Howden School
Year 7 Mathematics
Homework Booklet
Half Term 1 L6-7
Please complete your maths homework regularly – each week
is broken into three sections. Section A, which checks your
recall of key ideas and skills Section B is a task based on
recent work and a ‘challenge’ task (a problem for you to try
and solve). Hand your work in regularly and your teacher will
let you know how well you are doing and what progress you
are making – good luck and have fun!
Name
Maths Teacher
Hand this booklet in
Tutor group
Dear Parent
As outlined on the front cover, mathematics homework in year 7 is
organised in a three section format. The Section B tasks are split
into different levels and your child should attempt work in line with
their working level and target. Your child should attempt Section A
and the level ____ task of Section B, each week unless otherwise
directed by their teacher – this may mean them completing
questions at one or both levels. The challenge tasks are short
problem solving activities that any pupil can attempt. These
questions are taken from ‘UKMT Mathematics Challenge’ papers –
some pupils will take part in the annual national UKMT Challenge
during year 7.
Your child’s working level at the start of year 7 and their end of
year 7 target level is shown at the bottom of this page.
Any task that has a bold heading or is marked with an asterisk (*)
indicates that the task is linked to a key area of maths, which needs
to be understood in order to contribute towards being confident
working at that level. These areas will be assessed in more detail in
lessons and formal assessments.
We hope that your child enjoys attempting their maths homework
and achieves success in the process.
Howden Mathematics Department.
KS2 level
End of Year 7 Target
2
HOMEWORK 1
SECTION A
1 What is the area of the shape?
Show your working.
2
What is the volume of the
solid? Show your working.
4cm
2cm
8cm
3cm
3
Calculate the circumference of
a circle with a diameter of
7.4cm.
5 Find the nth term for the
following sequence.
3, 5, 7, 9, 11, …
8cm
4
Given the function
x→x + 3
What is its inverse?
6
If a = 2, b = 3, and c = 5
What is the value of:
b2 – 4ac
7 Multiply 245 by 26. You must
show your working.
8
Divide 2871 by 3. You must
show your working.
9 Expand the bracket:
10 Find the median for the
following data:
5(3a – 4)
3, 8, 5, 3, 0, 1, 11, 4
3
SECTION B
Level 6
Work out the area of each of the shapes below:
1)
…………………………………………………………………………………………………………………
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…………………………………………………………………………………………………………………
4
2)
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
5
3)
The letter H below is from a helipad; it is drawn to scale. Each
centimetre represents one metre.
What is the area of the H on the helipad?
(You will need to measure the sides and use a calculator.)
………………………………………………………………
..................................................................
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6
LEVEL 7
Calculate the area of the following shapes. All
measurements are given in centimetres.
1
2
3
7
4
Find the missing length shown on the diagrams. All areas
are in square centimetres.
1
2
8
3
4
Challenge
Which of these calculations produces a multiple of 5?
1 2  3  4
C 1 2  3  4
E 1 2  3  4
A
1 2 3  4
D 1 2  3 4
B
From UKMT 2008
9
HOMEWORK 2
SECTION A
1 What is the area of the shape?
Show your working.
2
What is the volume of the
solid? Show your working.
9mm
9mm
4.5cm
12mm
3
Calculate the circumference of
a circle with a diameter of
12cm.
20mm
4
Given the function
x→x - 4
What is its inverse?
5 Find the nth term for the
following sequence.
5, 8, 11, 14, 17,…
6
If a = 11, b = 3, and c = 2
What is the value of
b2 – 4ac
7 Multiply 84 by 47. You must
show your working.
8
Divide 756 by 6. You must
show your working.
9 Expand the bracket:
10 Find the mode for the following
data.
5, 2, 7, 2, 3, 8, 5, 0
3(5c + 7)
10
SECTION B
Level 6
1)
Calculate the volume and surface area of the cuboid.
Volume=
………………………………………
………………………………………
7cm
5cm
9cm
………………………………………
………………………………………
Surface Area =
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
11
2)
Choose a box. This could be a cereal box
Sketch your box in the space below.
Label the lengths of the edges.
Calculate the volume.
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
Calculate the surface area =
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
LEVEL 7
Calculate the volume and surface area for the following prisms:
12
1.
10 cm
7 cm
……………………………………………………
4 cm
3 cm
3 cm
5 cm
……………………………………………………
……………………………………………………
…………
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13
2.
