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Examinations Council of Zambia — past paper

ECZ 2024 O-Level Paper 1 — Mathematics

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

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1.
Shade the region P∩R'∩Q on the Venn diagram in the answer space below.
Diagram for question 1
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
2.
Given that E={ natural numbers less than 10},A={ even numbers } and B={ prime numbers }, list A'∩B.
  1. A{1,3,5,7,9}
  2. B{3,5,9}
  3. C{3,5,7}
  4. D{3,5,7,9}
3.
Simplify 3(2x - 4) - 2(x - 1).
  1. A4x - 14
  2. B8x - 10
  3. C4x - 10
  4. D4x - 2
4.
Evaluate (-2)0 × (-2)-3.
  1. A18
  2. B-18
  3. C-8
  4. D8
5.
Factorise completely 27y2 - 3x2.
  1. A3(3y - x)(3y + x)
  2. B3(3y - x)2
  3. C3(9y - x2)
  4. D(3y - x)(3y + x)
6.
A straight line L is represented by the equation 2x - y = 5. Find the gradient of the line L.
  1. A-2
  2. B12
  3. C2
  4. D5
7.
The magnitude of PQ is 20 units. Given that OP = 50 and OQ = 17y, find the positive value of y.
  1. A8
  2. B12
  3. C16
  4. D20
8.
Given that A = 4511, find AT.
  1. A4511
  2. B4151
  3. C5411
  4. D4115
9.
Given that A = 4511 and B = x - 1120, find x if AB = 10421.
  1. A1
  2. B0
  3. C2
  4. D4
10.
Given that 99, 92 and 85 are the first three terms of an arithmetic progression, find the 6th term.
  1. A57
  2. B71
  3. C106
  4. D64
11.
Given that 99, 92 and 85 are the first three terms of an arithmetic progression, find the nth term.
  1. A99 - 7n
  2. B106 - 7n
  3. C106 + 7n
  4. D7n - 106
12.
A six-sided die is thrown once. Find the probability of getting a number which is a multiple of 3.
  1. A16
  2. B13
  3. C12
  4. D23
13.
Solve the equation (1 - 2t)2 = 25.
  1. At = -2 or t = 3
  2. Bt = 3
  3. Ct = -3 or t = 2
  4. Dt = -2 only
14.
In the following diagram, PQRSTU is a triangular prism such that PQ = QR. State the number of planes of symmetry of the prism.
Diagram for question 14
  1. A0
  2. B1
  3. C2
  4. D3
15.
The diagram shows the positions of towns A, B and C on the earth's surface. What is the time at C when the time at A is 11:22 hours?
Diagram for question 15
  1. A03:22 hours
  2. B11:22 hours
  3. C19:22 hours
  4. D23:22 hours
16.
A plane flies from A to B in 9 hours. Calculate its speed if the distance between A and B is 7200 nm.
Diagram for question 16
  1. A720 knots
  2. B800 knots
  3. C900 knots
  4. D64800 knots
17.
Solve the equation 31 - 2x + 4 = 5.
  1. Ax = -12
  2. Bx = 1
  3. Cx = 12
  4. Dx = 0
18.
The diagram shows a sector AOB whose area is 231cm2 and radius 14cm. The angle subtended at the centre is θ. Find the value of θ. [π = 227]
Diagram for question 18
  1. A120°
  2. B90°
  3. C135°
  4. D270°
19.
Given that f(x) = 3x + 5 and g(x) = x + 43, find g-1(x).
  1. Ax + 43
  2. B3x - 4
  3. Cx - 43
  4. D3x + 4
20.
Given that f(x) = 3x + 5 and g(x) = x + 43, find gf(x).
  1. Ax - 3
  2. Bx + 3
  3. C3x + 92
  4. D3x + 3
21.
Given that f(x) = 3x + 5 and g(x) = x + 43, find gf(4).
  1. A17
  2. B4
  3. C7
  4. D15
22.
A container of cooking oil has a mass of 15.4 kg. Find the tolerance of the mass of the container of cooking oil.
  1. A0.5kg
  2. B0.154kg
  3. C0.05kg
  4. D0.1kg
23.
A container of cooking oil has a mass of 15.4 kg. Write down the relative error of the mass of the container of cooking oil as a fraction in its simplest form.
  1. A1154
  2. B5154
  3. C120
  4. D1308
24.
The diagram in the answer space shows triangle ABC with vertices A(2, 3), B(4, 2) and C(4, 4). Triangle ABC is mapped onto triangle A1B1C1 under a reflection in the line x = 6. Draw triangle A1B1C1 on the diagram in the answer space.
Diagram for question 24
  1. AA1(10, -3), B1(8, -2), C1(8, -4)
  2. BA1(6, 3), B1(8, 2), C1(8, 4)
  3. CA1(4, 3), B1(2, 2), C1(2, 4)
  4. DA1(10, 3), B1(8, 2), C1(8, 4)
25.
The equation of a curve is y = x - 2x2 + 1x3. Find dydx.
  1. A1 - 4x - 3x4
  2. B1 - 2x - 3x4
  3. C1 - 4x + 3x4
  4. Dx - 4x - 3x4
26.
It is given that a varies as b and inversely as the square of c, and a = 9 when b = 12 and c = 2. Find the value of k, the constant of variation.
  1. A3
  2. B27
  3. C13
  4. D9
27.
It is given that a varies as b and inversely as the square of c, and a = 9 when b = 12 and c = 2. Find the value of a when b = 16 and c = 4.
  1. A48
  2. B3
  3. C12
  4. D1
28.
It is given that a varies as b and inversely as the square of c, and a = 9 when b = 12 and c = 2. Find the values of c when b = 25 and a = 3.
  1. Ac = 25 or c = -25
  2. Bc = 5 or c = -5
  3. Cc = 5
  4. Dc = 15 or c = -15
29.
