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C Practice
A collection of targeted
GCSE questions
C Practice 5
The C Practice 5 sets of questions are based closely on the requirements of the EdExcel Modular
GCSE course, targeting intermediate level entry.
Set A – The seventeen question sheets provide a resource targeting the content of the Stage 1
Intermediate exam and include valuable questions on most of the areas tested.
Set B – The twelve question sheets are targeted at the needs of the Stage 2 Intermediate paper
Set C – Stage 3 is the final assessment and the 23 question sheets provide a comprehensive
coverage of the likely content.
These materials of course will also provide very suitable practice for all Intermediate GCSE
examination course for mathematics.
C Practice 5 (set A)
Handling
Data
Shape and Space
Algebra
Number
Topic
Sheet
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
A13
A14
A15
A16
A17
Objectives
Write and understand numbers in terms
of its factors including HCF and LCM
The four rules of fractions
Change and order fractions, decimals and
percentages
Find percentages of amounts and
increase/decrease by percentages
Mixed percentage questions
Substitution positive and negative
numbers into formula and expressions
Simplifying algebraic expressions
Factorising algebraic expressions
Solving linear equations
Algebra mixture of substituting,
simplifying, expanding and factorising
Angles – Parallel Lines
Interior and exterior angles of Polygons
Construction of triangles, quadrilaterals
and bearings
Transformations – Reflections and
Rotations
Completing two way tables
Probability – particularly probability tables
Mixed bag - sequences (generalisation),
long multiplication, Simple Interest
Clueless
Close
Confident
Student self assessment – Assess how good you think you are before you start each section (sheet)
Can you cope with
these questions?
Decide how good
you think you are
before you look at
the questions – are
you confident, close
or clueless
Make a note here of
the areas of work
that you still feel you
need to improve on.
C Practice 5
The three sets of C Practice 5 questions can be used in a number of ways –
They may be used as a starter activity at the beginning of the lesson to refresh minds of
the topic to be learnt during that lesson.
They may prove useful as a round up of the work completed during a unit.
They may prove useful as quick revision practice before the module tests.
C Practice 5 (set B)
Handling
Data
Shape and Space
Algebra
Number
Topic
Sheet
B1
B2
Objectives
Rounding to significant figures and
decimal places
Expressing numbers in standard form
B3
Sharing amounts in a given ratio
B4
Expanding brackets and factorisation of
quadratic equations
Solving algebra equations through trial
and improvement. Formula questions
Drawing straight line graphs
B5
B6
B7
Area and Volume (cuboids)
B8
Area and circumference of circles.
Angles involved with tangents to a circle
Pythagoras’ Theorem and Trigonometry
B9
B10
B11
B12
Transformations – Scale factor
Enlargement
Stem and Leaf diagrams, Cumulative
Frequency and Box Plots
Pie Charts and Scatter Graphs
Clueless
Close
Confident
Student self assessment – Assess how good you think you are before you start each section
Can you cope with
these questions?
Decide how good
you think you are
before you look at
the questions – are
you confident, close
or clueless
Make a note here of
the areas of work
that you still feel you
need to improve on.
C Practice 5 (set C)
Shape and Space
Algebra
Number
Topic
Handling Data
Z
Sheet
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
C15
C16
C17
C18
C19
C20
C21
C22
C23
Objectives
Estimating solutions and rounding
Using Place Value and Lowest Common
Multiples
Working with Indices and using standard
form
Finding percentages and percentage
increase and decreases
Finding ratios of amounts and four rules
of fractions
Questions involving proportion
Number questions in context (money etc)
and Currency exchange
Simplifying expressions involving
expanding brackets
Solving simple algebra inequalities and by
graph
Algebra equations – linear, simultaneous
and quadratic
Straight line graphs
Travel graphs and curved graphs
Surface area and volume of prisms
Units of measure including length, area
and volume
Finding angles in polygons
Circle Geometry – involving angles
Construction of triangles, perpendicular
lines and drawing nets
Pythagoras’ Theorem and Trigonometry
Transformations – enlargement, and
elevations
Estimates for means and moving
averages
Stem and Leaf, cumulative frequency,
box plots and quartiles
Probability problems and Tables
Probability through probability Trees
Clueless
Close
Confident
Student self assessment – Assess how good you think you are before you start each section
Can you cope with
these questions?
Decide how good
you think you are
before you look at
the questions – are
you confident, close
or clueless
Make a note here of
the areas of work
that you still feel you
need to improve on.
‘C’ Practice 5 (set A1)
Number: Factors and Multiples
1. List all of the factors of 48
2. If the product of the primes is:
2x2x3x5
What is the number?
3. What is the Highest Common
Factor (HCF) of 16 and 40?
5. (a)
(b)
(c)
4. What is the Lowest Common
Multiple of 12 and 18?
Express 120 as a product of its Prime Factors
Express 75 as a product of its Prime Factors
Using the results above work out: (i) The HCF of 75 and 120
(ii) The LCM of 75 and 120
‘C’ Practice 5 (set A2)
Number: Fractions
1. Work out:
1
2
x
2. Work out:
4
5
1
8
3
4
+
Give your answer in its simplest
form
3. Work out:
2
3
÷
5. (a) Write
(b) Write
4. Work out:
1 23
4
3 23
1 56
(c) Work out:
x
1 45
as an improper fraction
as an improper fraction
3 23
-
1 56
Give you answer as a mixed number
‘C’ Practice 5 (set A3)
Number: Fractions, Decimals and Percentages
1. Work out 0.8 as a fraction
2. Write 30% as a decimal
3. Put these in order of size, starting
with the smallest:
4. Express
1
4
0.3, 28%,
16
64
as a percentage
2
5
5. Complete this table
Fraction
Decimal
Percentage
0.375
3
2
70%
8%
‘C’ Practice 5 (set A4)
Number: Percentages
2%
1.
