guide Foundation
T
D
S
8
T
T
Distance = Speed × Time
Time =
Distance
Speed
Speed =
Distance
Speed
Exam preparation
The following formulae will be provided
for students within the relevant examination
questions.
Perimeter, area, surface area and
volume formulae
Where r is the radius of the sphere or cone,
l is the slant height of a cone and h is the
perpendicular height of a cone:
Curved surface area of a
cone = π rl
Volume of a cone =
l
1 2
πr h
3
h
r
Surface area of a
sphere = 4π r 2
Volume of a
sphere =
4 3
πr
3
r
All other formulae and
rules must be learnt.
Exam technique
9
Key topics for revision
Here are some topics that students frequently make errors in during their
exam.
Number
Rules
1
2
3
A factor is a number that divides into another number, e.g. 2 is a
factor of 6.
A multiple is a member of the multiplication table of that number,
e.g. 6 is a multiple of 2.
A prime number is one that can only be divided by 1 and itself,
e.g. 2, 3, 5, 7, 11 …
Highest
Common
Factor (HCF)
Question
Working
Find the HCF
of 24 and 36.
Use factor trees to find all the factors of 24 and 36:
Answer
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
The common factors are:
2 × 2 × 3 = 12
Find the LCM
Lowest
of 9 and 12.
Common
Multiple (LCM)
Adding
12
List the multiples of 9 and 12:
9, 18, 27, 36, 45
12, 24, 36, 48
36
Question
Working
Answer
2 1
+
3 4
Write equivalent fractions:
2 4 6
8
1 2
3
= = =
and = =
3 6 9 12
4 8 12
12 is the LCM of 3 and 4 so write the fractions in
12ths:
8
3
8 + 3 11
+
=
=
12 12
12
12
Subtracting
2 1
−
3 4
You use the same method as adding but just take
away so we get:
8
3
8−3
5
−
=
=
12 12
12
12
Multiplying
2 3
×
5 8
5
12
Multiply the tops together and then the bottoms of the
fractions:
2×3
6
=
then cancel by 2
5 × 8 40
10
11
12
Edexcel GCSE Maths Revision Guide Foundation
3
20
Changing a
fraction to a
decimal
Write the first fraction down and turn the second
fraction upside down and multiply:
5 2
÷
12 3
5 3 15
× =
then cancel be 3
12 2 24
5
8
Question
Working
Answer
3
as a
8
decimal.
Divide the top number by the bottom number so
divide 3 by 8:
Write
0.3 7 5
3
Question
Finding a
fraction of an
amount
3
of
5
£4.80.
Exam preparation
Dividing
6 4
8 3. 0 0 0
0.375
Working
Answer
3
× £4.80
5
There is a simple rule for this calculation, which is
‘Divide by the bottom and Times by the top’
This can be written as
Find
You can sing it to the ‘Wheels on the bus’ song to help
you remember it.
£4.80 ÷ 5 = 0.96 then 0.96 × 3 = £2.88
Finding a
percentage of
an amount
Estimating
Work out 60%
of £4.80.
£2.88
60
× £4.80.
100
You can use the same rule so you divide by 100 and
times by 60:
This can be written as
£4.80 ÷ 100 × 60 = £2.88
£2.88
Question
Working
Answer
Estimate
Write each number to one significant figure so that:
76.15 × 0.49
19.04
76.15 becomes 80
0.49 becomes 0.5
19.04 becomes 20
Remember that the size of the estimate needs to be
similar to the original number.
Question
Using a
calculator
Work out
2
76.15 + 5.62
19.04
So 80 × 0.5 = 40 and 40 ÷ 20 = 2
2
Working
Answer
You either need to enter the whole calculation into
your calculator using the fraction button or work out
the top first then divide the answer by the bottom.
