CARDINAL NEWMAN CATHOLIC SCHOOL
Mathematics
Non Calculator Paper
Higher Tier
PRACTICE Year 9 Mid Year Assessment
Name :
Subject
Teacher :
Examination Instructions

•
•
•
Use black ink or black ball-point pen. Draw diagrams in pencil.
Answer all questions.
You must answer the questions in the spaces provided. Do not write
outside the answer space around each page or on blank pages.
Do all rough work in this book. Cross through any work you do not
want to be marked.
Examination Information
•
•
•
•
•
The marks for questions are shown in brackets.
The maximum mark for this paper is 80.
You have 80 minutes to complete the paper.
You may ask for more answer paper, graph paper and tracing
paper. These must be tagged securely to this answer book.
In all calculations, show clearly how you work out your answer.
Tutor
Group:
Tutor:
9
For Examiners Use
Question
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Total Marks
Percentage
Grade 1-9:
QCA Points:
Target
Mark
Awarded
Self-Assessment and Reflection
Question
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Maths Watch CD
Clip Number
17
91
78
81
79 & 80
120
121
124
33/34/35
93/94
95
74
70
66 & 67
177
133
96
97
208
Topic
Adding integers and decimals
Estimating answers
Product of Primes
Squares, Cubes and Roots
HCF and LCM
Angles in Parallel Lines
Angles in a Triangle
Bearings
Simplifying Expressions
Expanding and factorising brackets
Substitution
Dividing Fractions
Comparing Fractions
Multiplying and dividing by decimals
Recurring Decimals to fractions
Midpoint line on a graph
Straight line graphs
Gradients of straight lines
Perpendicular Lines
Page 2
Q1.Steve buys 60 plants for £2.50 each.
He sells 25 of the plants for £5 each.
He sells 20 of the plants for £4 each.
He wants to make £100 profit.
What should he sell each of the remaining plants for?
You must show your working.
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
.................................................................................................................................
Answer £ ...................................................................
(Total 6 marks)
Q2.
The table shows information about grocery items.
Small
Medium
Large
Bag of apples
−
495 grams
795 grams
Tin of fish
195 grams
285 grams
−
Packet of nuts
37 grams
57 grams
87 grams
Use approximations to estimate the total amount these items weigh.
2 large bags of apples
1 small tin of fish
2 medium packets of nuts
You must show your working.
...................................................................................................................................
...................................................................................................................................
Page 3
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
Answer ........................................................... grams
(Total 3 marks)
Q3.
(a)
Write 200 as the product of prime factors.
Give your answer in index form.
Answer ......................................................................
(3)
(b)
Circle the two pairs of numbers that have
Highest Common Factor (HCF)
4
and
Least Common Multiple (LCM)
4 and 60
4 and 30
4 and 12
60
12 and 30
12 and 20
(2)
(Total 5 marks)
Q4.
Here are some properties of numbers.
A
Even
B
Odd
C
Prime
D
Square
Page 4
E
(a)
Two-digit
Which two properties does the number 4 have?
Circle the correct letters.
A
B
C
D
E
(1)
(b)
Can one number have all of the properties?
Tick a box.
Yes
No
Cannot tell
Give a reason for your answer.
.........................................................................................................................
.........................................................................................................................
(1)
(c)
Write down a number with three of the properties.
State which properties it has.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
Number ........................
Properties ........................, ........................, ........................
(2)
(Total 4 marks)
Q5.
(a)
Write 132 as a product of prime factors.
Page 5
Answer ......................................................................
(2)
(b)
Work out the Highest Common Factor (HCF) of 110 and 132
Answer ......................................................................
(2)
(Total 4 marks)
Q6.
Not drawn
accurately
(a)
Work out the size of angle x.
Answer ........................................................ degrees
(1)
Page 6
(b)
Which one of these describes angles x and y?
Circle your answer.
alternate angles
corresponding angles
interior angles
vertically opposite angles
(1)
(Total 2 marks)
Q7.
