Download MT March 2016 Examination Paper – Final

Mathematical Techniques
9 March 2016
Examination Paper
Answer ALL questions.
Clearly cross out surplus answers.
Time: 2 hours
The maximum mark for this paper is 100.
Any reference material brought into the examination room must be
handed to the invigilator before the start of the examination.
Candidates are NOT allowed to bring a calculator into the examination
room.
Graph paper will be provided by the centre.
You must show your workings.
Marks are awarded for these.
Answer ALL questions
Marks
Question 1
a)
Give the value of each underlined figure.
i)
3420.4
1
ii)
7.821
1
iii) 0.124
1
b) Write the following as powers of 10.
c)
i)
10 × 10 × 10 × 10 × 10 × 10
1
ii)
1 ÷ 10000
1
Calculate:
i)
203.35 ÷ 10
1
ii)
7.14 × 100
1
iii) 7 ÷ 10
1
d) Round 2891 to the nearest:
e)
f)
i)
10
1
ii)
100
1
Round 4.516 correct to:
i)
the nearest whole number
1
ii)
ONE (1) decimal place
1
iii) TWO (2) decimal places
1
Find the difference between 502.14 and 275.54.
2
g) Use the following calculation to find the value of 1890 × 0.61.
18.9 × 6.1 = 115.29
2
h) Write 525 as a product of its prime factors.
3
Total 20 Marks
Page 2 of 7
Mathematical Techniques
© NCC Education Limited 2016
Marks
Question 2
a)
Work out the following. (You should simplify your answers where possible and
write any improper fractions as mixed numbers.)
i)
3 1
+
4 6
2
ii)
4 1
−
5 10
2
iii) 4 1
×
7 2
2
iv) 3 1
÷
5 11
2
b) A box contains 12 pens. Of the 12 pens, 3 are red, 4 are black and 5 are blue.
c)
i)
What proportion of the pens are black? Write your answer as a fraction and
simplify where possible.
2
ii)
What proportion of the pens are not red? Write your answer as a fraction and
simplify where possible.
2
Write down the following as a percentage.
i)
0.35
1
ii)
12
25
2
d) Calculate 5 + (−7) − 4
e)
2
Look at the following list of numbers.
11
6
5
16
i)
Write down a prime number from the list.
1
ii)
Write down a factor of 25 from the list.
1
iii) Write down a multiple of 3 from the list.
1
Total 20 Marks
Page 3 of 7
Mathematical Techniques
© NCC Education Limited 2016
Marks
Question 3
a)
Write the ratio 3:12 in its simplest form.
1
b) Sara and Ben share £140 in the ratio 1:6. How much does each receive?
4
c)
1
Which one of the following is an algebraic expression?



4𝑦 − 6
𝑎
=3
𝑏
3(𝑥 + 𝑦) = 4𝑝
d) If 𝑥 = 10 and 𝑦 = 2, find:
i)
𝑥 − 3𝑦
1
ii)
10 + 𝑦 2
1
iii) 2𝑥
+ 4𝑦
5
2
e)
Factorise 6𝑎2 + 3𝑎𝑏
2
f)
Expand 4𝑥(2𝑦 + 3𝑥)
2
g) Write down the first THREE (3) terms of the sequence 3 + 4𝑛
3
h) Find the 𝑛th term of the following sequence.
3
9, 13, 17, 21, 25, 29,…
Total 20 Marks
Page 4 of 7
Mathematical Techniques
© NCC Education Limited 2016
Marks
Question 4
a)
A box contains 6 green paperclips and 4 blue paperclips. Two paperclips are
selected at random without replacement.
i)
Draw a tree diagram to illustrate the possible outcomes.
4
ii)
What is the probability that both paperclips are green?
2
iii) What is the probability that both paperclips are blue?
2
iv) What is the probability that both paperclips are different colours?
3
b) Put the following in order, starting with the largest.
473 ml
c)
0.5 l
57 cl
0.523 l
4
60 cl
Find the length of side 𝑎. Give your answer in surd form (as a square root).
5
𝑎
15𝑐𝑚
10 𝑐𝑚
Total 20 Marks
Page 5 of 7
Mathematical Techniques
© NCC Education Limited 2016
Marks
Question 5
a)
The daily rainfall (in mm) in Smalltown is recorded for a month as follows.
22
31
34
29
33
30
19
27
14
18
14
36
18
17
41
24
12
28
32
12
34
27
37
16
23
40
21
14
11
15
i)
Is this data quantitative or qualitative?
1
ii)
Construct an ordered stem and leaf diagram for the data.
4
iii) Find the median value.
2
iv) What is the range of the daily rainfall?
1
Question 5 continues on next page
Page 6 of 7
Mathematical Techniques
© NCC Education Limited 2016
Marks
Question 5 (continued)
b) A group of shoppers were surveyed and asked what their preferred supermarket
was: A, B, C, D or E. The responses are recorded below.
A
C
E
E
A
E
A
E
E
A
A
E
C
A
A
D
D
A
D
D
B
A
C
E
D
A
C
C
D
E
i)
How many shoppers were surveyed?
1
ii)
Copy and complete the following tally chart using the data.
3
Supermarket
Tally
Frequency
A
B
C
D
E
iii) Construct a bar chart to illustrate the data.
4
iv) The researcher decides to present the data as a pie chart. Calculate the
angle for supermarket A and supermarket D.
4
Total 20 Marks
End of paper
Page 7 of 7
Mathematical Techniques
© NCC Education Limited 2016