Download Maths Sets 8.1 Practice Questions

Set 8.1 – Practice Questions A
Name
A calculator may be used from Question 10 onwards.
1 Use index notation to write each of the following as the product of its prime factors.
a 120
…………………………
b 72
…………………………
(4 marks)
2 Use your results from Question 1 to find
a the highest common factor of 120 and 72
…………………………
b the lowest common multiple of 120 and 72
…………………………
(4 marks)
3 Write each of these as a single power.
a 73 × 77
…………………………
b 1815 ÷ 183
…………………………
(2 marks)
4 Round each number to the given number of significant figures.
a 60 799 (2 s.f.)
…………………………
b 0.006 058 7 (3 s.f.)
…………………………
(2 marks)
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Set 8.1 – Practice Questions A
5 Estimate 30.92
…………………………
(2 marks)
6 Fill in each empty box to make the statement true.
a 10 + 5(x + 3) ≡ 5(x +
b 10 − 3x + 4 ≡
)
+ 3(4 − x)
(2 marks)
7 Expand and simplify 6x(2x − 4) − 5(2 + x)
…………………………
(3 marks)
8 Find the value of each expression when a = 4 and b = −5
a 2 + 3a2
…………………………
b 5 + (15 − 3b)2
…………………………
(3 marks)
9 Solve the equation 20 − 3(2x − 7) = 5(x + 5) − 6
…………………………
(4 marks)
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Set 8.1 – Practice Questions A
10 A wheel has a diameter of 70cm. Work out its circumference.
….…………………cm2
(2 marks)
11 A circle fits exactly inside a square as shown.
The square has sides of length 10cm.
a Work out the area of the circle.
……………………cm2
b Work out the area shaded grey.
…………………………cm2
(4 marks)
12 A rectangle has length 5cm and width 12cm. Work out the length of the diagonal of the rectangle.
…………………………cm
(2 marks)
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Set 8.1 – Practice Questions A
13 The cross-section of a prism is in the shape of a trapezium as shown.
The volume of the prism is 630cm 3. Work out its length.
………………………cm
(3 marks)
14 A water bottle in the shape of a cylinder holds 1 litre of water when full. Its height is 15cm.
Work out the radius of the water bottle. (1 litre = 1000cm3)
………………………cm
(3 marks)
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Set 8.1 – Practice Questions A
15 The graph shows the cost of cleaning a patio for company A and company B.
a Quentin uses one company to clean the patio of the hotel that he manages and he uses the
other company to clean his small patio at home. Assuming he wants to keep costs low, use the
graph to explain which company he uses for the hotel and which for his house.
.………………………………………………………………………………………………………………
.………………………………………………………………………………………………………………
.………………………………………………………………………………………………………………
b Work out which company is cheaper, and by how much, to clean a patio with area 50m 2.
£…………………………
(8 marks)
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Set 8.1 – Practice Questions A
16 Jan walks 1200 metres in 10 minutes. This would be shown as a straight line on a distance–time
graph. Her walking speed varies throughout the 1200 metres.
a What does the steepness of the straight line represent?
.………………………………………………………………………………………………………………
.………………………………………………………………………………………………………………
b The owners of a holiday house consider three different ways of charging for electricity.
Use the graphs to describe the way each option is charged.
Option 1:……………………………………..………………………………………………………………
.………………………………………………………………………………………………………………
Option 2:………………………………………..……………………………………………………………
.………………………………………………………………………………………………………………
Option 3:…………………………………………..…………………………………………………………
.………………………………………………………………………………………………………………
(6 marks)
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Set 8.1 – Practice Questions A
Answers
All answers are worth 1 mark unless otherwise indicated.
From Question 12 onwards, deduct no more than 2 marks across the paper for rounding errors.