This triangle is drawn accurately.
What type of triangle is it?
Tick two boxes.
acute-angled
obtuse-angled
equilateral
isosceles
scalene
Page 7
(Total 1 mark)
Q8.The map shows the positions of two ships A and B, and a port O.
Scale: 1 cm represents 10 km
(a)
Ship A is North-East of O.
What is the three-figure bearing of North-East?
Answer .................................................................... °
(1)
(b)
Ship A sails directly to O.
Page 8
In which direction does it travel?
Answer ......................................................................
(1)
(c)
Measure the bearing of ship B from O.
Answer .................................................................... °
(1)
(d)
How far is ship B from O?
.........................................................................................................................
.........................................................................................................................
Answer ...................................................................... km
(2)
(Total 5 marks)
Q9.
(a)
Work out the value of
81 + 80
..........................................................................................................................
Answer ......................................................................
(2)
(b)
Write
610 ÷ 62
as a single power of 6
..........................................................................................................................
Answer ......................................................................
(1)
(c)
Simplify fully
5x3y2 × 3x4y3
..........................................................................................................................
..........................................................................................................................
Answer ......................................................................
(2)
Page 9
(Total 5 marks)
Q10.
(a)
(x + 5)(x + 9)
Expand and simplify
..........................................................................................................................
..........................................................................................................................
..........................................................................................................................
Answer ......................................................................
(2)
(b)
5x2 − 10xy
Factorise fully
..........................................................................................................................
..........................................................................................................................
Answer ......................................................................
(2)
(Total 4 marks)
Q11.
Kelly is trying to work out the two values of w for which 3w − w³ = 2
Her values are 1 and –1
Are her values correct?
You must show your working.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
(Total 2 marks)
Page 10
Q12.
Bag A contains £7.20 in 20p coins.
Bag B contains only 5p coins.
The number of coins in bag B is three-quarters of the number of coins in bag A.
How much money is in bag B?
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
Answer £ ...................................................................
(Total 4 marks)
Q13.(a)
Write 80% as a decimal.
Answer ......................................................................
(1)
(b)
Write 0.7 as a fraction.
Page 11
Answer ......................................................................
(1)
(c)
Write
as a decimal.
Answer ......................................................................
(1)
(d)
Write 80%, 0.7 and
in order with the smallest first.
........................................................................................................................
........................................................................................................................
Answer .................... , .................... , ....................
(1)
(Total 4 marks)
Q14.(a)
Work out
0.6 × 0.1
Answer ......................................................................
(1)
(b)
Work out
0.5 − 0.18
Answer ......................................................................
(2)
(Total 3 marks)
Q15.
Convert
to a fraction in its lowest terms.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
Page 12
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
Answer ............................................
(Total 3 marks)
Q16.A is the point with coordinates (x, 2y).
B is the point with coordinates (3x, 4y).
The midpoint of AB has coordinates (−4, 15).
Work out the values of x and y.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
x = .............................................................................
y = .............................................................................
(Total 4 marks)
Q17.
One of these graphs is a sketch of
y = 1 – 2x
Which one?
Circle the correct letter.
Page 13
(Total 1 mark)
Q18.
Here is a sketch of the line
x + 2y = 8
Page 14
Work out the gradient of the line.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
Answer ......................................................................
(Total 3 marks)
Q19.
(a)
Draw a line parallel to the line below.
_________________________________________
(1)
Page 15
(b)
Draw a line perpendicular to the line below.
__________________________________________
(1)
(Total 2 marks)
Page 16
M1.
60 × 2.5 (= 150)
M1
25 × 5 (+) 20 × 4 or 205
M1
their 150 + 100 − their 205
oe
M1
45
A1
their 45 ÷ 15
Dependent on 3nd M1
M1dep
3
A1 ft
Alternative method
5 − 2.5 and 4 − 2.5 or 2.5 and 1.5
M1
25 × their 2.5 (+) 20 × their 1.5, or 92.5
M1
100 − their 92.5
oe
M1
7.5
A1
Their 7.5 ÷ 15 or 0.5 ( + 2.5)
Dependent on 3nd M1
M1dep
3
AIft
[6]
Page 17
M2.