35%
25%
17.5%
10%
£120
70%
2.5%
20%
99%
1%
50%
5%
2. Increase £350 by 10%
3. SALE 20% OFF
How much would a jacket priced at
£90, cost in the sale?
4. The cost of a CD player is £200 +
VAT. The rate of VAT is 17.5%.
What is the cost of the CD player?
5. A house cost £50 000 three
years ago. I sold it for £90 000.
What percentage profit have I
made?
‘C’ Practice 5 (set A5)
‘C’ Practice 5 (set A5)
Percentages: General
1. Increase £250 by 10%
2. Fiona had £12.50 she gave
8% to charity, how much had
she left?
3. The cost of a digital camera is
£240 plus VAT.
The rate of VAT is 17.5%.
What is the cost of the camera?
4. Put these in order of size.
Smallest first.
0.345, 1/3, 35%, 2/5
5. Here are 6 numbers:
0.8, 3/5, 75%, 80%, 2/3,
a. Circle the two numbers that are equal to 4/5
b. Explain why 5/8 is not 58%.
c. What is 3/5 as a percentage?
5/8
‘C’ Practice 5 (set A6)
Algebra: Substitution
1. If a = 3, b = 5 find the value of:
2. When n = 8, evaluate the
expression 3(2n - 2)
a) 2a + b
b) 2ab
3.
T = 3x + 4y
Find the value of T
when x = -5 and y = 3.
4. Evaluate A = 3(2b – 4) when:
(i) b = -2
(ii) b = -5
5. Given that P = Q 2 - 2Q, find the value of P when Q = -3.
‘C’ Practice 5 (set A7)
Algebra: Expressions
5.1. Simplify the expression:
2. Simplify the expression:
4p + 9q + 5p – 3q
5p 2 + 3q - p 2 + 2q
3. Multiply out:
4. Find the perimeter of this
shape:
6(4x – 3)
(t + 3)
(t - 2)
B#
(t - 1)
5. Find
perimeter
this
shape:
Find
the the
perimeter
of of
this
shape:
4(x - 2)
3x
‘
C’ Practice 5 (set A8)
Algebra: Factorising
1. Factorise 12x + 4.
2. Factorise 6x + 18y.
3. Factorise 8xy + 12x.
4. Factorise 6x 2 - 3xy.
5. (a) Multiply out each of these:
8(2x – 3)
3(4x + 1)
(b) Now simplify this expression and factorise
8(2x – 3) + 3(4x + 1)
‘C’ Practice 5 (set A9)
Algebra: Solving Equations
1. Solve the equation:
2. Solve the equation:
4(3n + 7) = 16
8x – 3 = 21
3. Solve the equation:
4. Perimeter = 38cm
4(x + 2) = 6x + 4
(t + 4)
(t + 3)
(t - 1)
Find the value of t.
5. Solve the following equations:
(12 + x) = 5
3
x
3
-5=3
‘C’ Practice 5 (set A10)
Algebra: General
1. If T = x² - 6x
Work out the value of T if x = -7
2. P = 4x – 3y
Work out the value of P
if x = -3 and y = 5
3. (a) Simplify 5q + 7q + 3p – 2q
(b) Factorise 6x + 18y
4. (a) Expand 3(4x –2)
(b) Factorise 4xy – 6x
5. Work out the value of x
3xº
(x + 40)º
‘C’ Practice 5 (set A11)
Angles (Parallel Lines)
1. Write down the size of angles x & y. 2. Write down the size of angles x
Give reasons for your answers
& y. Give reasons.
125º
62º
x
x
y
40º
y
3.
4. Find angles x & y. Give
reasons for your answers.
28º 95º
g
68º
y
120º
Find the angle marked g.
Give a reason for your answer
x
5. Find all of the missing angles in this question, giving a reason for
each.
21º
z
x
y
92º
‘C’ Practice 5 (set A12)
Shape and Space: Polygons
1.
x
x
2. The exterior angle of a regular
polygon is 45°.
How many sides has the polygon?
x
x
x
(a) What do the external angles total
(b) What is the value of x?
3.
4.
107°
34°
63°
48°
47°
x
Find the value of x
Find the size of the interior angle of
this regular octagon.
5. (a) Work out the size of the interior
angle of the regular hexagon.
(b) Use this information to work out
the value of x.
x
‘C’ Practice 5 (set A13)
Shape and Space: Scale Drawing
1. Here is a sketch of a triangle.
2. Here is a sketch of a
quadrilateral
4cm
140º
5cm
5cm
75º
7cm
85º
6cm
Draw it accurately
Draw it accurately
3. Construct this triangle accurately
AB = 5.3cm, BC = 6cm,
Angle ABC = 112º
4. Measure the Bearing of
(a) A from B
(b) B from A
N
x
N
A
Bx
5. An airplane is at a bearing of 050º from Birmingham and 290º from
Norwich.
