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Examinations Council of Zambia — past paper

ECZ 2026 GCE Paper 1 — Mathematics

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

G12 Titan
1.
Evaluate 276413.
  1. A964
  2. B43
  3. C34
  4. D38
2.
Factorise completely pq - 3p - q2 + 3q.
  1. A(q + 3)(p - q)
  2. B(q - 3)(p - q)
  3. C(q - 3)(p + q)
  4. D(p - 3)(p - q)
3.
Simplify 8x + 4 - 3(2x - 3).
  1. A2x - 5
  2. B2x + 13
  3. C14x + 13
  4. D2x + 1
4.
Solve the equation 2x2 - 72 = 0.
  1. Ax = 6 only
  2. Bx = -36 or x = 36
  3. Cx = -6 or x = 6
  4. Dx = -12 or x = 12
5.
Shade (P∪Q)′∩R on the Venn diagram in the answer space below.
Diagram for question 5
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
6.
The market value of a share is K25.00. How many shares can be bought from K25 250.00?
  1. A101
  2. B1 010
  3. C10 100
  4. D1 100
7.
The first and seventh terms of an arithmetic progression are -11 and 13 respectively. Find the common difference, d.
  1. A247
  2. B-4
  3. C24
  4. D4
8.
The first and seventh terms of an arithmetic progression are -11 and 13 respectively. Find the nth term.
  1. A4n - 11
  2. B4n - 15
  3. C-11n + 4
  4. D4n + 15
9.
The cards 1, 2, 3, 4, 5 and 6 are placed in a box. If a card is selected at random from the box, find the probability that the number on the card is a prime number.
  1. A23
  2. B12
  3. C13
  4. D16
10.
If A is the point (1, 1) and AB = 65, find the coordinates of B.
  1. A(7, 6)
  2. B(-5, -4)
  3. C(6, 5)
  4. D(5, 4)
11.
Given that matrix A = 34-10, find AT.
  1. A0-413
  2. B3-140
  3. C-3-410
  4. D430-1
12.
Given that matrix A = 34-10 and matrix B = -13, find AB.
  1. A-6-4
  2. B151
  3. C91
  4. D19
13.
Given that R = {x: 0 ≤ x < 10, x is an even number}, list the elements of set R.
  1. A{2, 4, 6, 8}
  2. B{2, 4, 6, 8, 10}
  3. C{0, 2, 4, 6, 8, 10}
  4. D{0, 2, 4, 6, 8}
14.
A point F(-4, 1) is mapped onto a point G(5, -4) by a translation T. Express T as a column vector.
  1. A-95
  2. B1-3
  3. C9-3
  4. D9-5
15.
In the diagram, NS is the Prime Meridian. The positions of towns A and B are (30°S, 30°W) and (30°N, 30°W) respectively. Find the distance between A and B in nautical miles.
Diagram for question 15
  1. A1800 nautical miles
  2. B3600 nautical miles
  3. C60 nautical miles
  4. D3118 nautical miles
16.
In the diagram, NS is the Prime Meridian. The positions of towns A and B are (30°S, 30°W) and (30°N, 30°W) respectively. If the local time at B is 09 35 hours, what is the local time at the Prime Meridian?
Diagram for question 16
  1. A07 35 hours
  2. B10 05 hours
  3. C11 35 hours
  4. D12 35 hours
17.
The absolute error of a number n is 5 and the relative error for the same number is 0.2. Find the value of n.
  1. A25
  2. B1
  3. C0.04
  4. D2.5
18.
The absolute error of a number n is 5 and the relative error for the same number is 0.2. Find the percentage error.
  1. A20%
  2. B0.2%
  3. C2%
  4. D25%
19.
Triangle ABC is right angled at B, BCD is a straight line and cos ACD = -1213. Find the value of sin CAB.
Diagram for question 19
  1. A513
  2. B-1213
  3. C1213
  4. D512
20.
Find ∫(12x3 - 3x2) dx.
  1. A6x2 - x3 + c
  2. B-36x4 - 6x + c
  3. C-12x2 - x3 + c
  4. D-6x2 - x3 + c
21.
The points A, B, C and D are on the circumference of a circle centre O such that angle OBC = 50° and angle OCD = 25°. BT is a tangent to the circle at B. Find angle BDC.
Diagram for question 21
  1. A80°
  2. B50°
  3. C25°
  4. D40°
22.
The points A, B, C and D are on the circumference of a circle centre O such that angle OBC = 50° and angle OCD = 25°. BT is a tangent to the circle at B. Find angle BAD.
Diagram for question 22
  1. A105°
  2. B75°
  3. C115°
  4. D130°
23.
The points A, B, C and D are on the circumference of a circle centre O such that angle OBC = 50° and angle OCD = 25°. BT is a tangent to the circle at B. Find angle BTD.
Diagram for question 23
  1. A40°
  2. B45°
  3. C35°
  4. D25°
24.
Two buckets A and B are geometrically similar. The height of bucket A is 20 cm and that of bucket B is y cm. Given that the volumes of bucket A and bucket B are 1 000 cm3 and 8 000 cm3 respectively, find the value of y.
  1. A160
  2. B40
  3. C80
  4. D2.5
25.
The diagram shows a straight line AB passing through the points A(5, 0) and B(14, 6). C is the point (2, 9). Find the equation of the line perpendicular to AB that passes through the point C.