800 or 1600 or 200 or 60 or 120 or 100
M1
800 or 1600
and
200
and
60 or 120 or 100
M1
1920 or 1900 or 2000
SC1 1900 without working
or 1900 from 1899
A1
[3]
M3.
(a)
2 (×) 100 or 5 (×) 40
oe conditional on one prime factor in a correct product
equal to 200 or one prime factor shown in a correct section
on a factor tree starting from 200
Any order
allow on prime factor tree or repeated division using 2 or 5
correctly
condone 100 (×) 2 (×) 1 etc for this mark
M1
2 (×) 2 (×) 2 (×) 5 (×) 5
Any order
allow on prime factor tree or repeated division
A1
23 × 52
Strand (i) correct index notation
Any order
ft correct product of prime numbers in index form from their
working
Q1ft
Page 18
Additional Guidance
23 + 52
M1A1Q0
(200 =) 2 (×) 2 (×) 5 (×) 5 and 22 × 52 is minimum Q1ft
200 ÷ 2 = 100
M1
2 (×) 10 (×) 10 as a product or shown on a correct section of factor tree
M1
20 (×) 5 (×) 2 as a product or shown on a correct section of factor tree
M1
20 (×) 5 (×) 4 as a product or shown on a correct section of factor tree
M0
(b)
4 and 60 and 12 and 20
B1 one correct
or one correct and one incorrect
or two correct and one incorrect
Any indication
B2
[5]
M4.
(a)
A and D
B1
(b)
No and a number cannot be both odd and even
or
No and a number cannot be both square and prime
or
No and a number cannot be two-digit, even and prime
oe
Accept eg
No and a number cannot be both A and B
B1
(c)
16 or 36 or 64 and A, D, E
or
Page 19
25 or 49 or 81 and B, D, E
or
11 or 13 or 17 or 19 or 23 or 29 or
31 or 37 or 41 or 43 or 47 or 53 or
59 or 61 or 67 or 71 or 73 or 79 or
83 or 89 or 97 and B, C, E
B1 Any of the correct possible numbers (listed for B2) but
with incorrect properties
or
any even square number and A, D
or
any odd square number and B, D
or
any prime number > 2 and B, C
or
2 and A, C
B2
[4]
M5.
(a)
2 (×) 66 or 3 (×) 44 or 2 (×) 6 (×) 11
or 3 (×) 4 (×) 11 or 12 (×) 11
or 2 (×) 2 (×) 33 or 2 (×) 3 (×) 22
Any order
Allow on prime factor tree or repeated division.
Condone 2 (×) 66 (×) 1 etc
M1
2 × 2 × 3 × 11
or 22 × 3 × 11
Any order
A1
Additional Guidance
2, 2, 3, 11
M1A0
(b)
Alternative method 1
2 (×) 5 (×) 11 = 110
M1
22
SC1
11
A1
Page 20
Alternative method 2
List of factors of 110 and 132 up to 22 with 2 errors or omissions
(1), 2, 5, 10, 11, 22 (55, 110)
and
(1), 2, 3, 4, 6, 11, 12, 22
(33, 44, 66, 132)
M1
22
SC1
11
A1
Additional Guidance
(1, 55, 110) and (1, 33, 44, 66, 132) are not omissions
[4]
M6.(a)
130
B1
(b)
Vertically opposite
Strand (i)
Q1
[2]
M7.
acute-angled and isosceles
B1
[1]
M8.(a)
045
Strand (i) for a 3 figure bearing
0.45 or 45 is Q0
Q1
(b)
South West or 225 (°)
SW but not West South
B1
Page 21
(c)
[115, 119]
B1
(d)
[11, 11.5] (× 10)
M1
[110, 115]
SC1 for any measurement seen (in cm)
correctly multiplied by 10
A1
[5]
M9.
