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Examinations Council of Zambia — past paper

ECZ 2025 O-Level Paper 1 — Mathematics

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

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1.
Shade A'∩(B∩C) on the diagram in the answer space below.
Diagram for question 1
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
2.
If P={1,3,5,7},P∪Q={1,2,3,4,5,6,7} and P∩Q={5,7}, list Q.
  1. A{1,2,4,5,6}
  2. B{2,3,4,6,7}
  3. C{2,4,5,6,7}
  4. D{1,2,4,6,7}
3.
Simplify 3(x + 3) - 2x(x - 1).
  1. A−2x2 + x + 9
  2. B2x2 + 5x + 9
  3. C−2x2 + 5x − 9
  4. D−2x2 + 5x + 9
4.
Factorise completely 3a - c - 3ab + bc.
  1. A(3a − c)(1 − b)
  2. B(3a + c)(1 − b)
  3. C(3a − c)(1 + b)
  4. D(3a − c)(b − 1)
5.
Solve the equation (x − 1)2 − 25 = 0.
  1. Ax = 6 or x = −4
  2. Bx = 6
  3. Cx = 4
  4. Dx = 4 or x = −6
6.
A village banking cooperative for women declared a dividend at the end of a financial year. What was the dividend per share if Mrs Spencer, who owned 1 025 shares, received R2 050.00?
  1. AR2 050.00 per share
  2. BR1.00 per share
  3. CR0.50 per share
  4. DR2.00 per share
7.
Evaluate 412 × 4.
  1. A16
  2. B6
  3. C8
  4. D2
8.
Given that 7, 11, 15, 19, … is an arithmetic progression, find: (a) the tenth term; (b) the sum of the first twelve terms.
  1. A(a) 43 (b) 348
  2. B(a) 47 (b) 396
  3. C(a) 39 (b) 324
  4. D(a) 43 (b) 290
9.
The probability that a learner will not miss the school bus on any particular day is 18. What is the probability that the learner will miss the bus on any particular day?
  1. A68
  2. B17
  3. C18
  4. D78
10.
Two similar solids X and Y have surface areas 5 cm2 and 20 cm2 respectively. If the volume of solid Y is 200 cm3, calculate the volume of solid X.
  1. A50 cm3
  2. B25 cm3
  3. C100 cm3
  4. D12.5 cm3
11.
A bottle of mineral water has a capacity of 500 ± 0.5 millilitres. Find the (a) tolerance, (b) percentage error.
  1. A(a) 0.5 mL (b) 0.1%
  2. B(a) 500 mL (b) 0.1%
  3. C(a) 0.5 mL (b) 1%
  4. D(a) 1 mL (b) 0.1%
12.
Given that tan ∠BAC = 34, find the value of sin ∠BAC.
  1. A45
  2. B34
  3. C35
  4. D43
13.
The functions f and g are defined as f(x) = 2x + 1 and g(x) = 3x - 2, x ≠ 2. Find: (a) f-1(x), (b) gf(x), (c) gf(-2).
  1. A(a) f-1(x) = 1 - x2 (b) gf(x) = 32x - 3 (c) gf(-2) = 3-2
  2. B(a) f-1(x) = 2x - 1 (b) gf(x) = 3x - 1 (c) gf(-2) = -1
  3. C(a) f-1(x) = x + 12 (b) gf(x) = 32x + 1 (c) gf(-2) = 35
  4. D(a) f-1(x) = x - 12 (b) gf(x) = 32x - 1, x ≠ 12 (c) gf(-2) = -35
14.
Find ∫(6x2 - x + 3) dx.
  1. A2x3 - x22 + 3x + C
  2. B2x3 - x2 + 3x + C
  3. C18x2 - x + 3 + C
  4. D2x3 - x22 + 3x
15.
Solve the equation x32 = 8.
  1. Ax = 2
  2. Bx = 4
  3. Cx = 16
  4. Dx = 64
16.
In the following diagram, P is the point (0, 4), Q is the point (-4, 0) and O is the origin. Find the equation of a straight line through O which is perpendicular to the line PQ.
Diagram for question 16
  1. Ay = x - 4
  2. By = -x + 4
  3. Cy = -x
  4. Dy = x
17.
Given that A = 1-52437, find the transpose of A.
  1. A1-52437
  2. B123-54-7
  3. C1-52437
  4. D123-547
18.
Given that B = -24 and C = 31, find matrix BC.
  1. A-2
  2. B10
  3. C-10
  4. D-6
19.
The diagram shows the positions of three points P, Q and R on the earth's surface. A plane flying at a speed of 650 knots takes 6 hours to fly from P to R. Find the distance, in nautical miles, between P and R.
Diagram for question 19
  1. A390 nautical miles
  2. B108.3 nautical miles
  3. C3900 nautical miles
  4. D3250 nautical miles
20.
The diagram shows the positions of three points P, Q and R on the earth's surface. When it is 08 00 hours at P, the time at Q is 11 00 hours. Given that P is on longitude 15°W, find the longitude on which Q lies.
Diagram for question 20
  1. A30°E
  2. B60°E
  3. C45°E
  4. D30°W
21.
The diagram shows a circle centre O with six identical triangles. Triangle BOC is shaded. Name two other triangles that should be shaded so that the figure has rotational symmetry of order 3 about O.
Diagram for question 21
  1. ATriangles AOB and COD
  2. BTriangles AOF and DOE
  3. CTriangles COD and EOF
  4. DTriangles AOB and EOF
22.
In the following diagram L, K, and M are points on level ground. The bearing of M from L is 110°, angle LMK is 62°, and angle LKM is 85°. Find the bearing of K from M.
