www.studyguide.pk
Apex Grammar School O & A Level Evening Classes
‘O’ Level Power Revision Series
Elementary Mathematics
EVALUATION TEST PAPER
REAL EXAMINATION QUESTIONS
for Secondary 4
Name: ______________________
Time Start: ___________
Date: ______________________
Time End: ____________
Total Marks :
/ 100
16 questions
Total time: 120 min
DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO.
FOLLOW ALL INSTRUCTIONS CAREFULLY.
www.studyguide.pk
1.
(a) In this question, you are required to find Mr Lim’s household expenses. Mr
Lim save 15% of his monthly income and spend 20% of the remainder on
entertainment. If Mr Lim earns a monthly income of $2650, calculate the
amount he spends on entertainment each month.
[2]
(b) In a sale, all prices are reduced by 18%. Mr Lim bought a new oven in the sale
for $1250.
(i) Find the normal price of the oven.
[1]
(ii) Given that the shopkeeper still makes a profit of 18%, calculate the cost
price of the oven.
[1]
(iii) Calculate the percentage profit the shopkeeper would have made if he had
not given the 18% discount.
[2]
(c) Mr Lim goes to the bank to deposit some money and to exchange some local
dollars for British pounds (₤).
3
(i) Calculate the simple interest earned in 2 years if Mr Lim deposits $8500
4
in a fixed deposit account at an interest rate of 1.2% per annum.
[1]
(ii) Assuming that the exchange rate is 2.72 local dollars to 1 British pound,
how many British pounds will Mr Lim get if he exchange 6000 local
dollars? Give your answer to the nearest British pound.
[2]
2.
An area of 225 km2 is represented on a map by an area of 36 cm2. Calculate
[2]
(a) the scale of the map in the form 1:n.
(b) the length of a road on a map with an actual distance of 12.5 km.
[1]
3.
ABCDE…. Is part of a regular polygon in which each of its interior angle if four
times of each of its exterior angle. How many sides does the polygon have? [2]
C
D
B
E
A
4.
The point (2,1) is marked on each diagram in the answer space. On these
diagrams, sketch the graphs of
(a) x + y = 2,
[1]
[1]
(b) xy = 2,
[1]
(c) y = 2x.
(a)
(b)
y
x
(c)
y
x
y
x
1
O Level Power Revision Series
Elementary Mathematics
www.studyguide.pk
5.
y is directly proportional to x2.
(a) If the value of x is halved, find the percentage change in y.
[2]
(b) If the difference in the values of y when x = 4 and when x = 1 is 3, find y in
[2]
terms of x.
6.
An oil merchant packages his cooking oil in bottles of 1kg, 5kg, and 10kg. He
supplies his cooking oil to three supermarkets. The number of bottles of cooking
oil supplied to each supermarket is shown in the table.
Supermarket
P
Q
R
1 kg
65
120
250
Weight
5 kg
55
7
220
10 kg
40
60
130
The cost price of 1 kg, 5 kg and 10 kg bottles are $1.30, $3.60 and $7.20
respectively.
In a particular month, Supermarket P received 20 such deliveries, Supermarket Q
received 15 such deliveries and Supermarket R received 12 such deliveries.
(a) Write down two matrices such that the elements of their product under matrix
multiplication will give the total number of each type of bottle delivered to the
supermarkets in that month. Find this product.
[3]
(b) Write down two matrices such that the elements of their product under matrix
multiplication will give the total amount of money paid by each supermarket for
that month. Find this product and hence write down the total earnings of the
[3]
merchant by supplying oil to Supermarket P, Q and R.
7.
8.
Given that -5 ≤ x ≤ 3 and -2 ≤ y ≤ 7, find
(a) the largest possible value of x – 3y
(b) the smallest possible value of x2 – y2,
(c) the largest possible value of – 2xy.
[1]
[1]
[1]
1
x+6.
[2]
3
1 1 5 5 17 13
(bi) Write down the next two terms in the sequence , , , , , ,.... [1]
2 2 8 7 22 16
(bii) The first four terms of a sequence are 2, 8, 18, 32, …
Write down an expression, in terms of n, for the nth term of this sequence.
[1]
(a) Find the integer values of x such that 2x – 6 < 3x – 4 ≤
2
O Level Power Revision Series
Elementary Mathematics
www.studyguide.pk
9.
(a) Express
(i) 0.34 square metres in square centimeters,
[1]
(ii) 5.24 kilometres per hour in metres per minute.
[1]
(b) The numbers 784 and 980, written as the products of their prime factors, are
784 = 24 x 72
980 = 22 x 5 x 872
Find (i)
784,
[1]
(ii) the largest integer which is a factor of both 784 and 980,
[1]
(iii) the smallest positive integer value of p for which 784p is a multiple