In the following diagram, P, Q and R are points on the circumference of the circle, centre O. ARB is a tangent to the circle at R, angle ABP = 15° and angle ARP = 44°. Find (a) angle OPR.
Diagram for question 29
  1. A90°
  2. B46°
  3. C29°
  4. D44°
30.
In the following diagram, P, Q and R are points on the circumference of the circle, centre O. ARB is a tangent to the circle at R, angle ABP = 15° and angle ARP = 44°. Find (b) angle PQR.
Diagram for question 30
  1. A44°
  2. B29°
  3. C136°
  4. D46°
31.
In the following diagram, P, Q and R are points on the circumference of the circle, centre O. ARB is a tangent to the circle at R, angle ABP = 15° and angle ARP = 44°. Find (c) angle BPR.
Diagram for question 31
  1. A15°
  2. B46°
  3. C44°
  4. D29°
32.
A company declares a dividend of 8%. Mary owns 1 300 shares of value K75.00 each. How much dividend does she receive?
  1. AK97 500.00
  2. BK780.00
  3. CK7 800.00
  4. DK1 300.00
33.
The point (-1, -4) is the midpoint of the line PQ. Given that P is the point (2, -3), find the coordinates of the point Q.
  1. A(-4, -5)
  2. B(0, -7)
  3. C(4, 5)
  4. D(-3, -1)
34.
In the following diagram, A, B and C are three points on level ground. A is due north of C, angle ABC = 50° and angle ACB = 60°. Calculate the bearing of (a) A from B.
Diagram for question 34
  1. A290°
  2. B070°
  3. C110°
  4. D050°
35.
In the following diagram, A, B and C are three points on level ground. A is due north of C, angle ABC = 50° and angle ACB = 60°. Calculate the bearing of (b) B from A.
Diagram for question 35
  1. A070°
  2. B290°
  3. C110°
  4. D050°
36.
Two solid cylinders are geometrically similar. The ratio of their corresponding radii is 3 : 2. Given that the volume of the bigger cylinder is 216cm3, calculate the volume of the smaller cylinder.
  1. A96cm3
  2. B144cm3
  3. C32cm3
  4. D64cm3
37.
In the following diagram, ABCD is a trapezium. AB is parallel to CD and X is a point on CD such that AX is the perpendicular height of the trapezium. AB = a, CD = b and AX = h. In the answer space below is an incomplete program written in pseudocode for calculating the area (A) of the trapezium. Complete the program.
Diagram for question 37
  1. AEnter a and b; A = a * b
  2. BEnter a, b and h; A = 12 * (a + b) * h
  3. CEnter h; A = 12 * a * b
  4. DEnter a, b and h; A = (a + b) * h
38.
Write the three inequalities that define the unshaded region R in the diagram below.
Diagram for question 38
  1. Ay ≤ 4; y ≤ x + 4; y ≥ -2x - 8
  2. By ≤ 4; y ≥ x + 4; y ≤ -2x - 8
  3. Cy ≤ 4; y ≥ x + 4; y ≥ -2x - 8
  4. Dy ≥ 4; y ≥ x + 4; y ≥ -2x - 8
39.
A straight line L is perpendicular to the line y = 3x + 4. Given that line L passes through the point (3, a) and has 3 as its y intercept, find the value of a.
  1. A-2
  2. B4
  3. C3
  4. D2
40.
The diagram shows a sketch of a curve passing through A(-5, 0) and B(-1, 0). Find the (i) equation of the curve.
Diagram for question 40
  1. Ay = (x + 5)(x + 1)
  2. By = -(x - 5)(x - 1)
  3. Cy = x2 + 6x + 5
  4. Dy = -(x + 5)(x + 1)
41.
The diagram shows a sketch of a curve passing through A(-5, 0) and B(-1, 0). Find the (ii) coordinates of the turning point of the graph.
Diagram for question 41
  1. A(-2, 4)
  2. B(-3, 4)
  3. C(3, 4)
  4. D(-3, -4)
42.
The following diagram is a speed-time graph of a particle moving in a straight line. The particle decelerates uniformly from a speed of 35m/s to 20m/s in 10 seconds. It then moves at a constant speed of 20m/s for 15 seconds before it decelerates uniformly to come to rest at the 40th second. Calculate the (a) retardation of the particle in the first 10 seconds.
Diagram for question 42
  1. A1.5m/s2
  2. B2m/s2
  3. C15m/s2
  4. D3.5m/s2
43.
The following diagram is a speed-time graph of a particle moving in a straight line. The particle decelerates uniformly from a speed of 35m/s to 20m/s in 10 seconds. It then moves at a constant speed of 20m/s for 15 seconds before it decelerates uniformly to come to rest at the 40th second. Calculate the (b) speed of the particle when t = 31 seconds.
Diagram for question 43
  1. A12m/s
  2. B20m/s
  3. C15m/s
  4. D8m/s
44.
The following diagram is a speed-time graph of a particle moving in a straight line. The particle decelerates uniformly from a speed of 35m/s to 20m/s in 10 seconds. It then moves at a constant speed of 20m/s for 15 seconds before it decelerates uniformly to come to rest at the 40th second. Calculate the (c) average speed of the particle for the whole journey.
Diagram for question 44
  1. A17.5m/s
  2. B145m/s
  3. C20m/s
  4. D18.125m/s