Download O Level E.Maths Paper 1, Set A

1
Name: ____________________________________________
School: ___________________________________________
MATHEMATICS
4016/01
Paper 1
2 hours
Candidates answer on the Question Paper
READ THESE INSTRUCTIONS FIRST
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
Answer all questions.
If working is needed for any question it must be shown with the answer.
Omission of essential working will results in loss of marks.
The use of an approved scientific calculator is expected, where appropriate.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give
the answer to three significant figures. Give answers in degrees to one decimal place.
For π, use either your calculator value or 3.142, unless the question requires the answer in
terms of π.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total marks for this paper is 80.
For Examiner’s Use
80
This paper consists of 13 pages
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Answer all the questions.
1
Arrange the following in descending order.
27
39
0.60.67
√0.49
0.701
Answer …….., …….., ……., ……..
largest
2
[2]
smallest
The sine of an angle is 0.645.
Give the larger of the two possible angles.
3
4
Answer …………………..
[2]
Answer ………………….
[2]
Given that 9 x 27k = 1, find the value of k
Malik is travelling from Singapore to Sweden.
In Singapore, the exchange rate is 1 Singapore Dollar = 6.20 Swedish Krona.
In Sweden, the exchange rate is 1 Swedish Krona = 0.16 Singapore Dollars.
Malik wants to change 600 Singapore Dollars into Swedish Krona.
How much more Swedish Krona will he get by changing his money in Sweden?
Answer………………….
5
[2]
A train 360m long passes through a tunnel 3.9km long.
The average speed of the train in 33 km/h.
(a) Change km/h to m/s
Answer (a)…………….. m/s
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(b) Calculate the time taken for the train to pass completely through the tunnel.
Give your answer in minutes and seconds, to the nearest second.
Answer (b)………minutes ……..seconds [3]
6
Andy invested some money in a savings account for 6 years.
The rate of compound interest was fixed at 5% per annum.
At the end of the 6 years there was $ 17243.89 in his account.
How much did Andy invest in the savings account?
Answer $...................................
7
[3]
The line 2x – 7y = 18 crosses the x-axis at A and the y-axis at B.
(i) Find the coordinates of
(a) point A,
Answer ……………………….
[2]
Answer ……………………….
[1]
(b) point B
(ii) Another line has an equation 2x – 7y = 28. Will the two lines intersect? Briefly
describe why.
Answer ……………………………………………………………………………
……………………………………………………………………………………..
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8
The length of a pendulum, L, is directly proportional to the square of time taken for
one complete oscillation, T. When the time taken for one complete oscillation is 5
seconds, the length of the pendulum is 80 cm.
(a) Write an equation connecting L and T.
Answer L = ………………
[2]
(b) The length of the pendulum is changed to 100 cm. Find the time taken for one
complete oscillation.
Answer ……………………s [1]
(c) Find the percentage change in the length of the pendulum when the time taken for
one complete oscillation is doubled.
Answer……………………
9
[1]
The cash price of a refrigerator is $1020. The hire-purchase price of the same
refrigerator is $1132. The hire-purchase price is a deposit of 10% of the cash price
plus 12 equal monthly payments.
Calculate one monthly payment.
Answer $………………….
10
[3]
2
Adam collects coloured stamps. 7 of the stamps are red. 40% of the remaining
stamps are blue. The other 24 stamps are black. How many stamps are in Adam’s
collection?
Answer…………………..
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11
The diagram is the speed-time graph of a motorcycle’s journey.
For this journey, calculate
25
20
Speed
(m/s)
10
28
(a)
50
70
Time
(s)
the acceleration of the motorcycle during the first 28 seconds,
Answer…………….m/s2
(b)
the total distance travelled by the motorcycle in 70 seconds,
Answer…………….m
(c)
[1]
[2]
the speed of the motorcycle at time 65 seconds.
Answer…………….m/s
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12
13
Solve the inequalities - 4 < 4x – 10 < 14.
[2]
Answer…………………..