6 cm
……………………………………………………………………………………
14cm
cm
……………………………………………………………………………………
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14
Challenge
Which of these diagrams could be draw without taking the pen off
the page and without drawing along a line already drawn?
A
B
D
E
C
From UKMT 2008
15
HOMEWORK 3
SECTION A
1 What is the area of the shape?
Show your working.
2
What is the volume of the
solid? Show your working.
3
4
Given the function
x→2x
What is its inverse?
5 Find the nth term for the
following sequence.
4, 9, 14,19, 24, …
6
If a = 7, b = 1, and c =-1
What is the value of
b2 – 4ac
7 Multiply 16.5 by 12. You must
show your working.
8
Divide 45.6 by 4. You must
show your working.
9 Expand the bracket
x(x +5)
10 Find the range for the following
data:
7, 6, 8 ,2, 9, 0, 12, 4, 7
Calculate the circumference of
a circle with a radius of 6cm.
16
SECTION B
Level 6
Write the first 6 terms of the following sequences from the
descriptions.
1)
Starts at -3 and doubles each time.
…………………………………………………………………………………………………………………
2)
Starts at -4 and halves each time.
…………………………………………………………………………………………………………………
3)
Starts at -3 and decreases by 11.
…………………………………………………………………………………………………………………
4)
Start at 7 add 1 then divide by 2.
…………………………………………………………………………………………………………………
Fill in the spaces and describe the pattern.
5)
……, 15, 18, ……, 24, ……, …….
…………………………………………………………………………………………………………………
6)
72, 63, ……, 45, ……, ……,
…………………………………………………………………………………………………………………
7)
1, 1, 2, 3, 5, ……, 13,…… , …… , 55
…………………………………………………………………………………………………………………
17
LEVEL 7
Find the inverse functions f-1(x) for the following:
1. f(x) = x + 5
2. f(x) = x – 4
3. f(x) = 4x
4. f(x) = 2x + 3
5
3
5. f(x) = 2x

6. f(x) = 2x
5
3
Challenge
At Spuds-R-Us, a 2.5kg bag of potatoes costs £1.25. How much
would 1 tonne of potatoes cost?
A £5
B £20
C £50
D £200 E £500
From UKMT 2008
18
HOMEWORK 4
SECTION A
1 What is the area of the shape?
Show your working.
2
What is the volume of the
solid? Show your working.
3
4
Given the function
x→3x
What is its inverse?
5 Find the nth term for the
following sequence.
6, 10, 14, 18, 22,…
6
If a = 3, b = -5, and c = 1
What is the value of
b2 – 4ac
7 Multiply 5.65 by 17. You must
show your working.
8
Divide 13.25 by 5. You must
show your working.
9 Expand the bracket
10 Find the mean for the following
data.
7, 5, 9, 6, 4, 5,
Calculate the circumference of
a circle with a radius of 5.7m
4a(3 – 2b)
19
SECTION B
Level 6
Find the nth term for the following sequences.
a)
3,
5,
7,
9, …
……………………………………………………………………………………………………………………………
………………………………………………………………………………………………………
b)
8,
11,
14,
17, …
……………………………………………………………………………………………………………………………
………………………………………………………………………………………………………
c)
50,
45,
40,
35, …
……………………………………………………………………………………………………………………………
………………………………………………………………………………………………………
d)
-5,
-11, -17, -23, …
……………………………………………………………………………………………………………………………
………………………………………………………………………………………………………
e)
1,
4,
9,
16, …
……………………………………………………………………………………………………………………………
………………………………………………………………………………………………………
20
Write the first 5 terms for the nth terms below.
f)
2n + 7
……………………………………………………………………………………
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g)
5n – 3
……………………………………………………………………………………
…………………………………………………………………………
h)
3n - 8
……………………………………………………………………………………
…………………………………………………………………………
i)
10 – 3n
……………………………………………………………………………………
…………………………………………………………………………
j)
n2 + 6
……………………………………………………………………………………
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21
LEVEL 7
Generate the first 5 terms for these sequences:
a) 2n2 + n
……..…………………………………………………………………………………………………………
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b) 5n2 – 2n
……..………………………………………………………………………………………………………………
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c) 3n2 + n -12
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22
Find the nth term for the following:
a)
2, 8, 18, 32, …
……..………………………………………………………………………………………………………………
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……………………………………………………………………………………………………………………..
b)
2, 11, 27, 47. …
……..………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………
c)
-2, 5, 16, 31, …
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23
Challenge
The diagram shows a single floor tile in which the outer square has
side 8cm and the inner square has side 6cm. If Adam Ant walks
once around the perimeter of the inner square and Annabel Ant
walks once around the perimeter of the outer square, how much
further does Annabel walk than Adam?
