Sets 8.2 & 8.3 – Practice Questions A
1
Name
Estimate each square root to the nearest whole number.
a √50
…………………………
b √80
…………………………
(2 marks)
2 Work out the highest common factor of 36 and 54
…………………………
(2 marks)
3 Work out
a 6 × −8
…………………………
b −72 ÷ −9
…………………………
(2 marks)
4 Work out
a 40 × 52
…………………………
b 200 × 152
…………………………
(4 marks)
5 Use index notation to write 3600 as the product of its prime factors.
…………………………
(3 marks)
3
6 Work out 3( √27 + √64 )
…………………………
(3 marks)
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Sets 8.2 & 8.3 – Practice Questions A
7 Work out
( 11
13 )
3
…………………………
(1 mark)
8 Work out the area of this triangle, stating the units of your answer.
…………………………
(3 marks)
9 This drink carton contains 0.6 litres of liquid.
Work out the height of the drink carton.
…………………………
(3 marks)
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Sets 8.2 & 8.3 – Practice Questions A
10 A three-dimensional letter H is formed by joining two identical cuboids and a cube.
The H has height 10cm, width 15cm and depth throughout of 5cm.
Work out the surface area of the shape.
…………………………
(3 marks)
11 The table shows the number of sweets of each colour in a bag.
Colour
Frequency
Red
10
Yellow
05
Blue
15
White
06
Angle
a Complete the table.
b Draw a pie chart for the data.
(5 marks)
12 Work out the mean of these numbers using an assumed mean of 100.
102.6
99.4
105
104
99
…………………………
(2 marks)
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Sets 8.2 & 8.3 – Practice Questions A
13 This scatter graph shows the History and Geography test marks of 20 students in a class.
a What type of correlation is there between the History marks and the Geography marks in the class?
…………………………
b Draw a line of best fit.
c Maisie scored 90 in History, but she was absent for the Geography test. Use your line of best fit
to estimate what she might have achieved in Geography.
…………………………
(4 marks)
14 Solve each equation to find x
a 4x + 1 = 25
…………………………
b 8x − 2 = 30
…………………………
(4 marks)
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Sets 8.2 & 8.3 – Practice Questions A
15 Work out 2x + x2 for x = 5
…………………………
(2 marks)
16 Expand
a x(x + 8)
…………………………
b 6x(2 − 5x)
…………………………
(4 marks)
17 Factorise fully
a 21a + 24b
…………………………
b 12a + 18b
…………………………
(4 marks)
18 Simplify 4x2 + 5x + 5x2 − 3x by collecting like terms.
…………………………
(2 marks)
19 Solve the equation 3x − 2 =
5x + 8
3
…………………………
(3 marks)
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Sets 8.2 & 8.3 – Practice Questions A
Answers
All answers are worth 1 mark unless otherwise indicated.
1 a 7
b 9
2
18 (2)
1 mark for finding common factor 6 or 9; no marks if 2 is the only common
factor found
3 a −48
b 8
4 a 1000 (2)
1 mark for sight of digits 100
b 45 000 (2)
1 mark for sight of 225 or the digits 450
5 24 × 32 × 52 (3)
2 marks for any two of 24, 32, 52 or for correct product with prime
factors; 1 mark for identifying
6 33 (3)
2 marks for sight of 11 or 1 mark for a correct method with at
least 1 correct step
1331
7 2197 or 0.605826…
1
8 24cm2 (3)
1 mark for correct units and 1 mark for 2 × 6 × 8 or equivalent
9 12cm (3)
2 marks for 5 × 10 × ? = 600 or equivalent or 1 mark for sight of 600; allow
lack of units
10 550cm2 (3)
2 marks for sight of 450 or 1 mark for sight of both 50 and 25 or 1 mark for a
correct method with at least one correct step
11 a
Colour
Frequency
Angle
Red
10
100°
Yellow
05
050°
Blue
15
150°
White
06
060°
(2) 1 mark for 3 correct angles
b
angles within 1 degree (3)
12
102 (2)
2 marks for 3 angles within 2° or for 2 angles within 1°;
1 mark for 2 angles within 2° or 1 angle within 1°
1 mark for sight of 2.6 − 0.6 + 5 + 4 − 1 or for full correct
method with one error
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Sets 8.2 & 8.3 – Practice Questions A
Answers
13 a positive
b
line of best fit drawn that joins (or would extend to) a point between (0, 5) and (0, 20) to a point
between (100, 80) and (100, 95) (2)
1 mark for a straight line, with positive gradient, with at least some points
either side
c 72.5–87.5 (for line of best fit within bounds given in part b)
accept value read off correctly using their line of best fit
14 a 6 (2)
1 mark for 4x = 24; 1 mark for x = 24 ÷ 4
