Sets 7.2 & 7.3 – Practice Questions A
Name
1 Sharon and Tim work in a shoe shop. Sharon recorded the sizes of the last 12 pairs of shoes that
she sold.
4
11
1
72
1
52
8
7
1
42
9
6
10
5
6
a Write down the mode.
…………………………
b Work out the range.
…………………………
Tim recorded the sizes of the last 12 pairs of shoes that he sold. His results: mode = 7, range = 5
c Use the modes and ranges to write two sentences comparing the sizes of shoe sold by Sharon
and Tim.
………………………………………………………………………………………………………………..
………………………………………………………………………………………………………………..
………………………………………………………………………………………………………………..
………………………………………………………………………………………………………………..
(5 marks)
2 Find the median of the shoe sizes sold by Sharon in question 1.
…………………………
(2 marks)
3 The mean of three numbers is 8
Two of the numbers are 6 and 11
Work out the third number.
…………………………
(3 marks)
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Sets 7.2 & 7.3 – Practice Questions A
4 The table shows the ages of people who are members of the Dolphin swimming club.
Draw a dual bar chart to show this information. Label the axes of your chart.
Age
Girls
Boys
3–4
14
13
5–6
17
18
7–8
13
11
9–10
08
07
(5 marks)
5 A pair of trainers cost Pierre £26.16 in a sale.
a Work out the price of 5 pairs of trainers.
£…………………………
b Write your answer to part a in pence.
…………………………p
The trainers were reduced from £40.
c How much do you save if you buy 5 pairs?
£…………………………
(5 marks)
6 Fill in the missing numbers.
a 8×
+ 2 = 50
b 4+
× 2 = 20
(2 marks)
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Sets 7.2 & 7.3 – Practice Questions A
7 Write all of the factors of 24
…………………………………………………………………………
(2 marks)
___
8 Work out 82 × √100
…………………………
(3 marks)
9 Work out the outputs of each of these function machines.
a
input
output
6
Multiply
by 7
9
b
input
output
5
×4
÷5
10
(4 marks)
10 Fill in the empty boxes.
a 63 × 7 + 27 × 7 =
b 6 × (20 +
×7
) = 150
(3 marks)
11 Simplify x + y + x + x + y
…………………………
(2 marks)
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Sets 7.2 & 7.3 – Practice Questions A
Each side of this hexagon has length s.
12
a Write an expression for the perimeter of the hexagon.
…………………………
Patel increases the top and bottom length by 5 units.
The other four sides remain the same.
b Write an expression for the perimeter of this new hexagon.
Simplify your expression.
…………………………
(3 marks)
13 Multiply out the brackets.
a 5(x + 4) …………………………
b 7(3 − 2x) …………………………
(4 marks)
14 The perimeter of a square is 80cm.
a Find the length of one side, in centimetres.
………………………cm
b Work out the area of the square, in square centimetres.
………………………cm2
(3 marks)
15 Charlie has a 1 litre jug of water. She fills 3 glasses and has 10m l left over.
Work out how much water, in ml, is in each glass.
…………………………ml
(2 marks)
16 Richard is 1.75m tall.
a Write Richard’s height in cm.
……………………….cm
b Write Richard’s height in mm.
………………………mm
(2 marks)
17 The population of London is 8 308 000 and covers an area of 1572 square kilometres.
a Write the population to the nearest ten thousand. …………………………
b Write the area of London to the nearest 10km 2.
…………………… km2
(3 marks)
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Sets 7.2 & 7.3 – Practice Questions A
Answers
1 a 6 (1)
b 7 (2)
1 mark for sight of 4 and 11
c Statement linking higher mode for Tim with higher shoe sizes (1).
Statement linking higher range for Sharon with more variation in shoe size sold by Sharon (1).
Accept any indication that the sizes are more spread out.
2 6.5 (2)
1 mark for an ordered list
3 7 (3) 1 mark for sight of 24 and a further mark for sight of 17.
4 Vertical axis numbered, correctly and consistently, up to at least 18 (1). Vertical axis labelled (e.g.
‘frequency’ or ‘number of people’) (1). Bars on horizontal axis labelled correctly (e.g. 3–4 and axis
titled ‘Age’). (1). Key for Girls and Boys and spacing between bars of different age groups, but no
spacing between bar for girls and bar for boys of same age group (1). Bars at correct height (1).