A 2 cm
E 16 cm
B 4 cm
C 6 cm
D 8 cm
From UKMT 2008
24
HOMEWORK 5
SECTION A
1 What is the area of the shape?
Show your working.
5cm
2
What is the volume of the
solid? Show your working.
4
Given the function
x→2x + 6
What is its inverse?
5 Find the nth term for the
following sequence.
15, 12, 9, 6, …
6
If a = -1 , b = 4, and c = 2
What is the value of
√𝑎 2 + 𝑏 2
7 Multiply 32.5 by 4.3. You must
show your working.
8
Divide 39.48 by 12. You must
show your working.
9 Expand the brackets and
simplify.
3(x – 4) + 2(2x + 5)
10 Find the median for the
following data
5, 9, 5, 6, 3, 4, 7,12
6cm
8cm
3
Calculate the area of a circle
with a radius of 4cm
25
Section B of homework 5 will be issued as a separate
booklet by your teacher.
26
HOMEWORK 6
SECTION A
1 What is the area of the shape?
Show your working out.
2
What is the volume of the
solid? Show your working.
3
4
Given the function
Calculate the circumference of
a circle with a
What is its inverse?
5 Find the nth term for the
following sequence.
6
If a = , b = , and c =
What is the value of
7 Multiply by . You must show
your working out.
8
Divide by . You must show
your working out.
9 Expand the bracket
10 Find the for the following data
27
SECTION B
Level 6
Complete the table:
X10
X100
X1000
÷10
÷100
÷1000
5.5
13.45
248.9
603.07
28
LEVEL 7
Work out the following without using a calculator
1. 4.8 x 0.2 =
2.
324 x 0.1 =
3. 72.5 x 0.01 =
4.
14.6 x 0.04=
5. 15.4 ÷ 0.1 =
6.
12.8 ÷ 0.02 =
7. 245 ÷ 0.05 =
8.
0.4 x 0.4 =
9. 1.22 =
10. 2.25 ÷ 0.15 =
29
Work out the following showing a clear written method:
23.54 x 1.25
0.35672 ÷ 0.14 =
Challenge
All of the Forty Thieves were light-fingered, but only two of them
were caught red-handed. What Percentage was that?
A2
B5
C 10
D 20
E 50
From UKMT 2008
30
HOMEWORK 7
SECTION A
1 What is the area of the shape?
Show your working.
2
What is the volume of the
solid? Show your working.
4cm
2cm
8cm
3cm
3
Calculate the circumference of
a circle with a diameter of
7.4cm.
5 Find the nth term for the
following sequence.
3, 5, 7, 9, 11, …
8cm
4
Given the function
x→x + 3
What is its inverse?
6
If a = 2, b = 3, and c = 5
What is the value of:
b2 – 4ac
7 Multiply 245 by 26. You must
show your working.
8
Divide 2871 by 3. You must
show your working.
9 Expand the bracket:
10 Find the median for the
following data:
5(3a – 4)
3, 8, 5, 3, 0, 1, 11, 4
31
SECTION B
Level 6
Round the following to 2 and 3 decimal places
2 dp
3 dp
37. 4275
……………
……………
12.05062
……………
……………
84.3969
……………
……………
21.25843
……………
……………
248.0118
……………
……………
34.89959
……………
……………
32
Worded problems
1.
Holly buys three items costing £1.35, £5.47 and £6. 99. She
calculates the price then rounds to the nearest pound. How
much change, to the nearest pound, will she get from a £20
note?
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
2.
If Holly rounds the original prices to the nearest pound and
calculates the change. Why are the answers different?
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
33
Level 7
Round the following to 1 and 2 significant figures
1 sig fig
2 sig fig
37. 4275
……………
……………
12.05062
……………
……………
84.3969
……………
……………
21.25843
……………
……………
248.0118
……………
……………
34.89959
……………
……………
Estimate the solutions to the following, show your method.
214 x 29
19 x 34
945 ÷ 8.91
28.19 ÷ 6.33
5.4122
15.21 – 3.842
34
Challenge
King Harry’s arm is twice as long as his forearm, which is twice as
long as his hand, which is twice as long as his middle finger, which is
twice as long as his thumb. His new bed is as long as four arms. How
many thumb lengths is that?
A 16
E 256
B 32
C 64
D 128
From UKMT 2008
35