Shows its position on the map below
N
N
x
Norwich
x
Birmingham
‘C’ Practice 5 (set A14)
Shape and Space: Reflections and Rotations
2.
1. Draw a reflection of Triangle A in
the given line
y
Y
B
A
x
Z
(a) Reflect triangle B in the x axis
(b) Reflect triangle B in the line YZ
3.
4.
y
C
O
D
x
A
·
(a) Draw a reflection of C in the y axis
and label C’
(b) Rotate C 90º clockwise about O and
label C”
Rotate triangle D 45º anticlockwise
about the point A. Label the new
triangle D’.
5.
(a) Reflect triangle A in
the x axis and label B
A
(b) Rotate triangle A
anticlockwise 90º about O.
Label C
O
‘
C’ Practice 5 (set A15)
Handling Data: 2 Way Tables
2.
1.
Frenc
h
Male
Spanis
h
24
41
Total
Each student in Y11 studies exactly
one modern foreign language.
Complete this two-way table
3. Students were asked if they
preferred baked, chipped, or
mashed potatoes.
Boys
38
Girls
Total
bake
d
5
2
Total
Total
26
mas
h
Girls
Incorrect
58
Chips
Total
Boys
Correct
5
32
Female
Total
Germa
n
21
65
Complete the two-way table
40 Students answered a question
24 of the students were girls
7 boys got the question correct
11 girls got the question incorrect
Use this information to complete this 2 way table
4. 100 adults were asked which
sport they disliked most
football
Female
58
41
Male
59
Total
23
rugby
hocke
y
Total
11
24
35
38
100
The two-way table shows some of
the information about their answers
Complete the table.
5. Draw a two-way table to record whether boys and girls have completed
their maths homework.
Use this information to complete the table:
10 boys and 8 girls complete their homework.
There were 15 boys and 14 girls in the class.
‘C’ Practice 5 (set A16)
Handling Data: Probability
1. The probability of it raining is 0.3.
What is the probability of it not
raining?
2. A train can be early, on time, or
late.
The probability of it being late is
0.63, the probability early: 0.1.
What is the probability of it being
on time?
3. Complete this probability table:
Colour grey
Prob. 0.1
blue
4. Complete this table:
brown pink
0.3
0.2
Animal rabbit dog mouse cat
Prob. 0.22 0.4
0.26
Work out the probability of choosing
blue.
Work out the probability of a mouse
5. Complete this probability table (change all to decimals)
Colour
Probability
(a)
(b)
(c)
green
5%
yellow
red
3
10
Work out the probability of choosing yellow
What fraction chose green?
What percentage chose Blue?
blue
0.27
‘C’ Practice 5 (set A17)
Mixed Bag
1. Write the next two numbers in
each sequence
(a)
1, 5, 11, 19, 29 …..?
2. In each of these find the rule for
the nth term.
(a) 3, 7, 11, 15, …..
-8, -2, 5, 13, 22, ….?
(b) -1, 4, 9, 14, 19, ……
3. Two girls get different answers:
4. If 74 x 163 = 12062
(b)
3 + 4 x (5 – 2) = 15
Work Out:
3 + 4 x (5 – 2) = 21
(a)
0.74 x 163 =
(a) Who is correct?
(b)
12062 ÷ 740 =
(b) Explain why
(c)
75 x 163 =
5.
(a) What is the interest on £580
at 5% for 1 year?
(b) What is the Simple Interest on
£580 at 5% for 3 years?
(c) What is the Simple Interest on
£3800 at 4% for 2 years?
‘C’ Practice 5 (set B1)
Number: Accuracy and rounding
1. Write each of these numbers
correct to 1 significant figure
2. Write each of these numbers
correct to 2 decimal places
(a) 26 366
(a) 54.26741
(b) 0.0004349
(b) 0.026638
(c) 45 071
(c) 526.8449
(d) 0.050869
(d) 1.795
3. Work out the value of:
4. Work out the value of:
6.2 – 7.1²
0.7
(i) √59 – 3.4²
(write all of the figures on the
calculator display)
(a)
Write all of the figures on the
calculator display
(ii) Write down your answer to (i)
correct to 2 significant figures.
(b)
Write down your answer
correct to 2 decimal places
5. Alison said that the length of her kitchen was 3.5467m.
The length given by Alison is not sensible.
(a) Explain why her answer was not sensible
What is the length of her kitchen to
(a) 1 significant figure
(b)
2 decimal places
‘C’ Practice 5 (set B2)
Number: Standard Form
1.
(a) Write 2.7 x 10³ as an ordinary
number
2.
(a) Write 38 500 000 in standard
form
-3
(b) Write 3.12 x 10 as an ordinary
number
3.
(a) Write half a million in standard
form
(b) Write 0.000005 in standard
form
4.
Work out the value of 0.03 x 0.02
(a) Write the answer as an ordinary
number
(b) Write 0.00000036 in standard
form
(b) write the answer in standard
form
5. List these numbers in order of size smallest to largest
-5
3.7 x 10 ;
-6
0.04 x 0.008; 2.6 x 10 ;
0.05 x 0.08
‘C’ Practice 5 (set B3)
Number: Ratio
1. Share £250 in the ratio 3:7
2. Ann and John share £140 in the
ratio 2:5.
How much does Ann receive?
3. Andy, Belinda and Carl share
£126 in the ratio 5:3:1.