b 4 (2)
1 mark for 8x = 32; 1 mark for x = 32 ÷ 8
15 35 (2)
1 mark for sight of both 10 and 25; 1 mark for correct addition
16 a x2 + 8x (2)
1 mark for each correct term
b 12x − 30x2 (2)
17 a 3(7a + 8b) (2)
b 6(2a + 3b) (2)
1 mark for each correct term
1 mark for identifying correct factor; 1 mark for correct divisions
1 mark for identifying correct factor; 1 mark for correct divisions; 1 mark only
overall if not fully factorised
18 9x2 + 2x (2)
1 mark for each correct term (accept 2x + 9x2)
19 3.5 (3)
2 marks for 4x − 6 = 8 or 4x = 14 or 14 ÷ 4 or 1 mark for sight of 14
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Sets 8.2 & 8.3 – Practice Questions A
Answers
Find the HCF or LCM of 2
numbers less than 100
Multiply and divide integers –
positive and negative numbers
Mentally be able to calculate
the squares of numbers less
than 16 multiplied by a multiple
of ten e.g. 300
Find the prime factor
decomposition of a number
Combine laws of arithmetic for
brackets with mental
calculations of cubes roots and
square roots
Use the function key to enter a
fraction
Use a formula to calculate the
area of triangles
Solve equations of the form
(ax ± b)/c = (dx ± e)/f [One of c
or f should be 1]
Simplify simple expressions
involving index notation, i.e.
Multiply a single term over a
bracket, e.g. x(x + 4),
3x(2x − 3)
Use the distributive law to take
out numerical common factors,
e.g. 6a + 8b = 2(3a + 4b)
x2 + 2x2, p × p2
Understand the difference
between 2n and n2
Use a line of best fit drawn by
eye to estimate the missing
value in a two variable data set
Construct on paper pie charts
using categorical data – more
than three categories
Calculate the mean from a set
of data using assumed mean
ax + b = c e.g. 3x + 7 = 25
Solve simple two-step linear
equations with integer
coefficients, of the form
17
Calculate the surface area of
shapes made from cuboids
8
Solve volume problems;
Convert between cm3 and litres
7
Be able to estimate square
roots of non-square numbers
less than 100. (Give integers
that the roots lie between)
/ 56
Overall mark:
6
19
16
18
15
13
14
12
Objective
5
Objective
11
Question
4
10
3
9
2
1
Question
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Sets 8.2 & 8.3 – Practice Questions B
Name
1 Two cleaning companies, A and B, charge different rates. Their charges are based on the time
worked, to the nearest 15 minutes, and are shown on the graph.
a Use the graph to describe how you would choose which company to use.
……………………………………………………………………………………………………………….
……………………………………………………………………………………………………………….
……………………………………………………………………………………………………………….
b Work out how much per hour Company A charges.
…………………………
c Explain why the graph for Company B does not start at the origin.
……………………………………………………………………………………………………………….
……………………………………………………………………………………………………………….
……………………………………………………………………………………………………………….
d Company C is cheaper than company B for less than one hour and is more expensive for more
than one hour. Draw a line on the graph to show the possible charges of Company C. (Assume
the rate charged is linear.)
(8 marks)
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Sets 8.2 & 8.3 – Practice Questions B
2 Rose visits her sister. She stopped at a shop on the way there. The distance–time graph shows her
journey by car.
a How long did Rose spend at her sister’s house?
…………………………
b What was Rose’s speed between her home and the shop in km/hr?
…………………………
Rose returned home at a speed of 45km/hr.
c Plot a point on the graph to show how far from home Rose is one hour after leaving her sister’s.
d Draw a line to show Rose’s return journey.
(5 marks)
3 Work out
a 0.14 × 200
…………………………
b 1.6 × 16
…………………………
(3 marks)
4 Divide 55 in the ratio 1 : 3 : 7
…………………………
(2 marks)
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Sets 8.2 & 8.3 – Practice Questions B
5 Divide 4.8 in the ratio 3 : 5
…………………………
(2 marks)
6 Work out
a 67 × 0.1
…………………………
b 0.72 × 0.01
…………………………
(2 marks)
7 Work out
a 56 ÷ 0.4
…………………………
b 625 ÷ 2.5
…………………………
(4 marks)
8 Tick or cross each of these.
a −2.8 > −1.8
……………
b −4.1 > −4.88
……………
c −4.12 > −4.3
……………
(2 marks)
9 a A quadrilateral has two pairs of equal sides but no parallel sides. Name this quadrilateral.