(a)
(81 =) 8 or (80 =) 1
M1
9
SC1 91
A1
Additional Guidance
81 + 1 with answer 91
M1A0
81 + 0 with answer 81
M0A0
8 on answer line without working
M0A0
81 + 80 with answer 8
M0A0
8 × 1 = 8 and 8 × 0 = 0 with answer 8
M0A0
(b)
68
B1
(c)
15x7y5
B1 two terms correct
B2
Page 22
Additional Guidance
8x7y5
B1
15x6y5
B1
15x7× y5
B1
8x7× y5 or 15x7× y6
B1
15x12y6
B0
15x7+ y5
B0
8x7+ y5
B0
[5]
M10.
(a)
x2 (+) 9x (+) 5x (+) 45
Allow one error
Any order
M1
x2 + 14x + 45
Any order
A1
Additional Guidance
Terms may be seen in a multiplication grid
Do not ignore attempts to factorise after correct answer seen
x(x + 14) + 45
M1A0
x2 + 14x + 40 with no working seen is one error
M1A0
x2 + 10x + 45 with no working seen is two errors
M0A0
x2 + 5x + 45 with no working seen
M0A0
Page 23
(b)
5x(x − 2y)
B1 5(x2 − 2xy) or x(5 x − 10y)
B2
Additional Guidance
Condone missing final bracket 5x(x − 2y
B2
5x × (x − 2y)
B1
Condone missing final bracket 5(x2 − 2xy
B1
[4]
M11.
3 × 1 − 1³ = 3 − 1
= 2 and correct
B1
3 × (–1) – (–1)³ = –3 + 1
= –2 and incorrect
B1
Condone No, they should be 1 and −2 for B1B1
SC1 w = −2
[2]
M12.
Alternative method 1
720 ÷ 20 or 7.2(0) ÷ 0.2(0) or 36
oe
M1
their 36 ÷ 4 × 3 or 27
M1
Page 24
their 27 × 5 or 135 or their 27 × 0.05
dep on 2nd M1
oe
M1dep
1.35
A1
Alternative method 2
7.20 ÷ 4 × 3 or 5.4(0)
M1
their 5.4(0) ÷ 20 or 27
M1
their 27 × 5 or 135 or their 27 × 0.05
dep on 2nd M1
oe
M1dep
1.35
A1
Additional Guidance
£135
M1M1M1A0
£ crossed out and 135p
M1M1M1A1
Do not allow further work to add on or subtract from their 27 for third method mark
e.g. 36 ÷ 4 × 3 = 27 followed by 36 + 27 = 63 and 63 × 5
M1M1M0A0
Allow rounding, truncation or exact decimal for their 27 in third method mark
e.g. 720 ÷ 20 = 35, 35 ÷ 4 × 3 = 26.25, 26 × 5 (= 130)
M1M1M1A0
[4]
M13.
(a)
(0).8(0)
B1
(b)
oe eg
,
Page 25
B1
(c)
(0).75
B1
(d)
0.7,
, 80(%)
In any format
Allow correct answer or ft from their answers to a,b,c.
B1 ft
[4]
M14.(a)
(0).06 or
oe decimal or fraction
B1
(b)
(0).32
B1
(0).02 or (0).12 or (0).22 or (0).42 or −(0).32
B2
[3]
M15.
Alternative method 1
(n = 0.17272… and)
100n = 17.272…
oe
eg 10n = 1.7272… and
1000n = 172.72…
M1
Page 26
(99n = 17.272… – 0.17272… or
99n = 17.1 or
or
or
oe
eg 990n = 172.72… – 1.7272… or
990n = 171
M1dep
A1
Alternative method 2
0.07272… =
M1
or
M1dep
A1
[3]
M16.