4. When Bill reached his 100th
How much does Belinda get?
birthday he had 12 grand daughters
and 20 grandsons.
Write down the number of grand
daughters to the number of
grandsons as a ratio in its simplest
form.
5. The ratio of blue to black pens in a packet is 3:4
(a) What fraction of the pens are black?
There are 35 pens in the packet.
(b) How many more black pens than blue pens are there?
‘C’ Practice 5 (set B4)
Factorisation and Quadratics
2. Expand these brackets
1. Factorise
(a)
x² + 2x =
(a)
7(x + 3) =
(b)
y² - 6y =
(b)
x(x + 3)
(c)
8x² - 20xy =
(c)
2y(3y – 5) =
=
3. Expand these brackets
4. Factorise
(a) (x + 1)(x + 3) =
(a) x² + 3x + 2 =
(b) (x – 6)(x + 2) =
(b) x² + 7x + 12 =
(c) (x – 4)(x + 7) =
(c) x² + 2x – 15 =
(d) x² - 2x – 35 =
5. Match an expression in cloud A with an expression in cloud B.
A
(a) x² + 5x + 6
(b) 3x² + 6x
(c) x² + 2x - 8
(d) x² - 4x - 5
(e) 8x² - 20x
B
(1) (x + 1)(x – 5)
(2) (x + 3)(x + 2)
(3) 4x(2x – 5)
(4) 3x(x + 2)
(5) (x – 2)(x + 4)
‘C’ Practice 5 (set B5)
Algebra: Trial and Improvement + Formulae
1. Use trial and improvement to
solve: x³ + 2x = 50 to 1 dec. place
Where x lies between 3 and 4.
x
3
4
x³ + 2x
big/small
27 + 6 = 33
2. Use trial and improvement to
solve:
½ x³ - x = 90 (1 dec. pl)
Where x lies between 5 and 6
x
½ x³ - x
3. Find the value of:
4. If P = q² - 5q
(a) t² - 4t when t = 3
(a) Find P when q = -2
(b) p² - 3p when p = -4
(b) Find P when q = ½
big/small
5. If I buy n first class stamps at 30p and m second class stamps at 22p.
(a) Write a formula for the total cost (T) of buying these stamps.
(b) I buy 5 first class stamps and the total cost is £3.26. How many
second class stamps did I buy?
‘C’ Practice 5 (set B6)
Graphs
2. Complete this grid for the
function:
y = 2x - 5
1. Complete this grid for the
function:
y = 3x + 1
x
-3 -2 -1 0
y
1
-2
2
3
7
3. Use the grid box from Q1 to plot &
draw the graph of y = 3x + 1
9
8
7
6
5
4
3
2
1
-3
-2
-1
x
-3 -2 -1
y
-9
-3 -2 -1
3 x
2
y
6
0
1
2
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
y
1
2
3
x
y
5. Complete the grid box
for the function y = ½ x + 7
x -3 -2 -1
3
-3
2
1
1
1 2
4. Use the grid box from Q2 to plot
& draw the graph of y = 2x - 5
y
-1
-2
-3
-4
-5
-6
-7
-8
0
8
7
6
5
4
3
2
1
3
8
Now plot the function y = ½ x + 7
on the grid provided
-3
-2
-1
-1
-2
1
2
3
x
‘C’ Practice 5 (set B7)
Shape and Space: Area and Volume
1.
Work out the area of this trapezium.
13cm
7cm
2.
Work out the volume of this cuboid.
10cm
6cm
10cm
15cm
3. A cuboid has:
4. A cuboid has:
Height = 3m
Length = 9m
Width = 5m
What is its volume?
Volume = 160cm³
Length = 8 cm
Height = 4 cm
Work out the width of the cuboid
5. A box in the shape of a cube
has sides of length 2 cm.
These cube boxes are placed into
a larger cuboid box with dimensions
Height = 8cm
Length = 10cm
Width = 6cm
How many cubed boxes fit into
the cuboid box exactly?
‘C’ Practice 5 (set B8)
Shape and Space: Circles
2. The radius of a
circle is 5.2 m.
1. The radius of a
circle is 6.4 cm.
5.2m
6.4cm
Work out the area of
the circle. (Answer
correct to 3 sig. figs)
Work out the
circumference of the
circle. (correct to 2 d.p)
3
4. AS and AT are
tangents to a circle
centre O.
A
AT and BT are
tangents to a
circle centre O.
T
O
B
If angle AOB is 140º:
(a) Name any right angles
(b) Find the size of angle ATB
S
O
A
T
Calculate the size of angle
SAO if angle SOA is equal to 48º.
5. A cycle has a wheel diameter 0.8 m.
The wheel goes round 25 times.
How far has the cycle moved, give your
answer correct to 3 significant figures
‘C’ Practice 5 (set B9)
Shape and Space: Trigonometry and Pythagoras
1.
A
9m
2.
B
A
8.3m
2.5m
5m
B
Work out the length of BC
C
Use Pythagoras to work out the
length of AC.
3.
A
24º
B
4.
C
A
2.4m
7.4cm
Calculate the length AB
C
B
3.8m
Find angle BAC.
5. The diagram shows the distance between three towns.
Calculate the Bearing of Aitown from Beetown
C
Beetown
9.5 km
Ceetown
Aitown
15.2 km
‘
C’ Practice 5 (set B10)
Shape and Space: Transformations
1. The big triangle is a scale factor
enlargement of the smaller triangle.
