Download Maths Sets 7.1 Practice Questions

Set 7.1 – Practice Questions A
Name
1 Three numbers have a mean of 10 and a mode of 8.
Write the three numbers.
…………………………………………………………
(2 marks)
2 The table shows the number of cars of each colour in a show room.
Colour
Frequency
Black
6
Silver
5
White
2
Red
7
Angle
a Complete the table.
b Draw a pie chart for the data.
(5 marks)
3 a Work out 992 ÷ 32
…………………………
b Use your answer to part a to write the answer to 1024 ÷ 32
…………………………
(3 marks)
4 Find the missing numbers.
a 8−
= 21
…………………………
b 8−
= −21 …………………………
c −7 ×
= −21 …………………………
d −84 ÷
= 21 …………………………
(4 marks)
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Set 7.1 – Practice Questions A
__
__
3
5 Work out √27 × (−1 − √16)
…………………………
(3 marks)
6 Write an expression for
a 2 more than p
………………………………………
b double q ………………………………………
c half of r ………………………………………
(3 marks)
7 Max has a Saturday job and he earns £8 per hour.
a Write a formula connecting the amount he is paid, in pounds, P, with the number of hours he
works, h.
…………………………
It costs Max £5 for a return ticket to travel to work.
b Write a formula connecting the amount of money Max makes, in pounds, M, by working on
Saturday, with the number of hours he works, h.
…………………………
(3 marks)
8 Simplify 2x + 2y + x + 3x − y
…………………………
(2 marks)
9 Simplify 2x2 + 2y + 3x2 + 3x − 3y3 by collecting like terms.
…………………………
(2 marks)
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Set 7.1 – Practice Questions A
10 Find the value of each expression when a = 2 and b = −4
a 3a + b
…………………………
b 5a − 2b
…………………………
(3 marks)
11 Find the value of each expression when c = 5 and d = 7
a 3 + c2
…………………………
b (2c − d)2
…………………………
c (2c − d)2 × (c − d)2
…………………………
(4 marks)
12 Expand
a x(x + 4)
…………………………
b 7x(3 − 2x)
…………………………
(4 marks)
13 Factorise
a 12x + 15
…………………………
b 32 − 24x
…………………………
c 32x − 24x2
…………………………
(3 marks)
14 Write
4
a 27 as an improper fraction.
…………………………
b
37
5 as a mixed number.
…………………………
(2 marks)
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Set 7.1 – Practice Questions A
15 Work out
4
3
…………………………
b 6−4
5
1
…………………………
3
7
…………………………
a 7 + 14
c 8 + 12
(6 marks)
16 Each Year 7 student does an indoor sport: table tennis, badminton or squash. In form 7TW, there
are 24 students and three eighths play table tennis, one third play badminton.
a Work out how many more students in 7TW play table tennis than play badminton.
…………………………
b Work out what fraction of students in 7TW play table tennis or badminton.
…………………………
c Work out what fraction of students in 7TW play squash.
…………………………
(4 marks)
17 Work out
a 38 + 2 4
3
3
…………………………
1
4
…………………………
b 85 − 1 5
(4 marks)
18 Ayeesha has some beads in a bag.
One quarter of these are blue, 35% are yellow and the rest are red.
a Work out the percentage of red beads.
………………………%
b Work out the smallest number of beads that there can be of each colour.
