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Examinations Council of Zambia — past paper

ECZ 2025 GCE Paper 1 — Mathematics

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

G12 Titan
1.
Use set notation to describe the shaded region in the Venn diagram below.
Diagram for question 1
  1. AA∩(B∪C)′
  2. BA∩(B∪C)
  3. CA∪B′∪C′
  4. DA′∩(B∪C)
2.
Given that P={x:10≤x≤20,x is a prime number }, list set P .
  1. A{11,13,15,17,19}
  2. B{2,3,5,7,11,13,17,19}
  3. C{11,13,17,19}
  4. D{10,11,13,17,19}
3.
Simplify 2(y - 3) - 3(2 - y).
  1. A5y - 6
  2. B5y - 12
  3. Cy - 12
  4. D5y+12
4.
Evaluate (⁴√16/81)3.
  1. A49
  2. B827
  3. C1681
  4. D64729
5.
Factorise completely 2ab - 3b + 10a - 15.
  1. A(2a + 3)(b - 5)
  2. B(a - 3)(2b + 5)
  3. C(2a - 3)(b + 5)
  4. D(2a - 3)(b - 5)
6.
Solve the equation (12)x2 - 8 = 0.
  1. Ax = 4 only
  2. Bx = -4 or x = 4
  3. Cx = -16 or x = 16
  4. Dx = -4 only
7.
A company with 6 000 shares declared a dividend of K56 000.00. What amount will Betty receive for her 36 shares?
  1. AK56 000.00
  2. BK336.00
  3. CK3,360.00
  4. DK933.33
8.
The probability that Gift will not be late for a job interview is 0.05. What is the probability that he will be late for the interview?
  1. A0.95
  2. B0.05
  3. C0.5
  4. D1.05
9.
Solve the equation 2x - 1 - 4 = 0.
  1. Ax = 3
  2. Bx = 2
  3. Cx = 1
  4. Dx = 5
10.
The diagram shows a sector POQ. Arc PQ subtends an angle of 45° at the centre. Given that the area of POQ is 77 cm2, calculate the radius of the sector. [π = 227]
Diagram for question 10
  1. A7 cm
  2. B196 cm
  3. C14 cm
  4. D28 cm
11.
The diagram shows the positions of three towns A, B and C on the earth's surface. Town B is on longitude 40°W and town C is on longitude 65°E. What is the time difference between B and C?
Diagram for question 11
  1. A105 hours
  2. B4 hours 20 minutes
  3. C7 hours
  4. D8 hours
12.
The diagram shows the positions of three towns A, B and C on the earth's surface. A plane flying due south from A to B at 900 knots takes 7 hours. Find the difference in latitude between A and B.
Diagram for question 12
  1. A15°
  2. B7°
  3. C6300°
  4. D105°
13.
If a machine that loads mealie meal into 25 kg bags has a tolerance of 0.5%, find the highest acceptable mass of any bag loaded by this machine.
  1. A25.125 kg
  2. B25.5 kg
  3. C24.875 kg
  4. D12.5 kg
14.
If 12.5 litres of water was poured out of a container containing 20 litres of water, find the relative error of the volume of water that remained in the container.
  1. A11150
  2. B1150
  3. C0.625
  4. D0.375
15.
In the following diagram A, B, C, D and E are points on the circumference of a circle centre O. Angle ADB = 18°, angle EAD = 31° and BC = CD. Find angle EOD.
Diagram for question 15
  1. A118°
  2. B31°
  3. C62°
  4. D90°
16.
In the following diagram A, B, C, D and E are points on the circumference of a circle centre O. Angle ADB = 18°, angle EAD = 31° and BC = CD. Find angle ADC.
Diagram for question 16
  1. A45°
  2. B18°
  3. C49°
  4. D63°
17.
In the following diagram A, B, C, D and E are points on the circumference of a circle centre O. Angle ADB = 18°, angle EAD = 31° and BC = CD. The chord AD crosses EO at X. Find angle EXD.
Diagram for question 17
  1. A49°
  2. B80°
  3. C62°
  4. D100°
18.
In the diagram, AB = 8 cm, AD = 10 cm, DC = 12 cm and angle ABC = 90°. Find the value of tan ACB.
Diagram for question 18
  1. A34
  2. B49
  3. C23
  4. D810
19.
Use the diagram. C = (0, 4) and D = (6, 0). Line AB is perpendicular to CD and crosses the x-axis at (1, 0). Find the equation of line AB.
Diagram for question 19
  1. Ay = (23)x - 1
  2. By = -(32)x + 32
  3. Cy = (32)x - 32
  4. Dy = -(23)x + 4
20.
It is given that x = kzy2, where k is the constant of variation. The table shows some corresponding values of x, y and z. x24p12y23qz16618 Use the information given in the table to find the value of k.
  1. A12
  2. B24
  3. C6
  4. D3
21.
It is given that x = kzy2, where k is a constant of variation. x24p12y23qz16618 Given that k = 6, find p.
  1. A4
  2. B12
  3. C18
  4. D36
22.
It is given that x = kzy2, where k is a constant of variation. x24p12y23qz16618 Given that k = 6, find the values of q.
  1. Aq = 9 or q = -9
  2. Bq = 3 only
  3. Cq = 6 or q = -6
  4. Dq = 3 or q = -3
23.
Find ∫(3x3 + 4x) dx.
  1. A3x4 + 4x2 + C
  2. B(34)x4 + 2x2 + C
  3. C(34)x2 + 2x + C
  4. D(34)x4 + 4x2 + C
24.