1 a 23 × 3 × 5 (2)
b 23 × 32 (2)
1 mark for any equivalent form, using only the prime factors 2, 3 and 5
1 mark for any equivalent form, using only the prime factors (i.e. 2 and 3)
1 mark for identifying that 23 and 3 are factors of both numbers
2 a 24 (2)
b 360 (2)
1 mark for 120 × 72 ÷ 24 or equivalent
3 a 710
b 1812
4 a 61 000
b 0.006 06
5 900 (2)
1 mark for attempting to square 30
6 a 5
b 2
7 12x2 − 29x − 10 (3) 2 marks for 12x2 − 24x – 10 − 5x; or 1 mark for sight of at least two of these
four terms
8 a 50
b 905 (2)
1 mark for sight of 900
x = 2 (4)
9
3 marks for 11x = 22 or 41 = 11x + 19; or 1 mark for each side of
20 − 6x + 21 = 5x + 19
10 a 70πcm2 (2)
1 mark for approximation 219.9cm2; accept 3 or more s.f. of 219.911 48
correctly rounded
11 a ≈78.54cm2 (2)
accept 3 or more s.f. of 78.539 816 3 correctly rounded
b
≈21.46cm2
(2)
accept 3 or more s.f. of 78.539 816 3 correctly rounded or (100 − their part a
so long as the result is positive; 1 mark for method
12 13cm (2)
1 mark for sight of √52 + 122 or 52 + 122 or 25 + 144
13 15cm (3)
2 marks for sight of 42cm2 or 1 mark for (630 ÷ their 42)
14
≈4.607cm (3)
accept 3 or more s.f. of 4.606 588 66 correctly rounded; 2 marks for
1000 ÷ 15π or for sight of 21.22 or 1 mark for 1000 ÷ 15
15 a company A is cheaper for patios less than 22.5m2 and company B is cheaper for patios more
than 22.5m2, so he uses company A for the house and company B for the hotel (2)
b company A £162.50 (2)
company B £115 (2)
1 mark for correct method (e.g. 130 ÷ 40 × 50)
1 mark for £1.50 or for correct method (e.g. 40 + 60 ÷ 40 × 50)
∴ company B is cheaper by £47.50 (2)
1 mark for sight of 47.5
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Set 8.1 – Practice Questions A
Answers
Use the formula for the circumference of a
circle
Construct and solve equations that involve
multiplying out brackets by a negative
number and collecting like terms, e.g.
4(2a − 1) = 32 − 3(2a − 2)
Substitute positive and negative integers
into linear expressions and expressions
involving powers
Simplify expressions involving brackets and
powers, e.g. x(x2 + x + 4),
3(a + 2b) − 2(a + b)
Know and understand the meaning of an
identity and use the identity sign
Use numbers of any size rounded to 1
significant figure to make standardised
estimates for calculations with 1 step
Recognise graphs showing constant rates of
change, average rates of change and variable
rates of change
Discuss and interpret real-life graphs, e.g.
conversion graphs, water filling
baths/containers, graphs comparing e.g.
mobile phone tariffs – how you can see which
tariff is better for different numbers of calls
Use and apply Pythagoras’ theorem to solve
problems
Calculate the lengths, areas and volumes in
cylinders
Apply the index laws for multiplication and
division of small positive integer powers
13
Round numbers to a given number of
significant figures
Use prime factor decomposition to find the
HCF or LCM of 2 numbers
Use the formulae for area of a circle, given the
radius or diameter
/ 54
Overall mark:
Calculate the lengths and areas given the
volumes in right prisms
Find the prime factor decomposition of a
number
Objective
12
Question
10
9
8
7
6
16
15
14
11
Objective
accept any way of indicating that charge does not depend on
the number of units used (1)
b option 1: the charge is constant
5
4
3
2
1
Question
1 marks for speed
16 a her average walking speed (2)
option 2: the charge is proportional to the number of units used (1)
accept equivalent explanation
option 3: the charge per unit decreases with the number of units used until the graph is flat (1) at
which point there is no further charge for more units used (1)
accept equivalent explanation
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Set 8.1 – Practice Questions B
Name
Please use this grid for questions 1–4.
1 Describe the single transformation that moves shape A to shape B.
…………………………...………………………………………………………………………………………
(2 marks)
2 Reflect shape A in the line y = −x. Label the image C.
Show your answer on the grid.
(2 marks)
3 a Rotate shape B 90° anti-clockwise about the point (−1, 1). Label the image D.
Show your answer on the grid.
b Describe a single transformation that moves shape D to shape C.
……..………………...………………………………………………………………………………………
(4 marks)
4 Enlarge shape A, centre (3, 3), scale factor −2. Label the image E.
Show your answer on the grid.
(2 marks)
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Set 8.1 – Practice Questions B
5 Trapezium ABCD is enlarged to produce trapezium EFGH.
The perimeter of ABCD is 22cm.
a Work out length FG.
…………………………cm
b Work out the perimeter of trapezium EFGH.
………………………cm
(4 marks)
6 A cylinder has radius 4cm, height 5cm and volume 251.33cm 3.
It is enlarged using a scale factor of 3.
Work out the volume of the enlarged cylinder. Write your answer to the nearest whole number.
………………………cm3
(3 marks)
.
7 Work out 0.6 × £24
£…………………………
(2 marks)
..
8 Convert 0.37 to a fraction.
…………………………
(3 marks)
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Set 8.1 – Practice Questions B
9 The price of a pair of shoes was £30
The price was reduced to £23.40
Work out the percentage change in price.
………………………%
(3 marks)
10 The population of a town is now 200 000
An estimate of the population in the future is worked out by assuming that the population will keep
growing at 3% per year.
Work out an estimate of the population in 8 years’ time.
…………………………
(3 marks)
11 Here is a sketch of a triangle.
Use the given side length and angles to make an accurate drawing of the triangle.
