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Examinations Council of Zambia — past paper

ECZ 2023 O-Level Paper 1 — Mathematics

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

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1.
The Venn diagram shows three sets P,Q and R . Use set notation to describe the shaded part.
Diagram for question 1
  1. AP∩(Q∪R)
  2. BP∪(Q∩R)
  3. C(P∩Q)∪R
  4. DP′∩(Q∪R)
2.
Set A={x:1<x≤15,x is a prime number } and set B={x:0≤x<10,x is an odd number}. List the set A∩B.
  1. A{1,3,5,7,9}
  2. B{3,5,7}
  3. C{3,5,7,11,13}
  4. D{3,5,7,9}
3.
Evaluate 82713.
  1. A49
  2. B827
  3. C32
  4. D23
4.
Factorise completely 3x3 - 27x.
  1. A3x(x - 3)(x + 3)
  2. B3(x - 3)(x + 3)
  3. Cx(3x - 27)
  4. D3x(x2 - 9)
5.
Simplify 2a - 5b(a - b) + ab.
  1. A2a - 4ab + 5b2
  2. B2a - 6ab + 5b2
  3. C2a - 5ab + 5b2
  4. D2a + 6ab - 5b2
6.
The point A(-5, 3) and the point B have a midpoint (4, -2). Find the coordinates of B.
  1. A(9, 1)
  2. B(13, -7)
  3. C(-1, 1)
  4. D(-13, 7)
7.
Given that OP = 413 and the point Q is (16, 8), find |PQ|.
  1. A25 units
  2. B5 units
  3. C20 units
  4. D13 units
8.
Given that A = 124 and B = 304, find (a) AT,
  1. A142
  2. B421
  3. C124
  4. D124
9.
Given that A = 124 and B = 304, find (b) AB.
  1. A7
  2. B19
  3. C3016
  4. D16
10.
Given that 25 and 13 are the first and third terms of an arithmetic progression respectively, find the (a) second term,
  1. A18
  2. B19
  3. C21
  4. D6
11.
Given that 25 and 13 are the first and third terms of an arithmetic progression respectively, find the (b) formula for the nth term.
  1. A31 + 6n
  2. B31 - 6n
  3. C25 + 6n
  4. D25 - 6n
12.
A letter is chosen at random from the word “EXCELLENT”. What is the probability that the letter “E” is chosen?
  1. A13
  2. B38
  3. C29
  4. D19
13.
The areas of two similar shapes are in the ratio 25 : 36. If the length of the smaller shape is 2cm, find the length of the larger shape.
  1. A7225 cm
  2. B125 cm
  3. C6cm
  4. D53 cm
14.
Solve the equation 2x + 3 = 116.
  1. Ax = 7
  2. Bx = 1
  3. Cx = -1
  4. Dx = -7
15.
The diagram shows two towns A and B on the equator. A is on longitude 30°W and B is on longitude X. The time at B is 17 05 hours when it is 14 05 hours at A. Find the longitude X.
Diagram for question 15
  1. A15°E
  2. B15°W
  3. C75°E
  4. D45°E
16.
The diagram shows two towns A and B on the equator. A is on longitude 30°W and B is on longitude X. A ship sailed due east from A to B at an average speed of 450 knots. Find the time it took the ship to travel from A to B.
Diagram for question 16
  1. A3 hours
  2. B9 hours
  3. C60 hours
  4. D6 hours
17.
The functions g and h are defined by g(x) = 3x + 1 and h(x) = x - 12. Find g-1(x).
  1. Ax + 13
  2. B3x - 1
  3. Cx - 13
  4. Dx - 31
18.
The functions g and h are defined by g(x) = 3x + 1 and h(x) = x - 12. Find gh(x).
  1. Ax - 16
  2. B3x - 22
  3. C3x + 12
  4. D3x - 12
19.
The functions g and h are defined by g(x) = 3x + 1 and h(x) = x - 12. Find x if gg(x) = 22.
  1. A2
  2. B209
  3. C199
  4. D7
20.
In a practical examination, Nellie recorded the volume, v, of water as 6.4 litres, correct to one decimal place. Choose the statement that gives the range within which the true volume v must lie.
  1. A6.4 ≤ v < 6.5
  2. B6.3 ≤ v < 6.5
  3. C6.35 ≤ v < 6.45
  4. D6.35 < v ≤ 6.45
21.
The actual length of the longest side of a rectangular playing field is 102m. A boy measured the same side as 99.8m. Calculate the relative error.
  1. A11510
  2. B2.299.8
  3. C2.2
  4. D51011
22.
Find ∫(x3 + 2x + 3) dx.
  1. A3x2 + 2 + C
  2. Bx44 + 2x2 + 3x + C
  3. Cx4 + x2 + 3x + C
  4. Dx44 + x2 + 3x + C
23.
In the following diagram, triangle ABC is mapped onto triangle DEF by a single transformation M. Describe fully the transformation M.
Diagram for question 23
  1. ATranslation by 4-4
  2. BRotation 180° about the origin
  3. CReflection in the line y = x
  4. DReflection in the line y = -x
24.
The diagram shows three points P, Q and R on level ground. The bearing of Q from P is 100°, the bearing of R from Q is 150° and PQ = QR. Find (a) angle QPR.
Diagram for question 24
  1. A25°
  2. B130°
