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Examinations Council of Zambia — past paper

ECZ 2024 GCE Paper 1 — Mathematics

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

G12 Titan
1.
Evaluate 82723.
  1. A49
  2. B23
  3. C64729
  4. D94
2.
Simplify 4(x − 2) + 3(2x − 3).
  1. A10x − 11
  2. B10x − 17
  3. C10x + 1
  4. D−2x − 17
3.
Solve the equation (3x - 5)(x + 2) = 0.
  1. Ax = 53 or x = -2
  2. Bx = 5 or x = -2
  3. Cx = -53 or x = 2
  4. Dx = 53 only
4.
Factorise completely 7x2 - 7.
  1. A7(x - 1)2
  2. B7(x - 1)(x + 1)
  3. C7(x2 - 1)
  4. D(7x - 1)(x + 1)
5.
Use set notation to describe the shaded region in the Venn diagram below.
Diagram for question 5
  1. A(A∪B∪C)'
  2. BA∩(B∪C)
  3. CA'∪(B∩C)
  4. DA'∩(B∪C)
6.
A businessman got 800 shares worth K7 200.00. What was the cost of each share?
  1. AK90.00
  2. BK5,760,000.00
  3. CK0.09
  4. DK9.00
7.
The sequence 20, 17, 14, ... is an arithmetic progression. Find the 9th term.
  1. A-7
  2. B-1
  3. C-4
  4. D44
8.
The sequence 20, 17, 14, ... is an arithmetic progression. Find the sum of the first 10 terms.
  1. A-65
  2. B65
  3. C50
  4. D35
9.
A fair die is rolled once. Find the probability of a 4 showing up.
  1. A16
  2. B12
  3. C46
  4. D14
10.
In the diagram below, ABC is a straight line, AD = 5 cm, BD = 13 cm and angle BAD = 90°. Find the value of tan DBC.
Diagram for question 10
  1. A125
  2. B-125
  3. C512
  4. D-512
11.
Given that the universal set E = {1, 2, 3, 4, 5, 6, 7, 8, 9}, P = {2, 4, 6, 8} and Q = {2, 3, 5, 7}. List P′ ∩ Q.
  1. A{3,5,7}
  2. B{1,3,5,7,9}
  3. C{2}
  4. D{2,3,5,7}
12.
The diagram below shows trapezium S and trapezium T. Describe fully a single transformation which maps trapezium S onto trapezium T.
Diagram for question 12
  1. AReflection in the y-axis
  2. BTranslation by 0-4
  3. CRotation 180° about the origin
  4. DReflection in the x-axis
13.
Given that A = 2-13, find AT.
  1. A-21-3
  2. B2-13
  3. C3-12
  4. D2-13
14.
Given that A = 32 and B = 1−2, find AB.
  1. A3624
  2. B−1
  3. C3−6−24
  4. D3−62−4
15.
The diagram below shows positions of towns A, B and C. What is the time at A if it is 05:00 hours at B?
Diagram for question 15
  1. A05:00 hours
  2. B11:00 hours
  3. C01:00 hours
  4. D09:00 hours
16.
The diagram below shows positions of towns A, B and C. A plane flew from town A to town C in 5 hours. What was the speed of the plane in knots?
Diagram for question 16
  1. A5400 knots
  2. B1080 knots
  3. C900 knots
  4. D180 knots
17.
The diagram shows a sector AOB whose area is 34.65 cm2. The angle subtended at the centre is 81° and the radius is r cm. (π = 227) Find the radius (r) of the sector.
Diagram for question 17
  1. A49 cm
  2. B14 cm
  3. C7 cm
  4. D4.95 cm
18.
The ratio of the areas of two similar solids is 9:25. If the volume of the bigger solid is 375 cm3, what is the volume of the smaller solid?
  1. A225 cm3
  2. B81 cm3
  3. C135 cm3
  4. D15 cm3
19.
Given that y varies directly as x and inversely as the square of z, and that x = 8 when y = 4 and z = 2, find the constant of variation k.
  1. A2
  2. B1
  3. C8
  4. D4
20.
Given that y varies directly as x and inversely as the square of z, and k = 2, find y when x = 18 and z = 3.
  1. A4
  2. B36
  3. C2
  4. D12
21.
Given that y varies directly as x and inversely as the square of z, and k = 2, find the values of z when x = 25 and y = 2.
  1. Az = 10 or z = -10
  2. Bz = 5 only
  3. Cz = 5 or z = -5
  4. Dz = 25 or z = -25
22.
In the diagram, P, Q, R, S are points on the circle with centre O and angle PQR = 68°. TRU is a tangent at R. Find angle POR.
Diagram for question 22
  1. A136°
  2. B44°
  3. C112°
  4. D68°
23.
In the diagram, P, Q, R, S are points on the circle with centre O and angle PQR = 68°. TRU is a tangent at R. Find angle PSR.
Diagram for question 23
  1. A44°
  2. B68°
  3. C136°
  4. D112°
24.
In the diagram, P, Q, R, S are points on the circle with centre O and angle PQR = 68°. TRU is a tangent at R. Find angle PRO.
Diagram for question 24
  1. A34°
  2. B44°
  3. C22°
  4. D68°
25.
