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Examinations Council of Zambia — past paper

ECZ 2018 O-Level Paper 1 — Mathematics

44 questions · downloaded from g12titan.com, where this paper is marked free online

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1.
Use set notation to describe the shaded region in the diagram below.
Diagram for question 1
  1. AA∩(B∪C)′
  2. BA∩(B∩C)′
  3. C(B∪C)′
  4. DA∪(B∪C)′
2.
The Venn diagram below shows sets A and B . List A'∩B.
Diagram for question 2
  1. A{4}
  2. B{2,4,7,8}
  3. C{3,4,5,6}
  4. D{1,9}
3.
Find the value of x0 × 23.
  1. A23x
  2. B16
  3. C8
  4. D0
4.
Factorise completely 18 - 2x2.
  1. A2(x - 3)(x + 3)
  2. B(3 - x)(3 + x)
  3. C2(9 - x)(9 + x)
  4. D2(3 - x)(3 + x)
5.
Z is a point (-1, 8) and M is a point (2, 12). Find the magnitude of ZM.
  1. A7
  2. B25
  3. C√7
  4. D5
6.
Floyd had 125 shares in a company. At the end of a financial year, the company declared a dividend of K3.00 per share. How much was due to Floyd?
  1. AK375.00
  2. BK41.67
  3. CK128.00
  4. DK250.00
7.
A cylinder with diameter 2 cm has a volume of 5 cm3. Find the volume of a similar cylinder with diameter 8 cm.
  1. A20cm3
  2. B320cm3
  3. C80cm3
  4. D160cm3
8.
Express 140211324 -14522301-2 as a single matrix.
  1. A-116042302-8
  2. B712170111112013
  3. C712170101112013
  4. D701121120171113
9.
For an arithmetic progression 16, 25, 34, 43, 52, ........, write down the (a) next term.
  1. A59
  2. B60
  3. C61
  4. D70
10.
For an arithmetic progression 16, 25, 34, 43, 52, ........, write down the (b) nth term.
  1. A16n + 9
  2. B9n + 7
  3. C7n + 9
  4. D9n + 16
11.
A plane leaves a town P(0°, 30°W) and flies due East to a town Q(0°, 50°E) in 3 hours. The distance between P and Q is 4 800 nm. (a) Calculate its average speed.
  1. A1 600 knots
  2. B14 400 knots
  3. C800 knots
  4. D1 200 knots
12.
A plane leaves a town P(0°, 30°W) and flies due East to a town Q(0°, 50°E) in 3 hours. The distance between P and Q is 4 800 nm. (b) If the plane leaves P at 06 00 hours, what time will it arrive at Q?
  1. A14 20 hours
  2. B03 40 hours
  3. C11 20 hours
  4. D09 00 hours
13.
Given that matrix M = 3-10-2130-12, find MT.
  1. A3-10-2130-12
  2. B3-201-1-1032
  3. C30-2-11-1032
  4. D3-20-11-1032
14.
Expand and simplify (c + 3)2.
  1. A2c + 6
  2. Bc2 + 9
  3. Cc2 + 6c + 9
  4. Dc2 + 3c + 9
15.
A box contains 5 green, 3 yellow and 6 red beads of the same type. Find the probability of picking a yellow bead at random from the box.
  1. A314
  2. B311
  3. C13
  4. D614
16.
Find the equation of a straight line passing through (1, 5) and (2, 10).
  1. Ay = 5x
  2. By = 5x + 1
  3. Cy = x + 5
  4. Dy = 5x - 5
17.
y varies directly as the square of x and y = 96 when x = 4. Find the value of the constant k.
  1. A16
  2. B6
  3. C96
  4. D24
18.
y varies directly as the square of x and y = 96 when x = 4. Find the value of y when x = 5.
  1. A150
  2. B120
  3. C156
  4. D30
19.
y varies directly as the square of x and y = 96 when x = 4. Find the values of x when y = 24.
  1. Ax = 4 or x = -4
  2. Bx = 2 or x = -2
  3. Cx = 1 or x = -1
  4. Dx = 2 only
20.
Solve the equation 2x2 = 8.
  1. Ax = 4 or x = -4
  2. Bx = 2 only
  3. Cx = 16 or x = -16
  4. Dx = 2 or x = -2
21.
The mass (m) of a bag of mealie meal is 25 kg. Complete the statement in the answer space.
  1. A24.5 ≤ m ≤ 25.5
  2. B25 ≤ m < 25.5
  3. C24 ≤ m < 26
  4. D24.5 ≤ m < 25.5
22.
In the diagram below, F is due east of E, angle GEF = 60° and angle EFG = 40°. Calculate the bearing of (a) F from G.
Diagram for question 22
  1. A050°
  2. B040°
  3. C130°
  4. D230°
23.
In the diagram below, F is due east of E, angle GEF = 60° and angle EFG = 40°. Calculate the bearing of (b) E from G.
Diagram for question 23
  1. A150°
  2. B330°
  3. C030°
  4. D060°
24.
The point (5, 2) is the midpoint of a straight line joining A(x, 9) and B(3, y). Find the value of x and the value of y.
  1. Ax = 7, y = 5
  2. Bx = -7, y = -5
  3. Cx = 2, y = 11
  4. Dx = 7, y = -5
25.
The length of a line is 8 cm. If this is recorded as 8.2 cm, calculate the percentage error.
  1. A2.50%
  2. B0.20%
  3. C25%
  4. D2%
26.
Given that f(x) = 2x - 5 and g(x) = x + 3, find f-1(x).
  1. Ax + 32
  2. Bx - 52
  3. C2x + 5
  4. Dx + 52
27.
Given that f(x) = 2x - 5 and g(x) = x + 3, find f-1(-10).
  1. A52
  2. B-10
  3. C-2.5
  4. D-7.5
28.
Given that f(x) = 2x - 5 and g(x) = x + 3, find gf(3).