Diagram for question 22
  1. A228°
  2. B352°
  3. C290°
  4. D110°
23.
In the following diagram, L, K and M are points on level ground. The bearing of M from L is 110°, angle LMK = 62° and angle LKM = 85°. Find the bearing of L from K.
Diagram for question 23
  1. A143°
  2. B290°
  3. C037°
  4. D323°
24.
The following diagram shows a flowchart for a program to calculate the sum(S) of interior angles of a polygon with n sides. Use the flowchart to complete the table in the answer space below: n___18S1440°___
Diagram for question 24
  1. An = 8, S = 2880°
  2. Bn = 10, S = 2880°
  3. Cn = 10, S = 3240°
  4. Dn = 12, S = 2880°
25.
A, B, C and D are points on the circumference of a circle with centre O, such that angle OBC = 40°, angle DCA = 32° and TR is a tangent to the circle at B. The diameter AC and chord BD intersect at X. Find angle (a) ABT.
Diagram for question 25
  1. A40°
  2. B50°
  3. C80°
  4. D130°
26.
A, B, C and D are points on the circumference of a circle with centre O, such that angle OBC = 40°, angle DCA = 32° and TR is a tangent to the circle at B. The diameter AC and chord BD intersect at X. Find angle (b) OAB.
Diagram for question 26
  1. A40°
  2. B80°
  3. C50°
  4. D100°
27.
A, B, C and D are points on the circumference of a circle with centre O, such that angle OBC = 40°, angle DCA = 32° and TR is a tangent to the circle at B. The diameter AC and chord BD intersect at X. Find angle (c) CXD.
Diagram for question 27
  1. A64°
  2. B80°
  3. C98°
  4. D116°
28.
Three variables p, q and r are such that p varies as q and inversely as the square of r. p96aq127242r2b3 Find the value of k, the constant of variation.
  1. A1
  2. B3
  3. C9
  4. D27
29.
Three variables p, q and r are such that p varies as q and inversely as the square of r. p96aq127242r2b3 Given that k = 3, find the value of a.
  1. A378
  2. B126
  3. C42
  4. D14
30.
Three variables p, q and r are such that p varies as q and inversely as the square of r. p96aq127242r2b3 Given that k = 3, find the positive value of b.
  1. A2
  2. B3
  3. C6
  4. D36
31.
On the diagram in the answer space, draw triangle N, the image of triangle M under a translation T = -21. Which coordinates represent triangle N?
Diagram for question 31
  1. A(4, 0), (7, 0), (7, 2)
  2. B(0, 2), (3, 2), (3, 4)
  3. C(0, 0), (3, 0), (3, 2)
  4. D(4, 2), (7, 2), (7, 4)
32.
The vectors a = 72, b = m-3 and c = 5n are such that a + 2b = c. Find the values of m and n.
  1. Am = -2, n = -4
  2. Bm = -1, n = -1
  3. Cm = 1, n = -4
  4. Dm = -1, n = -4
33.
In the following diagram, the sector OAB of a circle has radius r and angle AOB = 63°. Given that the area of the sector AOB is 66.55 cm2, calculate the radius. [π = 227]
Diagram for question 33
  1. A10 cm
  2. B11 cm
  3. C12 cm
  4. D121 cm
34.
Write the three inequalities that define the unshaded region R on the diagram.
Diagram for question 34
  1. A2x + 5y ≤ 0 2x - 3y + 16 ≥ 0 x ≤ 1
  2. B2x + 5y ≥ 0 2x - 3y + 16 ≥ 0 x ≥ 1
  3. C2x + 5y ≥ 0 2x - 3y + 16 ≥ 0 x ≤ 1
  4. D2x + 5y ≤ 0 2x - 3y + 16 ≤ 0 x ≥ 1
35.
The following is the graph of y = -x2 + 12x - 11. The graph cuts the x-axis at A and B. Find the coordinates of the points A and B.
Diagram for question 35
  1. AA(1, 0) and B(11, 0)
  2. BA(-1, 0) and B(-11, 0)
  3. CA(0, 1) and B(0, 11)
  4. DA(-1, 0) and B(11, 0)
36.
The following is the graph of y = -x2 + 12x - 11. The graph cuts the x-axis at A and B. Find the maximum value of y.
Diagram for question 36
  1. A11
  2. B36
  3. C25
  4. D-25
37.
The diagram shows the speed-time graph of a moving object. Find the acceleration of the object in the first 8 seconds.
Diagram for question 37
  1. A1.6 m/s2
  2. B12.5 m/s2
  3. C160 m/s2
  4. D2.5 m/s2
38.
The diagram shows the speed-time graph of a moving object. Given that the object covered a distance of 115m in the first 10 seconds, find the value of V.
Diagram for question 38
  1. A10 m/s
  2. B15 m/s
  3. C20 m/s
  4. D35 m/s
39.
The diagram shows the speed-time graph of a moving object. Calculate the average speed of the object in the first 14 seconds.
Diagram for question 39
  1. A12.5 m/s
  2. B10 m/s
  3. C15 m/s
  4. D17.5 m/s
40.
Find the length of a straight line joining the points A(−13, 2) and B(−10, −2).
  1. A√7
  2. B5
  3. C7
  4. D25