of 980.
[1]
10.
Express as a single fraction in its simplest form
2
10 y
5x
−
x − 3 y 9 y2 − 2
x
11.
[3]
2
(a) Factorise 9 x −
y
2
+ 4y − 4
[2]
2
12.
13.
(b) Simplify (3y-2) - 9y(y-5)
(c) Solve the simultaneous equations
3x – 2y = 13
1
x + y−9= 0
2
2q − r
Given that 3 p =
,
q+r
(a) express r in terms of p and q,
(b) find the value of r if p = 1 and q = 2
15.
[2]
[2]
[1]
A cyclist cycles at a speed of 20 km h-1.
(a) What is his speed in ms-1. Give your answer correct to 2 decimal places. [2]
(b) How far can he cycle in 20 seconds? Give your answer to the nearest metre.
[1]
( )
1
14.
[1]
−
1
7 2 0 1 3
−9 +
.
(a) Evaluate 2
9
8
2
y × y
n
= y , find the value of n.
(b) Given that
−2
y
In the diagram, ABˆ C = 90°, AB = 12 cm and AN = 13 cm and CN = 12 cm.
A
Find the value of (a) cos ANˆ C ,
2
(b) AC
13
C
12
N
O Level Power Revision Series
Elementary Mathematics
[2]
[1]
[2]
[2]
12
B
3
www.studyguide.pk
16.
The diagram, which is not drawn to scale, shows four points A, B, C and D on
horizontal ground. T is the top of a building of height 500 m, at point C.
B is due north of A. The bearing of C from A is 063° and ∠ACD = 116°.
AC = 4 km, CD = 9 km and AB = 3.5 km.
(a) Calculate the distance from A to D.
[2]
(b) Find the bearing of D from A.
[3]
(c) Find the area of triangle ABC.
[2]
A man leaves D at 08 20. He walks directly to A, then goes on to B at a constant
speed of 2km/h. During his journey, he stops for 25 minutes along DA when he
reaches a point P when the angle of elevation of the top of the building, T, from P
is greatest.
(d) Calculate his greatest angle of elevation.
[3]
(e) At what time does he arrive at B?
[3]
4
O Level Power Revision Series
Elementary Mathematics
www.studyguide.pk
17.
The diagram, not drawn to scale, PQT and RST are tangents to a circle, centre O.
Given that QTˆS = 66° , SAˆ B = 33° and ACˆ Q = 83° ,
(a) name three right angles and state your reasons clearly.
[3]
(b) Calculate
(i) BSˆR,
[1]
[1]
(ii) SQˆ B,
(iii) TOˆ Q,
(iv) ABˆ Q .
[2]
[2]
18.
15 taps could fill a tank completely with water in 1 hour. If the number of taps
were to increase by 3, how many minutes would it take to fill the same tank
completely with water?
[2]
19.
The points A and B are (-3, 5) and (6, -1) respectively.
(a) Calculate (i) the gradient of the line AB.
[1]
(ii) the equation of the line passing through A and B
[1]
(b) Given that M is the midpoint of AB, find the coordinates of point M. [1]
Hence find the equation of the line passing through M and parallel to the line
2x + y – 6 = 0.
[1]
5
O Level Power Revision Series
Elementary Mathematics
www.studyguide.pk
20.
Answer the whole of this question on a sheet of graph paper.
The waiting time, in minutes, of 660 patients at a hospital for consultation was
recorded and the results were distributed as shown in the cumulative frequency
table below.
Waiting time
in minutes
No. of
patients
≤ 20
≤ 25
≤ 30
≤ 35
≤ 40
≤ 45
≤ 50
≤ 55
≤ 60
0
12
36
120
245
422
575
648
660
(a) Using a horizontal scale of 2 cm to represent a waiting time of 5 minutes, for
values from 20 minutes to 60 minutes and a vertical scale of 2 cm to represent
100 patients, draw a smooth cumulative curve to illustrate this information. [2]
(b) Showing your method clearly, use your graph to estimate
(i) the less number of patients whose waiting time at the hospital for
consultation is less than or equal to 38 minutes,
(ii) the median of the distribution,
(iii) the interquartile range.
(c) The table gives the information in a different form.
Waiting time
20 < x ≤ 30 30 < x ≤ 35 35 < x ≤ 40 40 < x ≤ 45
in minutes
No. of
48
p
125
177
patients
Find the value of p and of q.
[1]
[1]
[2]
45 < x ≤ 50
50 < x ≤ 55
153
q
(d) Two patients are selected at random.
(i) Find as a fraction in its simplest form, the probability that their waiting
time is more than 52 minutes,
[2]
(ii) “The probability that one of the patients’ waiting time was less than 44
minutes and the other more than 49 minutes is approximately 0.096.”
State, with reason, if the above statement is accurate.
[1]
6
O Level Power Revision Series
Elementary Mathematics
www.studyguide.pk
Answer Key:
1.
(a) 14 h 45 min
(b) 990 ÷ 5.5 = 180
2.
(a) 1: 250 000
(b) 12.5 km: 5 cm
3.
10 sides
y
y
4.
y
2
4
x
x
2
x
5.
x
2
(a) -75%
(b)
7.
(a) 9
(b) -49
8.
(a) x = -1, 0
(bi)
9.
(ai) 3400 cm2 (aii) 87
6.
5
 20 0 0  65 55 40   1300 1100 40 