  1. A1
  2. B6
  3. C9
  4. D4
29.
Given that y = 2x3 - 5x2 + 4x + 2, find dydx.
  1. A6x2 - 10x + 4
  2. B6x2 - 10x
  3. C2x2 - 10x + 4
  4. D6x2 - 5x + 4
30.
In the diagram below, AC = 10 cm, angle ABC = 90° and angle BAC = 30°. Calculate BC.
Diagram for question 30
  1. A20cm
  2. B5cm
  3. C10cm
  4. D5√3cm
31.
In the diagram below, O is the centre of the circle. A, B, C and D are points on the circumference. AD produced meets the line from C at E such that CD = DE and angle AOC = 120°. Calculate angle (a) ADC.
Diagram for question 31
  1. A120°
  2. B30°
  3. C60°
  4. D90°
32.
In the diagram below, O is the centre of the circle. A, B, C and D are points on the circumference. AD produced meets the line from C at E such that CD = DE and angle AOC = 120°. Calculate angle (b) ABC.
Diagram for question 32
  1. A30°
  2. B120°
  3. C60°
  4. D90°
33.
In the diagram below, O is the centre of the circle. A, B, C and D are points on the circumference. AD produced meets the line from C at E such that CD = DE and angle AOC = 120°. Calculate angle (c) DEC.
Diagram for question 33
  1. A120°
  2. B60°
  3. C30°
  4. D45°
34.
The diagram below shows a sketch of the graph of y = 2 + x - x2 passing through the points E and G. Find the (a) coordinates of E and G.
Diagram for question 34
  1. AE(0, -1), G(0, 2)
  2. BE(1, 0), G(-2, 0)
  3. CE(-1, 0), G(2, 0)
  4. DE(-2, 0), G(1, 0)
35.
The diagram below shows a sketch of the graph of y = 2 + x - x2 passing through the points E and G. Find the (b) maximum value of y.
Diagram for question 35
  1. A94
  2. B-2.25
  3. C12
  4. D2
36.
The diagram below shows a triangular prism with AB = BC = AC = DE = EF = DF and AD = BE = CF. State the number of planes of symmetry of the prism.
Diagram for question 36
  1. A1
  2. B4
  3. C3
  4. D6
37.
In the answer space below is an incomplete program in pseudo code to calculate the circumference of a circle of latitude x°, given the radius R of the earth. Complete the program by filling in the blank spaces with appropriate statements.
Diagram for question 37
  1. AEnter x and R; C = πR2cos x°
  2. BEnter C; R = C2πcos x°
  3. CEnter x and R; C = 2πR
  4. DEnter x and R; C = 2πRcos x°
38.
On the XOY plane below, region R is unshaded. Write the three inequalities that define the region R.
Diagram for question 38
  1. Ax ≥ -3; y ≤ (23)x + 2; y ≤ -x + 7
  2. Bx ≤ -3; y ≥ (23)x + 2; y ≤ -x + 7
  3. Cx ≥ -3; y ≥ (23)x + 2; y ≥ -x + 7
  4. Dx ≥ -3; y ≥ (23)x + 2; y ≤ -x + 7
39.
Solve the equation x13 = 4.
  1. A16
  2. B43
  3. C64
  4. D12
40.
In the diagram below, OPQ is a sector of a circle whose centre is O, radius x cm and angle POQ = 80°. Given that the area of the sector OPQ is 308 cm2, calculate the value of x. [π = 227]
Diagram for question 40
  1. A49cm
  2. B21cm
  3. C14cm
  4. D441cm
41.
The diagram below shows ΔA. If ΔA is mapped onto ΔB by a translation T = 3-2, draw ΔB on the diagram in the answer space below.
Diagram for question 41
  1. AReflect ΔA in the x-axis
  2. BTranslate every vertex 2 units right and 3 units down
  3. CTranslate every vertex 3 units right and 2 units down
  4. DTranslate every vertex 3 units left and 2 units up
42.
The diagram below is a speed-time graph of a particle which accelerates uniformly from rest for 12 seconds until it reaches a speed of 24 m/s. It moves at a constant speed for a further 12 seconds before it accelerates uniformly for another 6 seconds to a speed of V m/s. (a) Calculate its acceleration for the first 12 seconds.
Diagram for question 42
  1. A12m/s2
  2. B2m/s2
  3. C24m/s2
  4. D1m/s2
43.
The diagram below is a speed-time graph of a particle which accelerates uniformly from rest for 12 seconds until it reaches a speed of 24 m/s. It moves at a constant speed for a further 12 seconds before it accelerates uniformly for another 6 seconds to a speed of V m/s. (b) Find the distance which the particle covered in the first 24 seconds.
Diagram for question 43
  1. A432m
  2. B144m
  3. C576m
  4. D288m
44.
The diagram below is a speed-time graph of a particle which accelerates uniformly from rest for 12 seconds until it reaches a speed of 24 m/s. It moves at a constant speed for a further 12 seconds before it accelerates uniformly for another 6 seconds to a speed of V m/s. (c) Given that the total distance covered was 600 m, calculate the value of V.
Diagram for question 44
  1. A24m/s
  2. B40m/s
  3. C32m/s
  4. D28m/s