Find x and y
y
15cm
3cm
2. The big trapezium is a scale
factor 4 enlargement of the smaller
trapezium. Find x, y and z.
z
x
y
4cm
60º
5cm
4cm
x
8cm
12cm
16cm
3. Enlarge this L by scale factor 2
about point A.
4. Enlarge this shape by scale
factor ½ about point X.
X
A
5. Describe fully the single translation that takes shape A to shape B
B
A
‘C’ Practice 5 [less 1] (set B11)
Handling Data: Stem and leaf and cumulative frequency
1. Complete this stem and leaf
diagram for the weights of 10 newly
born boys.
2. The stem and leaf table shows
the number of students late each
day to school last month
4.1kg, 3.6kg, 4.5kg, 2.9kg, 3.8kg,
3.2kg, 3.6kg, 2.8kg, 3.7kg, 2.5kg
1 2 3 3 6 6 8 9
2 0 1 1 5 6 9
3 0 0 2 2 2 4 6 7
Weight of boys
2
3 6
4 1 5
Key
1 2 means
12 students
absent
(a) Find the median
(b) Work out the range
3. 60 students took a test, the graph shows information about their marks
Cumulativ
e
60
Frequency
55
(a) What was the median
mark?
50
45
40
35
30
25
20
15
10
5
(b) What was the lowest
mark?
(c) Estimate how many
students scored 12 or less
marks.
2 4
6 8 10 12 14 16 18 20
Mark
(c) Estimate the interquartile
range?
4. This box plot shows information about 40 students’ test marks
20
56
22
58
24
26
28 30
32
34
36
38 40
42
44
46
48
Decide which of these statements are true and which are false
(a)
(b)
(c)
(d)
The top mark was 57
The lowest mark was 22
The Range was 35
The Median was 44
(e)
(f)
(g)
50 52
Mark
54
10 students scored less than 31
The interquartile range was 44
½ the students scored less than 38
‘C’ Practice 5 (set B12)
Handling data: pie charts and scatter graphs
1. Sixty Y11 students were asked –
What do you want to do next year?
Their replies are shown in the Pie chart
How many students hoped to go to
college?
College
120º
Sixth
Form
2. Forty students took the
Intermediate maths exam last year.
Grade ‘B’ - 3
Grade ‘C’ - 15
Grade ‘D’ - 14
Grade ‘E’ - 8
If these results were shown in a Pie
Chart, what is the size of angle for
each grade?
60º
Don’t Work
Know
3. Here is a scatter graph. One axis is
labelled ‘Height’
(a) For this
x xx xx
x x x x
graph state
x x x x
x
x x x
x
the type of
x x x x
correlation
x x x
x
4. For each scatter graph draw in
probable correlations
Height
Height
x
Height
(b) Circle the most appropriate label for
the other axis –
GCSE maths mark
No. of cousins
Size of feet
Colour of eyes
Colour of eyes
5. Lose-a-lot Comprehensive School played 30 hockey matches.
The table shows information about their results.
Won
Drawn
Lost
7
3
20
Complete the Pie Chart.
Age
‘C’ Practice 5 (set C1)
Rounding and Estimation
1. Estimate the value of:
79.7 _
2.13 x 7.85
No
3. The length of a newly born baby is
56cm. (to the nearest cm)
(a) What is the longest length
(b) What is the shortest length
That the baby can be?
2. Estimate this
14.74 x 19.3
6.076 + 3.85
No
4. The weight of a car is 843 kg (to
the nearest kg).
(a) What is the heaviest
(b) What is the lightest
weight that the car can be?
5. Using a calculator work out the value of –
14.23 x 3.98
2.31 + 5.84
(a) Write down the calculator display.
(b) Write down the answer to the
appropriate degree of accuracy.
‘C’ Practice 5 (set C2)
Place Value, LCM and Ordering
1. Using the information that
14 x 23 = 322
Write down the value of
2. Using the information that
58 x 117 = 6786
Write down the value of
(i) 1.4 x 2.3 =
(i) 0.58 x 117 000 =
(ii) 322 ÷ 2.3 =
(ii) 67.86 ÷ 5.8 =
3. Use the information that
4. Use the information that
11 x 19 = 209
39 x 17 = 663
To find the Lowest Common
Multiple (LCM) of 33 and 19.
to find the Lowest Common
Multiple (LCM) of 13 and 17.
5. Write these numbers in order of size.
Start with the smallest number
(i) 0.73; 0.084; 0.8; 0.82; 0.802 ………………………………………………
(ii) 4; -5; -9; 1; -3
(iii) 1
2
2
3
2
5
3
4
………………………………………………
.................................................................
‘C’ Practice 5 (set C3)
Indices and Standard Form
1. Work out the value of (3²)³
2. Work out the value of –
3
5
(i) 6 x 6
7
4
(ii) 6 ÷ 6
3. The approximate distance to the
Sun is 93 000 000 miles.
Write this number in standard form.
4. Work out
(6.1 x 105) x (5.8 x 104)
Give your answer in standard form
correct to 2 significant figures.
m
5. The number 28 can be written as 2 x n where m and n are prime
numbers.
Find the value of m and n.
‘C’ Practice 5 (set C4)
Percentages
1. I spend 35% of £600.
How much money have I left?