= –4
or 4x = 2 × –4 or 4x = −8
Page 27
or 2x = –4
oe
M1
x = –2
oe
A1
= 15
or 6y = 2 × 15 or 6y = 30
or 3y = 15
oe
M1
y=5
oe
A1
[4]
M17.
B
B1
[1]
M18.
Alternative method 1
2y = −x + 8
2y = 8 − x
or
or −2y = x − 8
or
−2y = −8 + x
M1
y=−
or
x+4
y=
y=4−
or
or
x
y=
Page 28
or
y=
or
y=
A1
−
oe
ft their y = mx + c if M1A0 awarded
B1ft
Alternative method 2
Identifies at least two correct points
Could be shown on sketch
(0, 4) and (8, 0) or 4 and 8 on axes
M1
Their
M1
−
oe
ft their two points if M0M1 awarded
A1ft
[3]
M19.
(a)
Parallel line drawn
Acetate will be provided to check that line is within ±2°
B1
(b)
Perpendicular line drawn, any length
Allow if lines have right angle indicated and line doesn’t
appear to be perpendicular.
Lines do not have to cross.
Acetate will be provided to check that line is within ±2°
B1
Page 29
[2]
Page 30
E1.
The majority of students made good attempts at this question. However, many
ignored the ‘profit of £100’ part of the question and merely divided their profit so far by 15.
Many students did not show working even though this was a requirement of the question.
There was some very good arithmetic seen but some students used inefficient methods
on calculations, for example using repeated addition for multiplication.
E2.
This question was well answered. Some students misread the question and did not extract
the correct information from the table. A common incorrect method was to add the exact
weights with an incorrect answer of 1899 grams.
E3.
Part (a) was well answered, although some students wrote 2 × 2 × 2 × 3 × 3 without the
correct use of index form. Part (b) was not as well answered. The large majority correctly
identified one of 4 and 60 or 12 and 20 as a correct pair but failed to identify both correct
pairs.
E5.
Part (a) was well answered, although some students did not find all prime factors or did
not write the correct prime factors as products. Part (b) was not as well answered. The
large majority identified 11 as a common factor instead of 22 as the highest common
factor.
E6.Foundation Tier
Part (a) was answered better than part (b). The common incorrect answer in (b) was
corresponding angles.
Higher Tier
Part (a) was well answered. Part (b) was not well answered.
Page 31
E8.Very few students gave correct bearings. In part (a) it was common to see answers of 135°
and 315° but also seemingly random angles. In part (d) some students estimated the
distance by counting the grid squares, so 10 cm leading to an answer of 100 km was
common. Many students were unable to multiply a decimal by 10, for example 11.2 × 10
was often evaluated as 11.20 km or 110.2 km.
E9.
Parts (b) and (c) of this question were answered better than part (a). In part (a) the most
common misconception was 80 = 0. Also frequently seen were 81+ 0, 161+ 0 and 81 = 8 × 1
with 80 = 8 × 0.
E10.
This question was very well answered. Common incorrect answers were adding to give 14
as the final term in part (a) and not fully factorising in part (b).
E12.
This provided an excellent start for many students. The majority chose to find the number
of coins first, 720 ÷ 20 = 36. Arithmetical errors and incorrect methods occurred in finding
¾ of 36. Those who adopted the approach of finding ¾ of £7.20 first usually progressed
no further than £5.40 which was a common incorrect answer.
E13.
Many students managed to put the three numbers in the correct order in part (d).
Common incorrect answers were 80% = 8.0, 0.7 = 1/7 and
Page 32
.
E14.Only a minority of students gave the correct response of 0.06 in part (a). By far the most
common incorrect answer was 0.6 but 6.0 was occasionally seen. There were better
responses in part (b). The most common incorrect answers were 0.22, 0.13 and −0.13.
E16.A large number of students did not attempt this question and many others little progress.
Many attempted to draw diagrams but showed no understanding of what to do next. A
common error was to add the coordinates giving 4x = −4 and 6y = 15
Page 33