  3. C100°
  4. D50°
25.
The diagram shows three points P, Q and R on level ground. The bearing of Q from P is 100°, the bearing of R from Q is 150° and PQ = QR. Find (b) the bearing of P from R.
Diagram for question 25
  1. A305°
  2. B330°
  3. C125°
  4. D280°
26.
In the diagram, BCE is a right angled triangle in which BC = 4cm and CE = 3cm. BE is produced to D. Find the value of cos CED.
Diagram for question 26
  1. A-0.8
  2. B-0.6
  3. C35
  4. D45
27.
The curved surface area of a cone with radius 4.2cm is 138.6cm2. Find its slant height. [π = 227]
  1. A10.5cm
  2. B21cm
  3. C33cm
  4. D4.2cm
28.
In the following diagram, A, B, C, D and E lie on the circumference of a circle centre O. BD = BE, angle CAD = 18° and angle BEC = 51°. Find (a) angle ADC.
Diagram for question 28
  1. A69°
  2. B18°
  3. C90°
  4. D51°
29.
In the following diagram, A, B, C, D and E lie on the circumference of a circle centre O. BD = BE, angle CAD = 18° and angle BEC = 51°. Find (b) angle BED.
Diagram for question 29
  1. A18°
  2. B90°
  3. C51°
  4. D69°
30.
In the following diagram, A, B, C, D and E lie on the circumference of a circle centre O. BD = BE, angle CAD = 18° and angle BEC = 51°. Find (c) angle EBC.
Diagram for question 30
  1. A69°
  2. B60°
  3. C30°
  4. D51°
31.
A sugar company paid K362 400.00 as dividend for 1 200 shares. A man had 20 shares in the company. Calculate the amount paid to him.
  1. AK60 400.00
  2. BK7 248.00
  3. CK6 040.00
  4. DK302.00
32.
Find the equation of a line parallel to the line 2x + y = 4 passing through (-5, 3).
  1. A2x + y = 4
  2. B2x - y = -7
  3. C2x + y = -7
  4. Dy = 2x - 7
33.
a varies jointly as b and the square root of c, and a = 21 when b = 5 and c = 36. Find the value of k, the constant of variation.
  1. A107
  2. B7
  3. C110
  4. D710
34.
a varies jointly as b and the square root of c, and a = 21 when b = 5 and c = 36. Find the value of a when b = 9 and c = 100.
  1. A630
  2. B63
  3. C90
  4. D70
35.
a varies jointly as b and the square root of c, and a = 21 when b = 5 and c = 36. Find the value of c when a = 70 and b = 25.
  1. A25
  2. B16
  3. C4
  4. D64
36.
In the answer space below is an incomplete simple program in pseudocode for calculating and outputting the volume, V, of a cone given the base radius r and height h. Complete the program by filling in the blank spaces with appropriate statements.
Diagram for question 36
  1. AEnter V and h; r = Vπh
  2. BEnter r; V = (13) * π * r2
  3. CEnter r and h; V = π * r2 * h
  4. DEnter r and h; V = (13) * π * r2 * h
37.
Shade two more sections of the diagram below so that it has rotational symmetry of order 2.
Diagram for question 37
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
38.
Write the three inequalities that define the unshaded region R.
Diagram for question 38
  1. Ay ≤ 6; y ≥ x; y ≥ -2x + 6
  2. By ≤ 6; y ≥ x; y ≤ -2x + 6
  3. Cy ≥ 6; y ≥ x; y ≥ -2x + 6
  4. Dy ≤ 6; y ≤ x; y ≥ -2x + 6
39.
Solve the equation x2 = 4(x - 3)2.
  1. Ax = 2 only
  2. Bx = -2 or x = -6
  3. Cx = 6 only
  4. Dx = 2 or x = 6
40.
The diagram shows the sketch of the graph of y = -4x - x2 cutting the x-axis at A and B. Find the coordinates of (i) A.
Diagram for question 40
  1. A(-4, 0)
  2. B(0, -4)
  3. C(4, 0)
  4. D(0, 0)
41.
The diagram shows the sketch of the graph of y = -4x - x2 cutting the x-axis at A and B. Find the coordinates of (ii) the turning point of the graph.
Diagram for question 41
  1. A(0, 4)
  2. B(-2, -4)
  3. C(-2, 4)
  4. D(2, 4)
42.
The diagram shows the speed-time graph of a car during a period of t seconds. Find the (a) acceleration of the car during the first 8 seconds.
Diagram for question 42
  1. A89 m/s2
  2. B9m/s2
  3. C98 m/s2
  4. D72m/s2
43.
The diagram shows the speed-time graph of a car during a period of t seconds. Find the (b) distance covered in the first 14 seconds.
Diagram for question 43
  1. A90m
  2. B36m
  3. C54m
  4. D126m
44.
The diagram shows the speed-time graph of a car during a period of t seconds. Find the (c) value of t if the average speed of the car is 7m/s.
Diagram for question 44
  1. A20 seconds
  2. B22 seconds
  3. C14 seconds
  4. D24 seconds