…………………………
b Name two types of quadrilateral which have exactly two lines of symmetry.
……………………………………………………………………………………………………………….
(3 marks)
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Sets 8.2 & 8.3 – Practice Questions B
10 A parallelogram has an angle of 35°. Find the other three angles.
…………………………
(2 marks)
11 The diagram shows a scalene triangle.
a Form an equation in x
…………………………
b Solve your equation to find x
…………………………
c Work out each of the angles in the triangle.
……………………………………………………
(8 marks)
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Sets 8.2 & 8.3 – Practice Questions B
12
…………………………
a Name the shape.
b Find angle a
…………………………
c Find angle b
…………………………
(5 marks)
13 A regular pentagon is enclosed by a kite as shown in the diagram.
a Calculate the exterior angle of the pentagon, DBAFE.
…………………………
b Calculate angle ABD.
…………………………
c Calculate angle BCD.
…………………………
d Write the four angles of the kite ACEF.
……………………………………………………
(7 marks)
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Sets 8.2 & 8.3 – Practice Questions B
Answers
All answers are worth 1 mark unless otherwise indicated.
Accept missing degree symbols throughout.
1 a Choose Company A if less than 2 hours cleaning needed and Company B if more than 2 hours
cleaning needed. For 2 hours, it does not matter which company is used. (3)
b £8
c There is a callout charge of £10 (2)
accept any sensible explanation; 1 mark for
sight of £10
d
any straight line from below 10 on the y-axis, crossing line B at 1 hour (2)
1
2 a 1 4 hours or equivalent
b 40km/h (2)
1
1 mark for 20 ÷ 2
c
point plotted at (4, 5), i.e. 4 hours across, 5 km up (or 5km from home)
d see diagram in part c – straight line down to the axis passing through (4, 5), i.e. so she arrives
home at approximately 4 hours and 7 minutes after first leaving
3 a 28
b 25.6 (2)
4 5 : 15 : 35 (2)
1 mark for a correct method
5 1.8 : 3 (2)
1 mark for sight of 0.6 or for 1.8
6 a 6.7
b 0.0072
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Sets 8.2 & 8.3 – Practice Questions B
Answers
7 a 140 (2)
1 mark for attempt at 560 ÷ 4
b 250 (2)
1 mark for attempt at 6250 ÷ 25
8 a cross
b tick
c tick
2 marks for all correct; 1 mark for any two correct
9 a kite
accept arrowhead
b rectangle, rhombus (2)
10 35°, 145°, 145° (2)
1 mark each
1 mark for sight of 35° or 145°
11 a 5x + 16 + x + 20 + 2x = 180° or equivalent (2)
b x = 18° (3)
2 marks for 144 ÷ 8 or 8x = 144
c 36°, 106°, 38° (3)
1 mark each – follow through from their x
12 a trapezium
b 148° (2)
1 mark for 180 − 32
c 12° (2)
1 mark for 180 – 20 − their 148
13 a 72° (2)
1 mark for sight of 360° ÷ 5
b 108° (2)
1 mark for (180° − their 72°) or for 540° ÷ 5
c 36° (2)
1 mark for (180° − twice their 72°) or for (360° − three times their 108°)
d 108°, 108°, 108°, 36°
accept angles written in any order
3
4
5
6
7
8
9
12
13
Use the interior and exterior angles of regular and
irregular polygons to solve problems
11
Solve simple problems using properties of angles,
of parallel and intersecting lines, and of triangles
and other polygons – by looking at each shape
separately
Classify quadrilaterals by their geometric
properties
Use > or < correctly between two negative
decimals (decimals should be to 2 or 3 significant
figures)
Multiply and divide by decimals, dividing by
transforming to division by an integer
Multiply any number by 0.1 and 0.01
Divide in a given ratio – decimal values and
answers
Divide a quantity in more than two parts in a given
ratio
Multiply integers and decimals with up to two
decimal places
10
Solve problems involving angles by setting up
equations and solving them
2
Draw and use graphs to solve distance–time
problems
Overall mark:
Draw, use and interpret conversion graphs
Objective
1
Solve geometric problems using side and angle
properties of special quadrilaterals
Question
/ 53
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