Diagram for question 25
  1. Ay = -(32)x + 12
  2. By = (23)x + 233
  3. Cy = -(32)x + 9
  4. Dy = -(23)x + 313
26.
P varies as q and inversely as the square of r, and when p = 6, q = 18 and r = 3. Find the value of k, the constant of variation.
  1. A3
  2. B1
  3. C9
  4. D13
27.
P varies as q and inversely as the square of r, and when p = 6, q = 18 and r = 3. Find the value of q when p = 9 and r = 5.
  1. A15
  2. B75
  3. C27
  4. D3
28.
P varies as q and inversely as the square of r, and when p = 6, q = 18 and r = 3. Find the values of r when p = 3 and q = 25.
  1. Ar = 5 or r = -5
  2. Br = 5 only
  3. Cr = 25 or r = -25
  4. Dr = 3 or r = -3
29.
The following figure is made up of five identical cubes. State the number of planes of symmetry for the figure.
Diagram for question 29
  1. A5
  2. B4
  3. C2
  4. D3
30.
In the answer space is an incomplete program written in pseudocode for calculating the volume (v) of a cylinder given the height (h) and radius (r): Start Enter …… v = …… Output v Stop Complete the program. [v = πr2h]
  1. AEnter v; v = π × r2 × h
  2. BEnter h, r; v = 2 × π × r × h
  3. CEnter h, r; v = π × r2 × h
  4. DEnter r; v = π × r2
31.
The diagram shows a sector of a circle with centre O and radius 10.5 cm. Angle POQ = 60°. Find the area of the sector. [π = 227]
Diagram for question 31
  1. A11 cm2
  2. B57.75 cm2
  3. C346.5 cm2
  4. D115.5 cm2
32.
The points P and Q have coordinates (3, 6) and (-9, 4) respectively. Find the coordinates of the midpoint of PQ.
  1. A(-3, 5)
  2. B(-6, 10)
  3. C(6, 1)
  4. D(3, -5)
33.
Given that f(x) = 2x - 9 and g(x) = x + 5, find f-1(x).
  1. Ax - 92
  2. B2x + 9
  3. C2 - 9xx
  4. D9x + 2x
34.
Given that f(x) = 2x - 9 and g(x) = x + 5, find fg(x).
  1. A2x - 9 + 5
  2. B2x + 14
  3. C2x - 4
  4. D2x - 14
35.
Given that f(x) = 2x - 9 and g(x) = x + 5, find the value of x for which fg(x) = 1.
  1. A11
  2. B2
  3. C6
  4. D4
36.
In the diagram, angle POQ = 55°, OQ = QP and the bearing of Q from O is 060°. Find the bearing of O from Q.
Diagram for question 36
  1. A240°
  2. B120°
  3. C300°
  4. D060°
37.
In the diagram, angle POQ = 55°, OQ = QP and the bearing of Q from O is 060°. Find the bearing of P from Q.
Diagram for question 37
  1. A310°
  2. B185°
  3. C125°
  4. D170°
38.
Write the four inequalities that define the unshaded region R on the XOY plane below.
Diagram for question 38
  1. Ax ≥ 2; y ≤ 5; y ≥ -1; x + y ≥ 9
  2. Bx ≤ 2; y ≤ 5; y ≥ -1; x + y ≤ 9
  3. Cx ≥ 2; y ≤ 5; y ≥ -1; x - y ≤ 9
  4. Dx ≥ 2; y ≤ 5; y ≥ -1; x + y ≤ 9
39.
Solve the equation 43x = 8.
  1. Ax = 23
  2. Bx = 12
  3. Cx = 32
  4. Dx = 13
40.
The diagram shows a sketch of the graph of y = (-2x + 4)(x + 5), which crosses the x-axis at A and B. Find the coordinates of A and B.
Diagram for question 40
  1. AA(-2, 0) and B(5, 0)
  2. BA(-5, 0) and B(4, 0)
  3. CA(0, -5) and B(0, 2)
  4. DA(-5, 0) and B(2, 0)
41.
The diagram shows a sketch of the graph of y = (-2x + 4)(x + 5), which crosses the x-axis at A and B. Find the maximum value of y.
Diagram for question 41
  1. A24.5
  2. B20
  3. C24
  4. D6.5
42.
The diagram shows the speed-time graph of a particle which starts from rest and accelerates uniformly to a speed of 10 m/s in 8 seconds. It then travels at a constant speed for 60 seconds before decelerating uniformly to rest in a further 32 seconds. Find the acceleration of the particle during the first 8 seconds.
Diagram for question 42
  1. A0.8 m/s2
  2. B80 m/s2
  3. C1.25 m/s2
  4. D0.125 m/s2
43.
The diagram shows the speed-time graph of a particle which starts from rest and accelerates uniformly to a speed of 10 m/s in 8 seconds. It then travels at a constant speed for 60 seconds before decelerating uniformly to rest in a further 32 seconds. Find the total distance covered by the particle.
Diagram for question 43
  1. A1 000 m
  2. B600 m
  3. C800 m
  4. D760 m
44.
The diagram shows the speed-time graph of a particle which starts from rest and accelerates uniformly to a speed of 10 m/s in 8 seconds. It then travels at a constant speed for 60 seconds before decelerating uniformly to rest in a further 32 seconds. Find the speed of the particle at t = 84 seconds.
Diagram for question 44
  1. A10 m/s
  2. B7.5 m/s
  3. C2.5 m/s
  4. D5 m/s