…………………………
(4 marks)
19 Work out
3
9
a 7 × 14
…………………………
3
9
b 7 ÷ 14
…………………………
(4 marks)
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Set 7.1 – Practice Questions A
Answers
1 8, 8, 14 (2) 1 mark for 8, 8, …, or for any three numbers with a mean of 10
2
a
Colour
Frequency
Angle
Black
6
108°
Silver
5
090°
White
2
036°
Red
7
126°
(3)
2 marks for 3 correct angles or 1 mark for two
correct angles or sight of 18°
b
angles within 1° (2)
3 a 31 (2)
1 mark for 2 angles within 1° or 3 angles within 2°
1 mark for use of a correct method with one arithmetic slip
b 32 (1) accept their part a increased by 1
4 a −13 (1)
b 29 (1)
c 3 (1)
d −4 (1)
5 −15 (3)
2 marks for sight of −5 and 1 mark for multiplying by 3
6 a p + 2 (1) accept 2 + p
b 2q (1)
r
c 2 (1)
accept 2 × q, but not q2
accept r ÷ 2
7 a P = 8h (2)
b M = 8h − 5 (1)
8 6x + y (2)
1 mark for sight of 8h or 8 × h or h × 8
accept their 8h − 5
1 mark for one correct term
9 5x2 + 2y + 3x − 3y3 (2)
1 mark for 5x2 or 2y + 3x − 3y3
10 a 2 (1)
b 18 (2)
1 mark for 8 or −8
11 a 28 (1)
b 9 (1)
c 36 (2)
accept their part b × 4, or 1 mark for sight of 4
12 a x2 + 4x (2)
b 21x − 14x2 (2)
1 mark for one correct term
1 mark for one correct term
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Set 7.1 – Practice Questions A
Answers
13 a 3(4x + 5) (1)
b 8(4 − 3x) (1)
c 8x(4 − 3x) (1)
14 a
accept adjustment of x in front of bracket of their part b
18
7 (1)
2
b 75 (1)
11
11
1 mark for fraction equivalent to 14 or for correct method
7
7
1 mark for fraction equivalent to 12 or for correct method
23
23
1 mark for fraction equivalent to 24 or for correct method
15 a 14 (2)
b 12 (2)
c 24 (2)
16 a 1 (2)
1 mark for sight of 8 badminton or 9 table tennis
17
b 24 (1)
7
c 24 (1)
1
49
17 a 68 (2)
1 mark for sight of 8
2
2
3
1 mark for sight of 5 or for 7 − 5
b 65 (2)
18 a 40% (1)
b 5 blue; 7 yellow; 8 red (3) 1 mark for sight of 20; further mark for at least one of 5, 7, 8
27
19 a 98 (2)
1 mark for numerator; 1 mark for denominator
2
2
b 3 (2)
Question
1
2
3
4
5
6
7
8
9
Simplify simple expressions
involving power but not brackets by
collecting like terms
Simplify simple expression by
collecting like terms
Derive more complex formulae
expressed in letter symbols
Construct expressions from
worded descriptions using all four
basic operations
Combine laws of arithmetic for
brackets with mental calculations
of cube roots and square roots
Multiply and divide integers –
positive and negative integers
Divide three-digit by two-digit
whole numbers
Construct on paper and using
ICT simple pie charts using
categorical data, e.g. two or
three categories
Calculate the mean of a set of
data
Objective
1 mark for numerator; 1 mark for denominator or 1 mark for fraction equivalent to 3
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Set 7.1 – Practice Questions A
Answers
Cancel common factors before
multiplying fractions
Recall of equivalent fractions and
decimals and percentage including
for fractions that are greater than 1
15
16
Substitute positive integers into
expressions involving small powers
Multiply a single term over a
bracket
Use the distributive law to take out
numerical common factors
Express time as a mixed number
Add and subtract simple fractions
with denominators of any size
Use fraction notation to express a
smaller whole number as a fraction
Subtract mixed number fractions
when the fractional part of the first
fraction is all that is required for the
calculation to take place
14
Substitute positive and negative
integers into simple formulae
13
Objective
/ 65
Overall mark:
19
18
12
17
11
10
Question
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Set 7.1 – Practice Questions B
1
Name
ABD is an equilateral triangle.
BCD is right-angled scalene triangle.
DEF is an isosceles triangle.
AD is parallel to BC.
a Identify a pair of alternate angles. …………………………
b Calculate angle DFE. You must show your working.
…………………………
(4 marks)
2 A regular pentagon is joined to a parallelogram as shown.
a
Calculate angle CFG.
…………………………°
b Calculate the reflex angle ACD.
…………………………°
(6 marks)
3 In a group of 20 students, 3 are left handed. Work out the percentage of left-handed students.
…………………………%
(2 marks)
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Set 7.1 – Practice Questions B
4 Complete the table.
Fraction
Decimal
Percentage
6.25
410%
19
5
(6 marks)
5 Round each decimal to two decimal places.
a 44.248
…………………………
b 40.208
…………………………
c 40.298
…………………………
d 40.998
…………………………
(4 marks)
6
A shopkeeper reduced a pair of trousers by 15% in a sale. The original price was £48
Work out the sale price of the trousers.