[2]
Answer…………………..
[2]
Write as a single fraction in its simplest form
(a)
(b)
14
Answer…………………..
3𝑥
(2𝑥−3)2
3𝑎2
7𝑏𝑐
÷
−
2
(2𝑥−3)
9𝑎
14𝑏
ξ = {integers x : 1 ≤ x ≤ 11]}
A = {even numbers}
B = {prime numbers}
(a) Draw a Venn diagram to illustrate this information.
Answer (a)
[2]
(b) List the elements contained in the set (A ∩ B)’.
Answer…………………..
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15
If three dice are thrown at the same time, what is the probability that
(a)
(b)
(c)
16
the total of the three numbers shown is 3,
Answer…………………..
[1]
Answer…………………..
[2]
Answer…………………..
[1]
the three dice show the same number
the three dice show different numbers
P and Q lie on the circle, centre O, of radius 14 cm. Angle POB is 2.2 radians.
O.
14
2.2
r
14
Q
P
Find
(a)
(b)
the area of major sector POQ.
Answer…………………cm
[2]
Answer…………………cm2
[3]
the area of major segment PQ.
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17
The waterfall from a dam has a width of 2470 m.
(a)
Express 2470 m in km.
Answer……………km
[1]
(b)
The rate of water flowing over this waterfall is 7.79 x 103 litres per second.
After a flooding incident, the rate of water flow increased to 1.49 x 104 litres per
second. Calculate the percentage increase in the rate of water flow.
Answer…………....%
[2]
(c)
The rate of water flow in another waterfall is 1.77 x 104 litres per second.
Calculate the volume of water flowing over this waterfall in 2 hours. Give your answer
in standard form, correct to 2 significant figures.
Answer………………litres
18
In triangle PRS, PR = 21 cm, SR = √341 cm, PS = 10 cm.
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(a)
Explain why triangle PRS is a right-angled triangle
Answer ……………………………………………………………………………
……………………………………………………………………………………..
(b)
SR is produced to Q and RQ = 5 cm.
(i)
Find the length of PQ.
Answer………………cm
(ii)
[2]
Write down the cosine of angle PRQ.
Answer……………….
19
[2]
[1]
The first four terms of a number sequence are 6, 11, 16 and 21.
(a)
Write down the 9th term of the number sequence
Answer……………….
(b)
Find an expression, in terms of n, for the nth term of the sequence.
Answer……………….
(c)
[1]
[1]
One term in the number sequence is 266. What is the value of n for this term?
Answer……………….
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20
Choose the most appropriate equation for the following graphs. You should select
your answer for each graph, from the box here. There is only one correct equation for
each graph.
y = - x2
y = x2
x=3
y = (x – 1)(x +3)
y=2
y=x+3
y = (x +1)(x – 3)
2y + 2x = 3
(a)
y
0
x
Answer……………..
[1]
Answer……………..
[1]
Answer……………..
[1]
y
(b)
0
(c)
x
y
0
x
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(d)
y
x
0
Answer……………..
21
[1]
In a car race between two drivers, Lewis Hazelton and Jameson Button, the average
time taken to complete a lap for each of these drivers is 60 seconds and 64 seconds
respectively. Assuming they both start the race next to each other and at the same
instance,
(a) Find the time taken for Lewis Hazelton to overlap Jameson Button. Give your
answer in minutes
Answer……………minutes
[2]
(b) How many more laps would Lewis Hazelton have completed compared to
Jameson Button during the first overlap?
Answer…………..lap(s)
22
The cross-section of silver pendant is a quadrilateral with two right angles and a
square hole, as shown below. All measurements are in cm.
1
3.2
1
3.2
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The length of the square hole is 0.71 cm.
The thickness of the pendant is 0.28 cm.
The mass of 1 cubic centimetre of silver is 13.3 grams.
The price of 1 gram of silver is $20.65.
Calculate the value of the silver pendant.
Give your answer to the nearest cent.
Answer $..................... [5]
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