2. There were 250 pupils in Y10.
120 of these were girls.
What is this as a percentage?
3. In the MIF kitchen sales, there
was 20% off every kitchen.
I paid £1200 for my kitchen units.
What was their price before the sale
4. Wow TV/DVD player 30% off.
New Price = £126
What is the normal price (pre sale
price).
5. A new motor-bike costs £2400 but depreciates 10% in value each year.
(a) What is its value after 1 year?
(b) What is its value after 3 years?
‘C’ Practice 5 (set C5)
Ratio and Fractions
1. Share £720 in the ratio 5:1
3. Work out
3 - 2
4 3
2. Share £320 in the ratio 1:3:4
4. Express
5 x 2
8
9
in its simplest form.
5. Amjad and Bhati share £270 in the ratio 2:7.
(a) How much do Amjad and Bhati each receive?
Amjad gives ¼ of his share to Chaz
Bhati gives 4/7th of his share to Chaz.
(b) How much does Chaz receive?
(c) What fraction is this?
‘C’ Practice 5 (set C6)
Proportion
1. If 8 pens cost 72p.
How much do 5 pens cost?
2. If 3 coffees cost £4.17
What would 7 coffees cost?
3. These two triangles are similar
Find x and y (lengths in cm)
4. A photo is enlarged as shown
65
90
30
20
y
x
12
50
70
5
5. This recipe will make 12 cookies
(a) How much sugar would you
need for 18 cookies?
(b) Rewrite the recipe to make
36 cookies.
Show that these two rectangles are
not similar (lengths in cm)
150g butter
200g granulated sugar
300g of self-raising flour
100g of chocolate chips
1 egg
A few drops of vanilla
essence
A pinch of salt
‘C’ Practice 5 (set C7)
Money Questions and Currency Exchange
1. A class go on a visit by train.
Each ticket costs £2.45.
How much will 27 tickets cost?
2. The weight of a box is 17.6 kg.
What is the weight of 38 boxes?
3.
4.
£1 = 1.47 euros
An iPod costs 118 euros in Spain
The same iPod costs £79.50 in
Birmingham. Which is best value?
£1 = 2.15 Australian dollars
What is the value of Aus $800 in
pounds?
5. Prize money in a similar TV Challenge game in different countries is –
USA - $100 000
where £1 = $1.85
Germany – 80 000 euros where £1 = 1.47 euros
Which is the greatest prize and by how much.
‘C’ Practice 5 (set C8)
Algebra: Expressions
1. Simplify:
(i)
x+y+x+y+x
2. Expand and simplify:
2(4a + 2) – 3(2a – 4)
(ii)
4d + 5e – 3d – 2e
3. Simplify:
(i)
r² + r² + r²
(ii)
4. Simplify
(i) 3a²b x 7ab³
(ii)
3q² - q²
(x + 2)²
(x + 2)
5. This table shows some expressions
3(y + y)
3y + y
2y x 3y
3y + 3y
3 + 3y
Two of the expressions always have the same value as 6y.
Tick the boxes underneath the two expressions
‘C’ Practice 5 (set C9)
Algebra: Inequalities
1. If -2 < m ≤ 4
And m is an integer
2. Given -3 ≤ p < 2
And p is an integer.
Write down all of the possible
values of m.
Write down all of the possible
values of p.
3. Solve the inequality
4. Solve the inequality
2x + 7 > 1
5.
3y - 6 < 15
y
4
The line with equation
2y + x = 4 is drawn on the
grid.
3
2
1
-1
O
-1
x
1
2
3
4
(i) On the grid, shade the
region of points whose
coordinates satisfy the four
inequalities y > 0; x > 0; 2x < 3;
2y + x < 4
‘C’ Practice 5 (set C10)
Algebra: Equations (and simultaneous!)
1. Solve
4x – 9 = 13
2. Solve 15r – 4 = 7r + 12
3. Solve 6 – 5x = 2(2x – 6)
4. Solve
5. (i) Factorise x² - 5x - 12
(ii) Solve the equation
x² - 5x - 12 = 0
x + 3y = 13
3x + 2y = 4
‘C’ Practice 5 (set C11)
Graphs: Straight Line
1. A straight line has equation
y = 3x - 8
2. A straight line has equation
y = 3(3 – 2x)
(i) Find the gradient of the line
Find the gradient of the straight
line
(ii) Find the intercept of the line
3. A straight line has equation
y = 3x + ½
y = ½ x +3
Write down the equation of a line
parallel to this line.
5.
y
7
The point P lies on the straight line.
P has a y-coordinate of 5.
Find the x-coordinate of P
ABCD is a rectangle
A is the point (0,1)
C is the point (0,7)
C
B
The equation of the straight line
through A and B is y = 2x + 1.
D
1 A
0
4. A `straight line has equation
x
Find the equation of the straight line
through D and C.
‘C’ Practice 5 [less 2] (set C12)
Graphs: Travel and curved
1.
This2.is part of a travel graph of Mo’s journey
from his house to the Sports Hall and back.
34
32
30
28
Distance 26
in km from 24
22
Mo’s
20
house
18
16
14
12
10
8
6
4
2
(i) Work out Mo’s speed for the first 30 mins of
his journey. Give your answer in km/h.
Mo spent 10 mins at the Sports Hall collecting
his sister. Then travels back to the house at
60 km/h.
(ii) Complete the travel graph
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Time in minutes
2.