In the diagram, quadrilateral P is mapped onto Q by a single transformation S. Describe fully the transformation S.
Diagram for question 24
  1. ARotation 180° about (4, 3)
  2. BTranslation by -32
  3. CTranslation by 3-2
  4. DReflection in the line x = 4
25.
The diagram shows three points O, P and Q on level ground. OPQ is an equilateral triangle and the bearing of Q from P is 135°. Find the bearing of P from O.
Diagram for question 25
  1. A075°
  2. B195°
  3. C015°
  4. D255°
26.
The diagram shows three points O, P and Q on level ground. OPQ is an equilateral triangle and the bearing of Q from P is 135°. Find the bearing of O from Q.
Diagram for question 26
  1. A255°
  2. B135°
  3. C075°
  4. D315°
27.
The diagram shows a cuboid with a rectangular base and square ends. PQ is the central axis of the cuboid. Write down the order of rotational symmetry of the cuboid about the axis PQ.
Diagram for question 27
  1. A2
  2. B1
  3. C8
  4. D4
28.
An incomplete flowchart calculates the area A of a triangle with base b and height h. Complete the input and process symbols.
Diagram for question 28
  1. AInput b and h; A = (12) * b * h
  2. BInput b; A = (12) * b * h
  3. CInput b and h; A = b * h
  4. DInput A; A = b + h
29.
The functions f and g are defined by f(x) = x + 32 and g(x) = 1 - 2x. Find f-1(x).
  1. Ax - 32
  2. B1 - 2x
  3. Cx + 32
  4. D2x - 3
30.
The functions f and g are defined by f(x) = x + 32 and g(x) = 1 - 2x. Find gf(x).
  1. A1 - 2x
  2. B-x - 2
  3. Cx + 1
  4. D2x - 3
31.
The functions f and g are defined by f(x) = x + 32 and g(x) = 1 - 2x. Find gf(-7).
  1. A11
  2. B5
  3. C-11
  4. D-5
32.
The points A and B are (−7, 1) and (−4, 5) respectively. Find the length of the line AB.
  1. A5 units
  2. B7 units
  3. C25 units
  4. D4 units
33.
Two similar pyramids A and B have surface areas 180 cm2 and 80 cm2 respectively. The volume of pyramid A is 810 cm3. Calculate the volume of pyramid B.
  1. A720 cm3
  2. B120 cm3
  3. C240 cm3
  4. D360 cm3
34.
Write three inequalities that define the unshaded region R in the diagram.
Diagram for question 34
  1. Ay ≤ 2x + 2; y ≤ −(52)x + 5; y ≤ −2
  2. By ≤ 2x + 2; y ≥ −(52)x + 5; y ≥ −2
  3. Cy ≥ 2x + 2; y ≤ −(52)x + 5; y ≥ −2
  4. Dy ≤ 2x + 2; y ≤ −(52)x + 5; y ≥ −2
35.
Given that PQ = 23 and OQ = 4-1, find the coordinates of P.
  1. A(-2, 4)
  2. B(6, 2)
  3. C(2, 4)
  4. D(2, -4)
36.
The sketch represents the graph of the curve y = x2 − 6x + 5 passing through A, B and C. Find the coordinates of A and B.
Diagram for question 36
  1. AA(1, 0) and B(5, 0)
  2. BA(0, 1) and B(0, 5)
  3. CA(-1, 0) and B(-5, 0)
  4. DA(1, 0) and B(6, 0)
37.
The sketch represents the graph of the curve y = x2 − 6x + 5 passing through A, B and C. Find the coordinates of the turning point of the curve.
Diagram for question 37
  1. A(-3, -4)
  2. B(3, 4)
  3. C(6, 5)
  4. D(3, -4)
38.
The formula for the nth term of an arithmetic progression is 2n − 3. Find the first term.
  1. A2
  2. B−1
  3. C−3
  4. D1
39.
The formula for the nth term of an arithmetic progression is 2n − 3. Find the common difference, d, if the sum of the first 8 terms is 48.
  1. A−2
  2. B4
  3. C2
  4. D7
40.
Given that A = −123014, find AT.
  1. A204−131
  2. B−131204
  3. C−123014
  4. D41032−1
41.
Given that −21x−2 31 = −57, find the value of x.
  1. A9
  2. B−3
  3. C3
  4. D53
42.
The diagram below shows the speed graph of a particle. The particle starts from rest and accelerates uniformly to a speed of 10 m/s in 5 seconds. It then moved at this constant speed for 5 seconds and then accelerates at 2 m/s2 for 5 seconds to reach a speed of v m/s. Find the acceleration during the first 5 seconds.
Diagram for question 42
  1. A4 m/s2
  2. B5 m/s2
  3. C2 m/s2
  4. D1.33 m/s2
43.
The diagram below shows the speed graph of a particle. The particle starts from rest and accelerates uniformly to a speed of 10 m/s in 5 seconds. It then moved at this constant speed for 5 seconds and then accelerates at 2 m/s2 for 5 seconds to reach a speed of v m/s. Find the value of v.
Diagram for question 43
  1. A12 m/s
  2. B20 m/s
  3. C10 m/s
  4. D25 m/s
44.
The diagram below shows the speed graph of a particle. The particle starts from rest and accelerates uniformly to a speed of 10 m/s in 5 seconds. It then moved at this constant speed for 5 seconds and then accelerates at 2 m/s2 for 5 seconds to reach a speed of v m/s. Find the average speed for the whole journey.
Diagram for question 44
  1. A16 m/s
  2. B10 m/s
  3. C4 m/s
  4. D8 m/s