…………………………
(4 marks)
7 Work out
a 0.5 × 0.6
…………………………
b 0.3 × 0.02
…………………………
c 0.15 ÷ 0.3
…………………………
d 0.8 ÷ 0.16
…………………………
(5 marks)
8 Solve the equation 3 + 2x = 11
…………………………
(2 marks)
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Set 7.1 – Practice Questions B
9 Solve the equation 65 − 4x = 1
…………………………
(2 marks)
10 Find both solutions to the equation x2 + 1 = 17
…………………………
…………………………
(3 marks)
11 A square has sides of length x − 2
An equilateral triangle has sides of length x + 1
The triangle and the square have the same perimeter.
a Form an equation.
…………………………
b Solve your equation to find x.
…………………………
c Write the length of the sides of the square.
…………………………
(5 marks)
12 Use trial and improvement to solve the equation x3 = 61
Give your answer to one decimal place.
Use the table to help you.
x
x³
Is x too big or too small?
3
Write the answer to one decimal place.
…………………………
(4 marks)
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Set 7.1 – Practice Questions B
Answers
^
^
^
^
1 a ADB (or BDA) and DBC (or CBD) (1)
b 75° (3)
accept the angles clearly marked on the diagram
1 mark for sight of 60°, 1 mark for sight of 30°
360°
1 mark for a valid method, e.g. 180° − int angle of pentagon = 180° − (180° − 5 )
2 a 72° (2)
^
b 216° (4) 1 mark for ACF = 108° or marked on diagram
1 mark for any correct method
^
1 mark for FCD = 108° or marked on diagram
^
^
1 mark for ACD + FCD
3
3 15% (2)
4
25
4
[6.25]
41
10
4.1
19
[5]
1 mark for sight of 20
625% (2)
1 mark each
[410%] (2)
1 mark each
3.8 380% (2)
1 mark each
5 a 44.25 (1)
b 40.21 (1)
c 40.30 (1) do not accept 40.3
d 41.00 (1) do not accept 41.0 or 41
6 £40.80 (4)
3 marks for £40.8 or 40.8, or 2 marks for sight of £7.20, or 1 mark for sight of £4.80
or 4.8 or £2.40 or 2.4; 1 mark for subtracting their £7.20 from £48
7 a 0.3 (1)
b 0.006 (1)
c 0.5 (1)
d 5 (2)
1 mark for 80 ÷ 16
8 4 (2)
1 mark for subtracting 3 or for dividing by 2
9 16 (2)
1 mark for sight of 64
10 4 and −4 (3) 1 mark for sight of 16, 1 mark for sight of 4 or −4
11 a 4(x − 2) = 3(x + 1) or equivalent (2)
1 mark for sight of 4(x − 2) or 3(x + 1) or equivalent
b x = 11 (2)
1 mark for sight of correct equation without brackets, i.e. 4x − 8 = 3x + 3
c 9 units (1)
accept their part b – 2
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Set 7.1 – Practice Questions B
Answers
Find the outcome of a given
percentage decrease
Round decimals to the nearest two
decimal places
Recall of equivalent fractions,
decimals and percentage including
for fractions that are greater than
1.
Express one given number as a
percentage of another
Use systematic trial and
improvement to find the
approximate solution to one
decimal place of equations such as
x3 = 29
Construct and solve equations of
the form a(x ± b) = c(x ± d)
Find a positive and negative
square root as a solution of an
equation involving x2
Solve simple two-step linear
equations with integer coefficients,
of the form ax + b = c with
negative x coefficient
Solve simple two-step linear
equations with integer coefficients,
of the form ax + b = c
/ 47
Overall mark:
12
11
10
9
8
7
Question
Use the interior and exterior angles
of regular and irregular polygons
Multiply and divide by decimals,
dividing by transforming to division
by an integer
Objective
Solve geometric problems using
side and angle properties of
equilateral and isosceles triangles
Objective
6
5
4
3
2
1
Question
Marks
accept results given to any level of
accuracy as long as correctly rounded
accept correct row for 3.94, although halfway test at 3.95 is all that is required (1)
x
x3
Is x too big or too small?
3
27
Too small
4
64
Too big
(1)
3.5
42.875
Too small
3.7
50.653
Too small
at least one of these rows correctly
completed (1)
3.8
54.872
Too small
3.9
59.319
Too small
3.95
61.630
Too big
12
x = 3.9 (1)
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