Howden School and
Technology College
Year 7 Mathematics
Homework Booklet
Half Term 2
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, two or even three
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 8
SECTION A
1 A rectangle has a length of 7cm
and an area of 21cm2. What is
its perimeter?
2
Change 5430ml into litres.
3 What is 12.3 + 2.035?
4
What is 11.06 – 2.035?
5 A cuboid has a base of 5cm,
length 10cm and height 6cm.
What is its surface area?
6
List all the factors of 24.
7 What is the outcome if I subtract 8
an even number from an even
number?
9 What is 652 x 13?
What is 14 squared?
10 Divide the following numbers by
10.
6
4.5
0.25
3
SECTION B
Note that there are 2 sections to this homework you need to do the
correct level from BOTH sections.
Level 4
Produce a tally chart for the data below:
Pink
Red
Pink
Green
Yellow
Pink
Colour
Yellow
Blue
Red
Red
Red
Blue
Blue
Green
Blue
Red
Blue
Green
Green
Red
Orange
Blue
Green
Pink
Pink
Blue
Blue
Green
Yellow
Purple
Tally
4
Use the following frequency table to complete the bar
chart.
Type of transport
Bike
Bus
Car
Lorry
Van
Frequency
10
10
50
15
5
5
Level 5
Produce a tally table by grouping the following data. They are
students’ heights in centimetres
153
152
149
159
161
164
152
152
156
162
157
141
152
149
164
137
142
166
148
152
149
158
153
168
167
Height (cm)
130 - 134
135 - 139
6
Draw a bar chart to show the following information:
Days off school
0-4
5-9
10-14
15-19
20+
frequency
18
6
3
2
1
7
Level 6
Time Taken to Travel to School
12
Frequency
10
8
6
4
2
0
0-10
11-20
21-30
31-40
41-50
Time (minutes)
Produce a frequency table for the data shown in the bar chart
above.
8
Draw a Duel bar chart for the following information:
Test result (out of 60)
0-10
11-20
21-30
31-40
41-50
51-60
Science
8
17
40
25
10
0
Maths
1
8
50
25
15
1
9
Second Section Homework 8
Use the bar chart to answer the questions you are set. (all
levels)
How Students Travel to School
Frequency
50
40
30
20
10
0
Walking
School
Bus
Service
Bus
Car
Bicycle
Method of Transport
Level 4
1.
Which method of travelling
to school is the mode?
2.
How many students travel
to school by car?
………………………………………
……………………………………..
10
Level 5
1.
2.
How many students does each
small section of the frequency
axis represent?
………………………………….
How many more students
walk to school than cycle?
………………………………….
Level 6
1.
How many students are represented
by the bar chart?
2.
True or False? More students travel to school by bus
than by all the other methods together.
………………………………….
………………………………….
Challenge
The faces of a cube are painted so that any two faces which
have an edge in common are painted different colours. What is
the smallest number of colours required?
A2
B3
C4
D5
E6
From UKMT 2008
11
HOMEWORK 9
SECTION A
1 Find 35% of 40.
2
What is ¾ of 60?
3 What is;
4
What is 564 ÷ 3
5 Write 0.24 as a percentage and
a fraction in its simplest form.
6
What is 33?
7 Find the median for the
following data:
8
Two angles in a triangle are 38°
and 74°. What is the third
angle?
4, 7, 5, 11, 3, 8, 4, 12
9 What is -7 + -13 ?
10 Find the HCF of 20 and 35
12
SECTION B
Level 4, 5 and 6
Decide if the following statements, about a standard pack of
playing cards, are true or false. CIRCLE your answer.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
There are 13 suits.
True/False
There are 12 picture cards.
True/False
There are 4 of each number card
True/False
There are 54 cards in a pack.
True/False
The suits are either black or red.
True/False
Jokers are part of a standard deck of cards.
True/False
All the cards are different.
True/False
Two of the suits are called ‘Clubs’ and ‘Diamonds’.
True/False
There are 8 Aces in a pack.
True/False
Playing cards are often referred to in probability
questions.
True/False
13
Level 4
Write a sentence using each of the following keywords:
Impossible
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
Certain
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
Even chance
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
Equally likely
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
Unlikely
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
14
Level 5
Answer the following questions based on the diagram above.
You must give answers as fractions, decimals or percentages to
achieve level 5.
What is the probability of choosing:
a)
A heart?
………
b)
A rectangle? ………
c)
A shaded triangle?
………
d)
An unshaded shape?
………
e)
An unshaded rectangle?
………
15
Level 6
An octahedral (8 sided) die is numbered from 1 to 8.
What is the probability of rolling:
a)
An even number?
………
b)
A prime number?
………
c)
A number less than 4? ………
d)
A number smaller than 7?
e)
A 10?
f)
Not a square number?
………
………
………
Challenge
In 1833 a ship arrived in Calcutta with 120 tons remaining of
its cargo of ice. One third of the original cargo was lost
because it had melted on the voyage. How many tons of ice was
the ship carrying when it set sail?