A4.
girl left home at 12 noon to go for a cycle ride.
The travel graph represents part of the journey.
20
At 12.30 pm the girl stopped for a rest
18
Distance
from 16
home
in km 14
(i) For how many minutes did she rest?
12
10
4
The girl stopped for another rest at 2 pm.
She rested for one hour.
Then she cycled home at a steady speed. It took
her 1hr 30 mins.
2
(ii) Complete the travel graph
8
6
12 noon
time
1pm
2pm
3pm
4pm
5pm
3. (a) Complete this table of values
For y = x³ + x - 2
x
-2
y
-12
-1
0
1
y
10
8
6
4
2
2
0
(b) On the grid draw the graph
-2
Of y = x³ + x - 2
-1
O
-2
-4
-6
-8
-10
1
2
x
‘C’ Practice 5 (set C13)
Shape and Space: Surface Area and Volume
1.
The area of the cross
section of the triangular
prism is 20 cm².
12 cm
2.
9
All measurements
10 are in cm.
The length is 12 cm
Work out the volume of
the prism.
20 cm²
3.
5 cm
10cm
The cylinder has
a height of 10cm
and a radius of
5cm.
Calculate the
volume of the
cylinder.
5.
7
4
4. Radius = 3cm
Height = 10 cm
Calculate
surface area
correct to 3
significant figs.
Work out the
surface area of
this triangular
prism
3cm
10 cm
This solid cylinder of ice has radius 4.2cm and
a thickness of 1.9cm.
1.9cm
The ice has a density of 0.9 grams per cm³
4.2 cm
Work out the mass of the ice, correct to three
significant figures.
‘C’ Practice 5 (set C14)
Shape and Space: Units change; Measures Length, Area, Volume
1. Change 4m² to cm² (Be careful!)
2. Change 45 cm² to mm².
3. In these expressions a, b and c
represent lengths. The numbers
have no dimension.
Two of the expressions could
represent areas, tick the box
underneath these expressions
4. In these expressions a, b and c
represent lengths. π and 2 have
no dimension.
Three of the expressions could
represent areas, tick the box
underneath these expressions
(a+b)c
ac + b
3abc
3a² + 2b²
ab + bc
2a
πa³
2ab
πa² + b² π(2a + b) a(b + c)
5. In these expressions a, b, c and d represent lengths. π and 2 have no
dimension.
The expressions could represent either: length(L), area(A) or volume(V) or
none(N) of these. Write in the box underneath each expression whether it
is length, area, volume or none.
2a²
πa²b
2a³
a(b + c)
ab + cd
πa
2a² - πb
2
2d(ab + c²)
‘C’ Practice 5 (set C15)
Shape and Space: Polygons and Angles
1. Work out the exterior angle of an
octagon.
2.
yº
108º xº
(i) Work out angle x (give reasons)
(ii) Work out angle y (give reasons)
?
3. ABCD is a quadrilateral, work out
the size of the largest angle.
A
B
119º
3yº
(x + 47)º
87º
yº
73º
D
C
5.E
4. Work out the size of the missing
angles in this pentagon.
A
xº
106º
(2x + 20)º
ABCD is a rhombus.
All the sides of the shape are equal in
length.
Work out the size of each of the angles.
B
D
C
‘C’ Practice 5 (set C16)
Shape and Space: Circle Geometry
1.
If AB is the diameter
of the circle, give a
reason why angle
B ACB is a right angle
A
C
2.
115º
B
D
Given angle BCD
equals 115º.
(i) Work out the
size of angle
BAD.
(ii) Give a reason
for your answer
C
A
4.
3. A, B, C and D
are points on a A
circle.
In the circle centre O
the angle BOD = 96º
A
B
O
(i) Find angle BAD
96º
Angle ADB = 54º
54º
D
x
B
C
(ii) Work out
Angle BCD.
C
Work out angle ACB
Give a reason for your answer.
5.
A, B, C and D are 4 points on the circumference
of a circle. Angle BAC = 35º. Angle EBC = 60º
C
D
D
E
(i) Find the size of angle ADC.
60º
B
35º
A
(ii) Find the size of angle ADB.
‘C’ Practice 5 (set C17)
Shape and Space: Construction
1. Use ruler and compasses to construct
an equilateral triangle of side length 3cm.
2. Construct a triangle of sides
length 3cm, 4cm and 5cm.
3. Use ruler and compasses to construct a
perpendicular to the line AB at point P.
4. Use ruler and compasses to
construct a right angle.
A
P X
B
5. The diagram shows a triangular prism
The cross-section of the triangular prism
is an equilateral triangle
Draw a sketch for the net
of the triangular prism
‘C’ Practice 5 (set C18)
Shape and Space: Trigonometry and Pythagoras
1. Find the length of AC in this right
angled triangle.
A
5 cm
B
2. Find the length of AC in this right
angled triangle.
A
10.5cm
B
12cm
17.5cm
C
C
3. Find the size of the angle marked
x. Give your answer to 1 dec. pl.
4. Find the length of AB. Give your
answer correct to 3 significant figs.
A
10cm
12cm
x
70º
B
5.2cm
C
5. A lighthouse L is due East of a harbour, H.
A yacht Y is 3.2 km due North of the lighthouse.
(a) Find the distance of the yacht from the harbour HY
(b) Calculate the size of the angle marked x.
