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Year 9 Higher Homework Autumn 2
Topic Test
Chapter 21: Processing, representing and interpreting data
Non-calculator
1 Lupando records the time t, in seconds, it takes each of the students in his class to complete a
puzzle. The histogram below shows his results.
7
The first class interval in the
6 diagram, in which there is
no students, represents the
5
interval 15 t < 20
Frequency
4
3
2
1
0
15 20 25 30 35 40 45 50 55
time (in seconds)
a Write down the modal class interval.
……………………………
b Work out the number of students in Lupando’s class.
……………………………
c How many students took less than 35 seconds to complete the test?
……………………………
2 The frequency polygon shows the number of half-days of absence in a year group for the
first six months of the year.
70
60
50
days absent
No of half
40
30
20
10
0
Jan Feb March April May June
Topic test 21: Processing, representing and interpreting data (continued)
a Write down the number of half-day absences in June. ………………………
b Write down the month in which there was the greatest number of half-day absences.
……………………………
c The number of half-day absences in April is low. Suggest a reason for this.
……………………………………………………………………………………………
3 In one month, Janet travelled by bus 25 times and by train 25 times.
The grouped frequency table records the number of minutes (x minutes) late each of her
buses and trains were.
Minutes late Bus Train
0 x5 5 9
5 x 10 15 6
10 x 15 4 6
15 x 20 1 2
20 x 25 0 3
a On the grid below draw two frequency polygons to illustrate this data.
b Use your polygons to compare the lateness of buses and trains and comment on any
differences you observe.
……………………………………………………………………………………………
……………………………………………………………………………………………
Topic Test
Chapter 7: Decimals and fractions
Non-calculator
1 a Write these decimals in order of size. Start with the smallest.
0.43 0.09 0.34 0.009 0.04
…………………………………………………………………………
b Write 0.34 as a fraction in its simplest form.
………………………….
c Work out 0.09 0.009
………………………….
d Work out 0.09 100
………………………….
2 Work out a 7.6 0.5 b 7.6 0.005
…………………………. ………………………….
c 7.6 1000 d 7.6 5000
…………………………. ………………………….
3 Work out a 0.2 0.3 b 0.02 0.03
…………………………. ………………………….
0.054
c
0.02 0.03
……………………………….……………………………….
4 Given that 18 73 1314 , work these out.
a 0.018 0.73 b 13.14 730
…………………………. ………………………….
c 13140 180000 d 0.01314 0.018
…………………………. ………………………….
19.404
5 Given that 1.5 , work these out.
7.7 1.68
19.404 19 404
a b
0.77 0.168 77 16.8
…………………………. ………………………….
0.194 04 1.9404
c d
0.077 16.8 23.11.68
…………………………. ………………………….
Topic test 7: Decimals and fractions (continued)
6 State which of the following fractions convert to a terminating decimal and which convert to
a recurring decimal.
33 7
a b
320 15
…………………………………. ……………………………………
73 73
c d
288 128
…………………………………. ……………………………………
7 The recurring decimal 0.63 can be written as the fraction 7
11
a Write the recurring decimal 0.063 as a fraction.
……………….
b Write the recurring decimal 6.36 as a mixed number.
……………….
c Write the recurring decimal 0.463 as a fraction.
……………….
Calculator
8 Use your calculator to write each of these fractions as a decimal.
15 17 5 8
a …………….. b …………….. c …………….. d ...…………..
32 80 70 99
9 a Express 2 as a recurring decimal.
9
…………………..
b Express the recurring decimal 0.362 as a fraction.
Give your answer in its simplest form.
…………………..
10 Convert the recurring decimal 4.643 to a mixed number.
Give your answer in its simplest form.
…………………..