A 40
B 80
C 120
D 150
E 180
From UKMT 2008
16
HOMEWORK 10
SECTION A
1 Find 65% of 70.
2
What is of 45?
3 What is;
4
What is 654÷ 6
5 Write 0.65 as a percentage and
a fraction in its simplest form.
6
What is 53?
7 Find the mode for the following
data:
8
Two angles in a triangle are
104° and 25°. What is the third
angle?
4, 7, 5, 11, 3, 8, 4, 12
9 What is -7 x -6 ?
10 Find the HCF of 16 and 48
17
SECTION B
Level 4
Shade in the given fractions.
1
2
4
12
1
3
2
3
Which of these fractions are equivalent?
………………………………………………………………………………………………………………
18
Write down the fractions shown in each diagram:
………………………
………………………
………………………
………………………
………………………
………………………
19
Level 5
Complete the lists of equivalent fractions.
a)
20
40
=
10
=
__
10
=
1
=
3
=
__
24
b)
15
=
__
30
=
6
=
3
5
=
30
=
__
40
c) Write down 3 fractions which are equivalent to three
quarters.
…………………………………………………………………………………………………………………
d)
Cancel down the following fractions to their simplest
form:
15
18
…………
27
36
………….
16
24
…………
24
52
…………
20
Level 6
Find the Lowest Common Multiple (LCM) of the following pairs
of numbers:
a)
5 and 7
b)
12 and 15
c)
8 and 12
d)
6 and 9
e)
4 and 10
Answer the following questions. You must show your working
out.
f)
¼+¼=
g)
⅜+⅛=
h)
⅞+¾=
i)
⅝-¼=
j)
¾-⅛=
k)
½+⅝=
l)
2
+
3
¾=
21
m)
3
3
+
=
4
10
n)
7
2
=
12 15
Challenge
A rectangle PQRS is cut into two pieces along PX, where PX =
XR and PS = SX as shown. The two are reassembled without
turning either piece over, by matching two edges of equal
length. Not counting the original rectangle, how many
different shapes are possible?
A1
B2
C3
D4
E5
S
P
X
R
Q
From UKMT 2008
22
HOMEWORK 11
SECTION A
1 Find 32% of 120.
2
What is of 64?
3 What is;
4
What is 256 ÷ 8
5 Write 0.52 as a percentage and
a fraction in its simplest form.
6
What is the cube root of 1000 ?
7 Find the range for the following
data:
8
Draw a quadrilateral with
EXACTLY two right angles.
Mark the right angles on the
diagram.
4, 7, 5, 11, 3, 8, 4, 12
9 What is -7 - -6 ?
10 Find the LCM of 15 and 20
23
SECTION B
Level 4
a)
½
b)
g)
1
of 20 =
4
¼ of 12 =
h)
1
of 30 =
5
c)
½
of 32 =
i)
2
3
d)
½
of 60 =
j)
1
of 50 =
10
e)
¾
of 40 =
k)
3
of 40 =
10
1
3 of 18 =
l)
3
of 44 =
4
f)
m)
of 20 =
of 100 =
Half of an amount is 12. What is the amount?
……………………………………………………………………………………………………………….
n)
One quarter of an amount is 13. What is the original
amount?
……………………………………………………………………………………………………………
24
Level 5
a)
1
8 of 48 =
g)
6
x 42 =
7
b)
¾ of 28 =
h)
10
x 81 =
9
c)
2
x 27 =
9
i)
13
x 30 =
6
d)
7
x 16 =
8
j)
6
x 52 =
13
e)
2
x 24=
3
k)
4
x 77 =
11
f)
5
x 35=
7
l)
7
x 45 =
15
m) Three quarters of an amount is 36. What is the original
amount?
………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………
n)
Two fifths of an amount is 22. What is the original
amount?
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
25
Level 6
a)
2
5x 5 =
h)
11 x
3
=
8
b)
12 x ¾ =
i)
8x
5
=
7
c)
18 x 3½ =
j)
32 ÷
4
=
9
d)
2
10 x 4 5 =
k)
56 ÷
7
=
8
e)
24 ÷
2
=
3
l)
12 x 1 =
f)
20 ÷
4
=
5
m)
22 ÷
g)
48 ÷ 2 =
2
5
n)
52 x 2
3
4
5
=
11
9
=
13
o)
Two fifths of an amount is 14. What is three fifths of
the amount?
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
p)
Three eighths of an amount is 21. What is one and one
eighth of the same amount?
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
26
Challenge
A solid wooden cube is painted blue on the outside. The cube is
then cut into eight smaller cubes of equal size. What fraction
of the total surface area of these new cubes is blue?
1
1
3
1
3
A
B
C
D
E
8
3
8
2
4
From UKMT 2008
27
HOMEWORK 12
SECTION A
1 Find 74% of 300.
2
What is
3 What is;
4
What is 1375 ÷ 5
5 Write 85% as a decimal and a
fraction in its simplest form.
6
What is the cube root of 8?
7 Find the mean for the following
data, you may use a calculator.
8
Is this a straight line? Give a
reason for your answer.
4, 7, 5, 11, 3, 8, 4, 12
of 33?