Give your answers correct to 3 significant figures.
Y
xº
3.2
H
3.7
L
‘C’ Practice 5 (set C19)
Shape and Space: Elevations and Transformations
1. On the grid enlarge the shape
with a scale factor of 2
2. On the grid enlarge the shape
with a scale factor of ½.
3. Given the elevations of a 3D shape
4. The diagram shows a solid object
plan
side
elevation
front elevation
sketch it below.
Draw a plan, front and side elevation
for this object
5. Here is a plan and front elevation of a prism
plan
Front elevation
(ii) Make a 3D sketch
of the prism
(i) On the grid draw a side elevation
‘C’ Practice 5 (set C20)
Handling Data: Means and Moving Averages
1. The table shows how much TV 20
students watched in a week.
No. of hours
0<h≤20
20<h ≤40
40<h≤60
Frequency
8
7
5
2. This table shows how much
money 25 students had at school.
Amount (£)
0<t≤4
4<h ≤8
8<h≤12
Frequency
11
3
11
Work out an estimate for the mean
number of hours that students
watched the TV.
Work out an estimate for the mean
amount of money that each
student has.
3. The table shows the number of
flower bouquets delivered each day
of a week
4. The table shows the daily
takings for an ice-cream salesman.
day
No.
Mon
12
Tue
8
Wed
13
Th
15
Fri
14
Sat
19
Work out the 3 day moving average
for this data.
Day Mo
(£) 50
Tu
36
We
24
Th
90
Fr Sa Su
130 156 264
Work out the 4 day moving average
for this data
5. The table shows information about how much 50 students earn from
their part-time jobs per week
Amount (£)
0<a≤10
10<a ≤20
20<a≤30
30<a≤40
40<a ≤50
50<a≤60
Frequency
6
4
12
6
16
6
Work out an estimate for the
mean amount each receives.
‘C’ Practice 5 [less 1] (set C21)
Handling Data: Mixture
1. Shahid listed the number of goals
scored by each team in his local
hockey league in order -
2. Here are the times, in minutes
taken to complete maths homework
7, 12, 13, 18, 19, 24, 31, 34, 39, 42, 56
12, 25, 19, 24, 27, 31, 37, 11, 28,
29, 35, 38, 10, 11, 27, 32, 29, 16
Find (i) The lower quartile
(ii) The upper quartile
Draw a stem and leaf diagram to
show this.
4.
3. 100 students took a test, the graph shows
information about their marks
No. students
(i) Estimate the lowest and
100
highest marks?
90
80
70
(ii) Estimate the median
60
score?
50
40
30
(iii) Find the inter-quartile
20
range?
10
00 10 20 30 40 50 60 70 80 90
marks
100
4. This box plot shows information about the time taken for 24 girls at the
swimming club to swim 800m in training.
Describe the times
of the swimmers
with reference to
median, slowest,
fastest and interquartile range.
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 mins
24 25
‘C’ Practice 5 (set C22)
Handling Data: Probability and Tables
1. Mrs Green, the head of the Sports
College, plays one sport every day. She
chooses hockey, swimming or netball.
The probability she chooses hockey is 0.3.
The probability she chooses netball is 0.25.
What is the probability she chooses
swimming?
2. 120 people who buy coffee were
surveyed as follows –
powder
50g
100g
200g
Total
2
15
12
granules
4
21
filter
0
Total
50
55
120
Complete the two-way table
3. A box contains cubes that are red,
yellow, blue and purple.
flavours mint, fruit, cola, fizz and choc
The probability of taking a cube of a
certain colour is shown in the table.
The probability of taking a flavour of
sweet is shown in the table.
Colour red
Prob
0.15
Flavour mint fruit cola fizz
Prob
10% 0.35 0.15 25%
yellow
blue
0.3
0.4
purple
Work out the probability that you will
take a purple cube.
4. A packet contains sweets with
Work out the probability that you
will take a choc flavoured sweet.
5. A dice is biased
The probability that the dice will land on each of
the numbers 1, 3 and 4 is given in the table.
The probability that the dice will land on either
a 2, 5 or 6 are equal.
Number
1
2
3
4
Probability
0.2
x
0.15
0.2
(i) Work out the value of x
(ii) The dice is thrown 200 times
Write an estimate for the number
of times it will land with a 3.
choc
4
6
5
x
5
6
x
‘C’ Practice 5 (set C23)
Handling Data: Probability and Probability Trees
1. Shay throws a dice 60 times. He
scores 6 twenty times.
Is the dice fair? Explain.
2. The probability of a green light
at traffic lights is 50%.
What is the probability of hitting
green lights at two consecutive
traffic lights?
3. Complete this Probability tree for
throwing a fair red dice and a fair
Blue Dice
blue dice.
4. Look at question 3.
What is the probability of not
throwing a six with either a red or a
blue dice?
six
Red Dice
1
6
six
Not
six
six
Not
six
b
5. We have 10 CDs in the car. Four belong to my mother and are by Cliff
Richard.
I take one of these CDs at random and play it and then put it back.
I then take another CD at random to play.
(i) Complete this probability
Cliff
tree diagram
…….
Richard
0.4
…….
Cliff
Richard
…….
Not Cliff
Richard
…….
Cliff
Richard
…….
Not Cliff
Richard
Not Cliff
Richard
(ii) What is the probability of
picking a Cliff Richard CD
twice?