5 a £130.80 (2)
b 13 080p (1)
1 mark for sight of 130.8
allow ft from answer above
c £69.20 (2)
1 mark for correct method, attempting to find the difference between £40 and
£26.16 and then multiplying by 5 or for sight of £13.84
6 a 6 (1)
b 8 (1)
7 1, 2, 3, 4, 6, 8, 12, 24 (2)
none incorrect
8 640 (3)
1 mark for any 5 of these and up to 1 incorrect or for 4 of these with
1 mark for sight of 64, a further mark for sight of 10
9 a 42, 63 (2)
b 4, 8 (2)
10 a 90 (1)
b 5 (2)
1 mark for sight of 25
11 3x + 2y (2)
12 a 6s (1)
1 mark for one correct term
accept 6 × s
b 6s + 10 (2)
13 a 5x + 20 (2)
b 21 − 14x (2)
1 mark for sight of s + 5
1 mark for one correct term
1 mark for sight of 14x, with or without negative sign
14 a 20cm (1)
b 400cm2 (2)
15 330ml (2)
1 mark for attempting to square result from part a
1 mark for attempt to divide 990 by 3
16 a 175cm (1)
b 1750mm (1)
17 a
8 310 000 (2)
1 mark for sight of digits 83
b 1570 (1)
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Sets 7.2 & 7.3 – Practice Questions A
Answers
Extend mental calculations to
squares and square roots
Find outputs of simple functions
in words and symbols
17
Convert between whole
numbers of metric units
Convert between decimal
numbers of metric units
Round positive numbers to any
given power of 10
13
14
Simplify simple linear algebraic
expressions by collecting like
terms
Construct expressions from
worded description, using
addition, subtraction and
multiplication
Begin to multiply a positive
integer over a bracket
containing linear terms
Use the formulae to calculate
the area of squares or
rectangles
Interpret the display of a
calculator in different contexts
Construct compound bar charts
Calculate the mean of a set of
data
Objective
Know and use the order of
operations
Calculate the median of a set of
data (up to 20 items)
12
Use distributive law with
brackets with numbers
Compare two simple
distributions using the range
and the mode
Find all the factor pairs of a
number (without any support)
16
11
Question
/53
Overall mark:
15
10
Objective
9
8
7
6
5
4
3
2
1
Question
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Sets 7.2 & 7.3 – Practice Questions B
Name
…………………………
1 Find 10% of 60
(1 mark)
2 What fraction of each shape is shaded?
a
…………………………
b
…………………………
(2 marks)
3 Complete the table.
Fraction
Decimal
Percentage
0.9
29%
(4 marks)
4 Convert each of these to mixed numbers.
7
…………………………
29
7
…………………………
a 4
b
(2 marks)
5 Work out
a 50% of 70
…………………………
b 25% of 400
…………………………
c 20% of 50
…………………………
(6 marks)
6 Work out
1
4
a 9+9
…………………………
3
2
b 7+7
…………………………
(2 marks)
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Sets 7.2 & 7.3 – Practice Questions B
7 Write each fraction in its simplest form.
70
…………………………
18
…………………………
a 200
b 24
(3 marks)
8 Each Year 7 student plays table tennis, badminton or squash. There are 28 students in form 7AT.
One seventh play table tennis, and three sevenths play badminton.
Work out how many students in 7AT play
a table tennis
…………………………
b badminton
…………………………
c squash.
…………………………
(4 marks)
9 I have a spinner with the numbers 1 to 8 inside each equal triangular section.
Use one of these words to describe how likely each of these is.
You may use the same word more than once.
impossible
unlikely
even chance
likely
certain
I throw the spinner and it lands on
a the number 4
…………………………
b a number greater than 4 …………………………
c a number less than 10
…………………………
(3 marks)
10 There are 6 red beads, 4 blue beads and 1 yellow bead in a bag. A bead is taken at random. Each
bead is equally likely to be taken. Work out these probabilities. Write each answer as a fraction.
a The bead is yellow.
…………………………
b The bead is red. …………………………
c The bead is red or yellow.
d The bead is green.
…………………………
…………………………
(4 marks)
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Sets 7.2 & 7.3 – Practice Questions B
11 A train was on time on 18 days and late on 13 days.
Estimate the probability that the train will be late tomorrow.
…………………………
(2 marks)
13
12 The probability that it rains tomorrow is 22.
Work out the probability that it does not rain.
…………………………
(2 marks)
13 There are two shaded squares and five unshaded squares in this rectangle.
Write the ratio of shaded to unshaded squares.
…………………………
(1 mark)
14 It took Eric half an hour to paint two fence panels. He continues painting panels at the same rate.
Work out how long it will take him to paint three more panels.
…………………………
(3 marks)
15 Divide £45 into the ratio 2 : 3
…………………………
(2 marks)
16 Jo lives 1.5 km from school. She passes a shop. The shop is 300 metres from school.
a How far is the shop from where Jo lives? Write your answer in both kilometres and in metres.