 

(a)  0 15 0  120 7
60  =  1800 105 900 
 0 0 12  250 220 130   3000 2640 1560 


 

 1300 1100 800  1.3  11410 

  

(b)  1800 105 900  3.6  =  9198 
 3000 2640 1560  7.2  14636 

  

(bi) 28
37 25
,
44 29
(c) 70
(bii) 37.5 cm2
2
m/min
5
(bii) 196
(biii) 5
10.
− 5( x + 2 y )( x + y )
(3 y + x )(3 y − x )
11.
(a) (3x + y - 2)(3x – y + 2)
(b) 44y + 4
(c) y = 4, x = 7
7
O Level Power Revision Series
Elementary Mathematics
www.studyguide.pk
q (2 − 3 p)
3p +1
(b) −
1
2
12.
(a)
13.
(a) 5.56 ms-1
14.
(a) 2
15.
(a) -
16.
(a) 11.4
17.
(a) TQˆ B = PQˆ B = RSˆO = TSˆO = 90°
(bi) 33°
(bii) 33 °
(biii) 57°
18.
19.
20.
(b) 111 m
2
3
(b) 4
1
2
5
13
(b) 433 cm
(b) 108.5
(c) 6.24
50 mins
2
2
(aii) 26 y = − x + 3
(ai) −
3
3
(bi)
190 patients
(bii) 42.5 minutes
(biii) 10.5 minutes
(c)
p = 84, q = 85
26
(di)
7249
380 660 − 550
= 0.192 , No
(dii) 2 ×
×
660
659
(d) 9.9
(e) 1610
(biv) 50°
(b) y = −2 x + 5
8
O Level Power Revision Series
Elementary Mathematics