Topic Test
Chapter 8: Expanding brackets and factorising
Non-calculator
1 Expand
a p 2 3 p3 4 b x 2 x xy x 2
…………………………… …………………………..…
c t t 3 2t 2 t 1
……………………………………………………..…
2 Expand and simplify the following.
a 2 a 3b 3 a b
………………………………………………………………………
b 4 x y 2 x 2y
………………………………………………………………………
c x x 4 3 x 2
………………………………………………………………………
d y 2 y 2 2 y y 2 1
………………………………………………………………………
3 Factorise
a x 2 25 x b 6 x 12 y 18z
……………………………… ………………………………
c 9 x 2 6 x3 d 3y 2 y
……………………………… ………………………………
4 Factorise
a 3a 2bc 6ab2c 3abc 2
……………………………………………………………………
b x3 yz x 2 y 2 z 2 x 4 y 3
……………………………………………………………………
5 Expand and simplify.
a x 4 x 8 b y 3 y 6
……………………………… ……………………………
c z 4 z 9 d p 5
2
……………………………… ……………………………
Topic test 8: Expanding brackets and factorising (continued)
6 Expand and simplify where possible.
a x 3 y x 5 y b 3 p q p 2q
……………………………… ……………………………
z 3y d a 2b c 3d
2
c
……………………………… ……………………………
7 Factorise these completely.
a x x 4 3 x 4 b p a b 2q a b
……………………………..………… ……..……………..…………………………
c x y 6 x y d 9 x 2 y 3 x 2 y
2 2
……………………………..………… ……..……………..…………………………
e ac 3bc 2ad 6bd f pq pr q r
……………………………..………… ……..……………..…………………………
8 Factorise a x 2 9 x 20 b x2 19 x 20
……………………………..………… ……..……………..…………………………
c y 2 2 y 24 d y 2 5 y 24
……………………………..………… ……..……………..…………………………
9 a i Factorise x 2 36 ……………………….
ii Hence find the value of 1062 36
………………………
b Factorise i 9 x 25 y ii y 1 z 3
2 2 2 2
……………………………..……… ……..……………..…………………………
10 Factorise these completely.
a 3x 2 12 x 36
………………………………………………………………………
b 24 p 2 8qp 12 pr 4rq
………………………………………………………………………
c 27 2 y 1 12 y 2
2 2
………………………………………………………………………
Topic Test
Chapter 9: Two-dimensional shapes
Non-calculator
1 Here is a sketch of a triangle XYZ.
X
7 cm 8 cm Diagram NOT
accurately drawn.
Y Z
6 cm
a Make an accurate drawing of the triangle XYZ.
b Use a protractor to measure and write down the size of the smallest angle of the triangle
XYZ.
………………….
2 Work out the area of the shape below.
12 cm Diagram NOT
accurately drawn.
4 cm
10 cm
6 cm
………………..
Topic test 9: Two-dimensional shapes (continued)
3 Diagram NOT
accurately drawn.
A lawn is made up of a rectangle
4m with a semicircle added at one end.
The rectangle is 4 m long and 3 m
wide as shown in the diagram.
3m
a Work out the perimeter of the lawn.
Give your answer in terms of .
………………..
b Work out the area of the lawn.
Give your answer in terms of .
………………..
4 a Change
i 8 m 2 to cm 2 …………….………. ii 600 000 cm 2 to m2 ……….….………….
iii 8 km 2 to m2 …………..……….
b Diagram NOT Work out the area of the triangle in
accurately drawn. i mm 2
80 mm
15 cm
………………………..
2
ii cm
………………………..
Calculator
5 Work out the areas of the shapes below. The diagrams are NOT accurately drawn.
a 7.2 cm
5.4 cm
………………………..
Topic test 9: Two-dimensional shapes (continued)
b
4.3 m
9.2 m
………………………..
c This shape is a parallelogram.
8.3 cm
12.4 cm
………………………..
d This shape is a trapezium.
6.8 cm
4.2 cm
9.5 cm
………………………..
6 A sheet of A4 paper is 29.7 cm long and 21 cm wide. A sheet of B5 paper is 25 cm long and
17.6 cm wide.
a Work out the perimeter of a sheet of A4 paper.
………………………..
b Work out the difference between the area of a sheet
of A4 paper and the area of a sheet of B5 paper.
Give your answer to the nearest square centimetre.
………………………..
In questions 7 - 10, use a calculator. If your calculator does not have a button, take the value
of to be 3.142. Give your answers to 3 significant figures.
7 Old Sarum is a circular earthwork with perimeter 1180 m.
a Work out the radius of the earthwork.
………………………..
b Work out the area covered by Old Sarum.
………………………..