76.15 + 5.622 = 107.7344
107.73 ÷ 19.04 = 5.658319327
5.658319327
Key topics for revision
11
Exam preparation
Algebra
Rules
2y × y = 2y2;
2y + y = 3y;
2y − y = y;
y ×y =y
y ÷y =y
m
n
m+n
m
n
2y ÷ y = 2
(y ) = y
m−n
m n
Question
mn
Working
Answer
= 2ab + 3ab − 1ab
4ab
= 3y2 − 1y2
2y2
Question
Working
Answer
Simplify
=x
x9
Collecting like Simplify
terms
a 2ab + 3ab − ab
b 3y2 − y2
Index laws
a x4 × x5
b
=
a7
a3
c (y2)3
Multiplying
out the
brackets
Factorising
expressiona
a7
a3
= a7 ÷ a3 = a7− 3
= y2×3
d 7f g × 2f g
4 3
4+5
a4
y6
14f 7g4
= 7 × 2 × f 4 + 3 × g3+1
3
Question
Working
Answer
Expand
= 3 × 4p + 3 × 5
12p + 15
a 3(4p + 5)
= 7p − 4 × p − 4 × −q = 7p − 4p + 4q
3p + 4q
b 7p − 4(p − q)
=y×y+y×−4+3×y+3×−4
y2 − y − 12
c (y + 3)(y − 4)
= y2 − 4y + 3y − 12
Question
Working
Answer
Factorise completely
=5×a×b+2×5×b×c
5b(a + 2c)
a 5ab + 10bc
=3×4×e×e×f−3×3×e×f×f
3ef(4e − 3f)
b 12e f – 9ef
= x + (3 + 4)x + 3 × 4
(x + 3)(x+ 4)
Question
Working
Answer
Solve
3t = 4 + 2 so 3t = 6
t=2
a 3t − 2 = 4
4 + 3= 5f − 3f so 7 = 2f or 2f = 7
f = 3.5
b 3f + 4 = 5f − 3
5x + 10 = 3 so 5x = 3 − 10 or 5x = −7
x = −1.4
c 5(x + 2) = 3
(y + 2)(y − 5) = 0 so y + 2 = 0 or y − 5 = 0
y = −2 or y = 5
2
2
2
c x2 + 7x + 12
Solving
equations
d y − 3y − 10 = 0
2
12
Edexcel GCSE Maths Revision Guide Foundation
Exam preparation
Geometry and measure
Rules
The perimeter of a shape is the distance around its edge. You add all
the side lengths together.
The area of a shape is the amount of flat surface it has. You multiply
two lengths.
The volume of a shape is the amount of space it has. You multiply
three lengths.
Alternate angles are in the shape of a letter Z.
Corresponding angles are in the shape of a letter F.
Allied angles or co-interior angles are in the shape of a letter C.
Question
Perimeter of a Find the perimeter of
this shape.
shape
Working
Answer
For a rectangle you need to add the lengths
of the four sides.
16 cm
3 + 5 + 3 + 5 = 16
3 cm
5 cm
Area of a
shape
Question
Working
Find the area of this
shape.
For this right-angled triangle you need to use 9 cm2
the formula:
Area = ½ base × vertical height
3 cm
So the area = ½ × 6 × 3 = 9
6 cm
Volume of a
solid
Answer
You have multiplied two lengths
Question
Working
Answer
Find the volume of this
shape with radius 5 cm
and height 12 cm in
terms of π
For this cylinder you need to use the
formula:
300π cm3
Volume = π × r2 × h
So volume is π × 5 × 5 × 12 = 300π
You have multiplied three lengths
Angles
between
parallel lines
Question
Working and answer
Find the missing angles in this
diagram. Give reasons for your
answer.
a = 50° (Alternate angles are equal)
c = 50° (Corresponding angles are equal)
50°
a b
b = 130° (Allied angles add to 180°
(supplementary))
c
Key topics for revision
13
Exam preparation
Question
Working and answer
ABC is an isosceles triangle. BCD is
Finding
a straight line.
missing
angles and
Find, giving reasons, angle ACD.
giving reasons
A
50°
Angle ABC = (180 – 50) ÷ 2 = 65°
(The three angles of a triangle add to 180°)
Angle ACB = Angle ABC = 65°
(Base angles of an isosceles triangle are equal)
Angle ACD = 180 – 65 = 115°
(Sum of the angles on a straight line = 180°)
D
C
B
Statistics and probability
Mean from
a grouped
frequency
table
Pie chart
14
Question
Working
Answer
Work out an estimate
of the mean age from
this frequency table
Multiply the mid value of the age groups by
the frequency
24
5 × 4 = 20
Age
f
0  a < 10
4
10  a < 20
6
35 × 5 = 175
20  a < 30
12
45 × 3 = 135
30  a < 40
5
Divide the total of age × frequency by the
total frequency: 720 ÷ 30
40  a < 50
3
15 × 6 = 90
25 × 12 = 300
Note: Don’t forget to divide by the total
frequency and not the number of groups (5)
Question
Working
Answer
Draw a pie chart from
this information
As pie charts are based on a
circle then we need to divide
the number of degrees in a
whole turn (360°) by the total
frequency which is 20.