Two points A and B have coordinates (−5, −3) and (−1, a) respectively. Given that the gradient of the line AB is 2, find the value of a.
  1. A-5
  2. B1
  3. C5
  4. D8
26.
Given that y = 4x3 - 2x2 + 1, find dydx.
  1. A12x - 4
  2. B12x2 - 4x
  3. C12x2 - 4x + 1
  4. D4x2 - 4x
27.
The length of a sugarcane is measured as 2.6 m. Its true length is 2.5 m. Find the absolute error.
  1. A2.5 m
  2. B4m
  3. C0.1 m
  4. D0.04 m
28.
The length of a sugarcane is measured as 2.6 m. Its true length is 2.5 m. Find the percentage error.
  1. A0.04%
  2. B2.50%
  3. C4%
  4. D0.10%
29.
The functions f and g are defined by f(x) = 3x - 4 and g(x) = x + 13. Find f-1(x).
  1. Ax + 13
  2. B3x + 4
  3. Cx - 43
  4. Dx + 43
30.
The functions f and g are defined by f(x) = 3x - 4 and g(x) = x + 13. Find gf(x).
  1. Ax - 33
  2. B3x - 3
  3. Cx + 1
  4. Dx - 1
31.
The functions f and g are defined by f(x) = 3x - 4 and g(x) = x + 13. Find gf(-3).
  1. A4
  2. B-4
  3. C-2
  4. D-10
32.
The diagram shows a triangular prism ABCDEF in which AE = AD = DE. State the number of planes of symmetry for this triangular prism.
Diagram for question 32
  1. A4
  2. B2
  3. C1
  4. D3
33.
A program calculates the nth term Tn of an arithmetic progression from its first term a, common difference d and term number n. Complete the program: Enter ____; Tn = ____.
Diagram for question 33
  1. AEnter a and n; Tn = a + nd
  2. BEnter a, d and n; Tn = a + (n - 1)d
  3. CEnter Tn; Tn = a + d
  4. DEnter a, d and n; Tn = an + d
34.
Given that AB = 31 and BC = 1-3, find AC.
  1. A4-2
  2. B3-2
  3. C-42
  4. D24
35.
The straight line y = (12)x + p passes through (-2, 2). Find the coordinates of the y-intercept.
  1. A(-2, 2)
  2. B(0, 1)
  3. C(3, 0)
  4. D(0, 3)
36.
In the diagram, A, B and C are three points on level ground. The bearing of B from A is 137°, the bearing of C from B is 250° and angle ACB = 35°. Find the bearing of A from B.
Diagram for question 36
  1. A317°
  2. B137°
  3. C043°
  4. D180°
37.
In the diagram, A, B and C are three points on level ground. The bearing of B from A is 137°, the bearing of C from B is 250° and angle ACB = 35°. Find the bearing of A from C.
Diagram for question 37
  1. A105°
  2. B035°
  3. C070°
  4. D215°
38.
Use the diagram. Write the four inequalities that define the unshaded region R.
Diagram for question 38
  1. Ay ≥ x; x + 2y ≥ 6; y ≥ 1; x ≤ 6
  2. By ≤ x; x + 2y ≥ 6; y ≥ 1; x ≤ 6
  3. Cy ≤ x; x + 2y ≤ 6; y ≥ 1; x ≤ 6
  4. Dy ≤ x; x + 2y ≥ 6; y ≤ 1; x ≥ 6
39.
The diagram below shows a sketch of the graph of y = x2 + 3x + 2, passing through the points A and B. Find the coordinates of A and of B.
Diagram for question 39
  1. AA(-1, 0) and B(0, 2)
  2. BA(-2, 0) and B(2, 0)
  3. CA(-2, 0) and B(0, 2)
  4. DA(2, 0) and B(0, -2)
40.
The diagram below shows a sketch of the graph of y = x2 + 3x + 2, passing through the points A and B. Find the minimum turning point.
Diagram for question 40
  1. A(-32, 14)
  2. B(-3, -4)
  3. C(32, -14)
  4. D(-32, -14)
41.
Solve the equation 81 - 27x = 0.
  1. Ax = 4
  2. Bx = 34
  3. Cx = 43
  4. Dx = 3
42.
The diagram below shows the speed-time graph of an object. The object accelerates uniformly from O to P until it reaches a speed of 20 m/s in 4 seconds and then moves steadily from P to Q for 6 seconds and finally comes to rest. Find the acceleration in the first 4 seconds.
Diagram for question 42
  1. A80 m/s2
  2. B4 m/s2
  3. C5 m/s2
  4. D20 m/s2
43.
The diagram below shows the speed-time graph of an object. The object accelerates uniformly from O to P until it reaches a speed of 20 m/s in 4 seconds and then moves steadily from P to Q for 6 seconds and finally comes to rest. Find the total distance covered by the object.
Diagram for question 43
  1. A300 m
  2. B200 m
  3. C170 m
  4. D210 m
44.
The diagram below shows the speed-time graph of an object. The object accelerates uniformly from O to P until it reaches a speed of 20 m/s in 4 seconds and then moves steadily from P to Q for 6 seconds and finally comes to rest. Find the average speed in the last 4 seconds.
Diagram for question 44
  1. A4 m/s
  2. B10 m/s
  3. C8 m/s
  4. D16 m/s