………………………… km
..………………………… m
b Work out the ratio of the distance of the shop from school to the distance of the shop from Jo’s
house. Write your ratio in its simplest form.
…………………………
(4 marks)
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Sets 7.2 & 7.3 – Practice Questions B
17 Sam and James make two different shades of green by mixing yellow and blue in different ratios.
Sam mixes yellow and blue in the ratio 3 : 7
a Work out the percentage of yellow paint that Sam uses.
…………………………
1
James puts in 4 of yellow paint.
b What percentage of yellow paint does he use?
…………………………
c Whose shade of green is more blue – Sam’s or James’? Explain your answer.
……………………………………………………………………………………..…………………………
(4 marks)
18 Izzy and Jack do some cleaning. Izzy spends 40 minutes and Jack spends 1 hour.
a Work out the ratio of the time Izzy spent cleaning to the time Jack spent cleaning.
Convert your ratio to its simplest form.
…………………………
They are given £15 for this work.
b Work out how much they should each receive if they divide the money in the ratio of the time
they spent cleaning.
…………………………
(4 marks)
19 Kalil and Leta compare the amount of time they each spend awake and asleep.
Kalil says, ‘The ratio of time I spend asleep to that awake is 1 : 2.’ Leta says, ‘I spend three eighths
of my time asleep.’
Who spends longer awake? You must show your working.
…………………………
(5 marks)
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Sets 7.2 & 7.3 – Practice Questions B
Answers
1 6 (1)
2
2 a 5 (1)
3
b 10 (1)
9
3 10 90% (2)
1 mark each
29
100 0.29 (2)
1 mark each
3
4 a 14 (1)
1
b 47 (1)
5 a 35 (2)
1
1 mark for sight of 2
1
b 100 (2)
1 mark for sight of 4
c 10 (2)
1 mark for sight of 5
1
5
6 a 9 (1)
5
b 7 (1)
7
7 a 20 (1)
3
b 4 (2)
8 a 4 (2)
1 mark for an equivalent fraction that is not fully cancelled down
1 mark for attempt to divide 28 by 7
b 12 (1)
accept their part a × 3 so long as it does not exceed 20
c 12 (1)
accept their part b or subtraction of their answers to parts a and b from 28
9 a unlikely (1)
b even chance (1)
c certain (1)
1
10 a 11 (1)
6
b 11 (1)
7
c 11 (1)
d 0 (1)
13
11 31 (2)
9
12 22 (2)
1 mark for numerator or denominator correct
1 mark for numerator or denominator correct
13 2 : 5 (1)
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Sets 7.2 & 7.3 – Practice Questions B
Answers
10
9
8
Find and justify probabilities based
on equally likely outcomes in
simple contexts
Use the vocabulary of probability
Calculate simple fractions of
quantities
Simplify fractions by cancelling
common factors
Begin to add and subtract simple
fractions
Calculate simple percentages
Change an improper fraction to a
mixed number
Recognise the equivalence of
percentages, fractions and
decimals
Use fraction notation to describe
parts of shapes
17
18
19
Divide a quantity into two parts in a
given ratio, where ratio given in
ratio notation
Reduce a ratio to its simplest form
Use percentages to compare
simple proportions
Understand the relationship
between ratio and proportion
Recognise the links between ratio
and fractional notation
Know that if probability of event
is p, probability of not occurring is
1−p
Divide a quantity into two parts in a
given ratio, where ratio is given in
worded form
Use direct proportion in simple
contexts
16
Apply probabilities from
experimental data to a different
experiment in simple situations
/58
Overall mark:
accept any valid explanation
c James’ – he puts in less percentage of yellow paint (2)
comparing proportions of blue or yellow
7
6
5
4
14
13
12
11
Question
1 mark for 300 : 1200 or 4 : 1
b 1 : 4 (2)
3
1
3
15
Objective
Find simple percentages of whole
number quantities
Objective
1 mark for sight of 3
b £6 : £9 (2)
3
2
1
Question
1 mark for equivalent ratio
18 a 2 : 3 (2)
1 mark each
1200m (2)
16 a 1.2km
1 mark for sight of 15 or 4 and further mark for sight of 45 or 4, or for
14 45 minutes or 4 hour (3)
attempting to multiply 15 by 3.
15 £18 : £27 (2) 1 mark for £27, £18 or for sight of 9 or for correct method with one arithmetic slip
17 a 30% (1)
b 25% (1)
19 Kalil (1), Kalil 8 hours asleep or 16 hours awake (2), Leta 9 hours asleep or 15 hours awake (2)
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