So 360° ÷ 20 = 18°
Red = 7 × 18° = 126°
Favourite
colour
f
Red
7
Blue
4
Green
2
Yellow
3
Black
4
Blue = 4 × 18° = 72°
Green = 2 × 18° = 36°
Yellow = 3 × 18° = 54°
Black = 4 × 18° = 72°
The angle for each colour is then
Then draw the circular pie
calculated by multiplying its
chart
frequency by 18°
Edexcel GCSE Maths Revision Guide Foundation
One week to go
You need to know these formulae and essential techniques.
Number
Topic
Formula
When to use it
Negative numbers
++=+
––=+
Two signs next to each other
+–=–
–+=–
Multiplying integers
+×+=+
–×–=+
Dividing integers
+×–=–
–×+=–
+÷+=+
–÷–=+
+÷–=–
–÷+=–
Order of operations
BIDMAS
Percentages
20% of 50 =
Simple interest
SI for 5 years at 3% on £150
If you have to carry out a calculation. You
use the order Brackets, Indices, Division,
Multiplication, Addition and Subtraction
20
× 50
100
3
× 150 × 5
100
Compound interest
Standard form
Approximating
CI for 2 years at 3% on £150
Year 1
3
× 150 = £4.50
100
Year 2
3
× (150 + 4.50 )
100
To find the percentage of an amount e.g. 20%
of 50.
To find the simple interest you find the interest
for one year and multiply by the number of
years.
For compound interest you find the percentage
interest for one year, add it to the initial amount
and find the interest on the total and so on.
You can also do this using geometric
progressions and write £150 × (1.03)2 = 2.5 × 10 3 = 2500
A number in standard form is
2.5 × 10 −3 = 0.0025
(a number between 1 and 10) × (a power of 10)
Decimal places
You round to a number of decimal places by
looking at the next decimal place and rounding
up or down.
Significant figures
The first non-zero digit is always the first
significant figure and you count the number of
significant figures then look at the next figure
and round up or down. You should always keep
the idea of the size of the number.
One week to go
15
Exam preparation
Algebra
Topic
Formula
When to use it
Rules of indices
y ×y =y
m
n
m+n
ym ÷ yn = ym−n
(ym)n = ymn
Straight line graph
y = mx + c
When you multiply you add the indices or
powers.
When you divide you subtract the indices or
powers.
When you raise a power to a power you
multiply the indices or powers.
m is the gradient and (0, c) the intercept on the
y-axis
Geometry and measure
Topic
Formula
When to use it
Parallel sides
Parallel lines are shown with arrows
Equal sides
Equal lines are shown with short lines
Perimeter
Add lengths of all sides
To find the perimeter of any 2D shape
Areas of 2D shapes
Area = l × w
Area of a rectangle is length × width
w
Area = ½b × h
Area = b × h
Area = ½ (a + b) × h
l
Area of a triangle is ½base × vertical height
h
b
Area of a parallelogram is base × vertical
height
h
b
Area of a trapezium is
a
b
h
½ the sum of the parallel sides × the vertical
height
Circumference and
area of a circle
C = π × D or C = π × 2r
A = π × r2
Circumference or the perimeter
of a circle is:
pi × diameter or pi × double the
radius
Area of a circle is pi × radius
squared
16
Edexcel GCSE Maths Revision Guide Foundation
r
D
V=l×w×h
Volume of a cuboid is:
V = πr h
Length × width × height
2
Exam preparation
Volumes of 3D shapes
Volume of a cylinder is:
Area of circular end × height
Pythagoras’ theorem
h = a2 + b2
The hypotenuse of a right-angled triangle can
be found by finding the square root of the sum
of the squares of the two shorter sides.
A shorter side of a right-angled triangle can
be found by finding the square root of the
difference between the hypotenuse squared
and the other shorter side squared.
Trigonometry
sin =
o
a
o
;cos = ;tan =
h
h
a
You can find a missing side or a
missing angle by selecting and
using one of these formulae.
h
a
o
You use the trigonometry ratio that has two
given pieces of information and the one you
have to find.
Statistics and probability
Topic
Formula
When to use it
Probability
P(A and B) = P(A) × P(B)
You use this when you have two independent
events
P(A or B) = P(A) + P(B)
P(A or B) = P(A) + P(B) − P(A)
× P(B)
You use this when you have mutually exclusive
events
You use this when you do not have mutually
exclusive events
One week to go
17