35°
48°
9 What is13 + - 8
10 Find the LCM of 12 and 21
28
SECTION B
Section B of homework 12 is the second Key Skills homework
and will be set in a separate mini booklet by your teacher.
29
HOMEWORK 13
SECTION A
1 Find 28% of 50.
2
What is of 36?
3 What is;
4
What is 2763÷ 9
5 Write 12.5% as a decimal and a
fraction in its simplest form.
6
What is the cube root of 125?
7 Find the mean for the following
data, you may use a calculator.
8
Is this a straight line? Give a
reason for your answer.
21, 23, 15, 26, 7
35°
55°
9 What is13 - - 8
10 Find the LCM of 12 and 16
30
SECTION B
Level 4
The diagrams below are all RIGHT ANGLES. Calculate the
missing angles, a, b, c, d, e and f.
a
b
50
°
a = ……………
43
°
27
°
c = ……………..
c
e
35
°
b = ………….
d
40
° d
d = ………………
f
e
e = ……………
2f
f = ……………
31
Find the missing angles on the straight lines below.
………………………………
………………………………
130°
g
g = ………………………
………………………………
………………………………
30°
h
h = ………………………
32
Level 5
Find the missing angles in the diagrams below.
1.
b = …………………
c
c = …………………
55°
2.
b
d = ………………
68°
d
37°
3.
54°
4.
e
f
116°
f = …………………
98°
120°
f
e = ………………..
33
5.
……………………………………………
……………………………………………
g
38°
g = …………………………….
……………………………………………
……………………………………………
48°
h
h = …………………………….
……………………………………………
……………………………………………
2i
3i
i
i = …………………………….
34
Level 6
Complete the sentences below using the diagram and keywords
given.
Corresponding
a
b
c
Vertically Opposite
d
e
f
g h
Allied
Alternate
Angles a and d are equal because they are ……………………………………
angles.
Angles a and e are equal because they are ……………………………………
angles.
Angles c and f are equal because they are ……………………………………
angles.
Angles f and g are equal because they are ……………………………………
angles.
Angles b and f are equal because they are ……………………………………
angles.
Complete the sentence below;
Angles ……… and ……… are allied angles because……………………………
…………………………………………………………………………………………………………………
35
Calculate the missing angles. Give a reason for your answer.
a
1.
c
56°
b
115°
2.
e
d
a = ………………
e = ……………………………………………….
Reason …………………………………..
Reason……………………………………..
b = …………………
Reason …………………………………..
c = ………………….
Reason ……………………………………
d = …………………..
Reason ……………………………………
Challenge
An active sphagnum bog deposits a depth of about 1 metre of
peat per 1000 years. Roughly how many millimetres is that per
day?
A 0.0003
B 0.003
C 0.03
D 0.3
E3
From UKMT 2008
36
HOMEWORK 14
SECTION A
1 Find 43% of 480.
2
What is of 56?
3 What is;
4
What is 2763÷ 3
5 Write 140% as a decimal and a
fraction in its simplest form.
6
What is 43?
7 Find the median for the following 8
data.
Draw a diagram to show
alternate angles
21, 23, 15, 26, 7, 11
9 What is 3 x - 8
10 Find the HCF of 3, 4 and 5
37
SECTION B
Level 4 to 5
1.)
Draw a rectangle with a perimeter of 24cm2
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
2.)
A square has side length 10cm. What is it’s area?
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
3.)
Calculate 27 multiplied by 43.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
38
4.)
Continue the sequence by writing the next 3 terms.
3, 7, 11, 14, 17……
………………………………………………………………………………………………………………
What is the nth term?
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
5.)
Write the following numbers in order.
7, -3, 0.74, 0.08, -10
………………………………………………………………………………………………………………
6.)
Write 34786 to;
The nearest 10
………………………………………………………………………………………………………………
The nearest 100
………………………………………………………………………………………………………………
The nearest 1000
………………………………………………………………………………………………………………
7.)
27.5 – 34.6=
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
39
8.)
Simplify 4s + 4p + 3p – 2s
………………………………………………………………………………………………………………
9.)
If A = bh
Find A when b = 3 and h= 5
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
10.) Find the mean, median and mode of the following data,
6, 3, 5, 8, 3, 9, 1
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
40
Level 5 to 6
1.)
What is the 12th square number?
………………………………………………………………………………………………………………
2.)
A triangle has an area of 18cm2. It has a perpendicular
height of 6cm. How long is its base?
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
3.)
A cube has side length 3m. What is its surface area?
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
4.)
Multiply 3.27 by 2.4
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
41
5.)
What is 348 x 0.1?
………………………………………………………………………………………………………………
6.)
What is the inverse of doubling then adding one?
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
7.)
What is always true of corresponding angles?
………………………………………………………………………………………………………………
8.)
Write down the first 3 cubic numbers.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
9.)
3 + 5 x 9 ÷ (4 -1) =
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
10.) Write down three fractions that are smaller than ¼.
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
………………………………………………………………………………………………………………
42
Download

homework 8 - Howden School & Technology College