(3 marks)
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Set 8.1 – Practice Questions B
12 Construct the perpendicular bisector of this line. Leave in your construction lines.
(3 marks)
13 Use a ruler and compasses to construct the bisector of this angle.
(3 marks)
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Set 8.1 – Practice Questions B
14 A council officer is planning a path across a field. The path is to be equidistant from the sports
centre, S, and the youth centre, Y. Construct the locus of the points that are equidistant from the
two points.
(3 marks)
15 A highways architect is planning a new entrance road to a hospital. The road will join South Road
to the Accident and Emergency (A&E) entrance of the hospital.
The road needs to be placed so that it is the shortest distance possible between South Road and
A&E.
Use a straight edge and compasses to construct the position of the new road on this plan.
(3 marks)
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Set 8.1 – Practice Questions B
Answers
All answers are worth 1 mark unless otherwise indicated.
Grid for Answers 1–4
1 reflection in the line x = 1 (2) 1 mark for correct transformation; 1 mark for correct line equation
2 correct reflection with vertices of triangle at (−2, −3), (−1, −3), (−1, −5) (2)
1 mark for triangle of correct shape, size and orientation
3 a correct rotation with vertices of triangle at (−2, 1), (−1, 1), (−1, −1) (2)
1 mark for triangle of correct shape, size and orientation
b translation
( –04 ) (2)
accept follow through from their C and D as long as it is a translation
1 mark for ‘translation’; 1 mark for correct vector
4 correct enlargement with vertices of triangle at (3, 5), (3, 7), (−1, 7) (2)
1 mark for triangle of correct shape, size and orientation
5 a 12cm (2)
b 33cm (2)
1 mark for sight of 1.5
1 mark for attempting to multiply 22 by their scale factor
6 6786cm3 (3)
2 marks for 6785.91 or 6785.84;
or 1 mark for 27 × 251.33 or π × 12 × 12 × 15
7 £16 (2)
1 mark for sight of 3
37
2
8 99 (3)
1 mark for sight of 100x = 37.373 737 373 7…
and a further mark for sight of 100x − x = 37
9 22% (3)
2 marks for 0.22 or for 6.6 ÷ 30 × 100 or equivalent;
or 1 mark for 6.6 ÷ 30
10 253 354 (rounding down to whole person at end of eighth year)
or 253 352 (with rounding down to whole person at end of each year) (3)
if first method, then 2 marks for 1.038 = 1.266 77...;
or 1 mark for sight of 200 000 × 1.038
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Set 8.1 – Practice Questions B
Answers
11 triangle correct size with base of 8cm and measured angles of 30°, 40° and 110° (3)
2 marks for 2 correct angles within 1°; 1 mark for 8cm length within
1mm and either 30° or 40° within 1°; or 1 mark for 8cm length correct
within 2mm and 2 angles correct within 2°
12
construction arcs evident and angles either side of perpendicular between 89° and 91° (3)
2 marks for angles between 88° and 92° with construction arcs evident; or 1 mark for some
evidence of construction arcs; or 1 mark for angles between 89° and 91° without any evidence of
construction
13
construction lines and angles either side of the line of bisection are within 1° of each other (3)
2 marks for angles either side of bisection line different by no more than 2°, together with
construction lines; or 1 mark for some evidence of correct construction method
14
perpendicular bisector constructed; construction arcs left in and angles either side of bisector
between 89° and 91° (3)
2 marks for angles between 88° and 92° with construction arcs evident; or 1 mark for some
evidence of construction arcs; or 1 mark for angles between 89° and 91° without any evidence of
construction
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Set 8.1 – Practice Questions B
Answers
15
construction arcs evident and angles either side of perpendicular between 89° and 91° (3)
2 marks for angles between 88° and 92° with construction arcs evident; or 1 mark for some
evidence of construction arcs; or 1 mark for angles between 89° and 91° without any evidence of
construction
Convert a recurring decimal to
a fraction
Learn fractional equivalents to
key recurring decimals, e.g.
0.333 333..., 0.666 666 66...,
0.111 11..., and by extension
0.222 222....
Calculate the new volume of a
shape after enlargement
Understand the implications of
enlargement for perimeter
Enlarge 2D shapes, given a
centre of enlargement outside
the shape and a negative
whole-number scale factor
Recognise and visualise the
transformation of 2D shape
translation
Rotation on a coordinate grid
Recognise and use the
perpendicular distance from a
point to a line as the shortest
distance to the line
Draw the locus equidistant
between 2 points or from a
point
Use straight edge and
compasses to construct the
bisector of an angle
Use straight edge and
compasses to construct the
mid-point and perpendicular
bisector of a line segment
Draw an accurate triangle given
two angles and the included
side (ASA)
Calculate compound interest
and repeated percentage
change
/ 43
Overall mark:
15
14
13
12
11
10
9
Question
Reflection on a coordinate grid
in y = x, y = −x
Calculate percentage change,
using the formula actual
change / original amount × 100
– where formula is recalled
Objective
Describe a reflection, giving the
equation of the line of reflection
Objective
8
7
6
5
4
3b
3a
2
1
Question
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