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Examinations Council of Zambia — past paper

ECZ 2023 GCE Paper 1 — Mathematics

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

G12 Titan
1.
Shade (A∪B)∩C' on the Venn diagram in the space below.
Diagram for question 1
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
2.
The universal set E={0,1,2,3,4,5,6,7,8,9}, set A={ Prime numbers } and set B={3,6,9}. List A ∪ B′.
  1. A{0,1,2,4,5,7,8}
  2. B{2,3,5,6,7,9}
  3. C{0,1,2,3,4,5,7,8}
  4. D{0,1,3,4,6,8,9}
3.
Evaluate 32 + 3-1 × 20.
  1. A28
  2. B9
  3. C10
  4. D283
4.
Simplify 2(x + 3y) - 3(4x - 2).
  1. A-10x + 6y - 6
  2. B-10x + 6y + 6
  3. C-2x + 6y + 6
  4. D10x + 6y - 6
5.
Factorise completely 3x2 - 27.
  1. A3(x - 9)(x + 3)
  2. B(3x - 9)(x + 3)
  3. C3(x - 3)(x + 3)
  4. D3(x - 3)2
6.
Find the gradient of a line which passes through the points (-3, -1) and (0, 3).
  1. A-1.333333333
  2. B43
  3. C34
  4. D4
7.
The position vector of a point P is 34. Given that the point Q is (-1, 1), find PQ.
  1. A-2-5
  2. B-4-3
  3. C25
  4. D43
8.
Given that P = 4-10203 and Q = 123, find PT.
  1. A42-1003
  2. B40-1203
  3. C420-103
  4. D4-10203
9.
Given that P = 4-10203 and Q = 123, find PQ.
  1. A211
  2. B211
  3. C112
  4. D65
10.
An Arithmetic Progression is given as 1, 7, 13, ... Find the eighth term.
  1. A48
  2. B49
  3. C43
  4. D36
11.
An Arithmetic Progression is given as 1, 7, 13, ... Find the sum of the first fifteen terms.
  1. A555
  2. B645
  3. C5550
  4. D660
12.
In a bag there are 4 blue marbles, 3 red marbles and 2 white marbles. What is the probability of picking at random a red marble?
  1. A13
  2. B19
  3. C23
  4. D34
13.
Solve the equation 2x2 + x - 3 = 0.
  1. Ax = 3 or x = -12
  2. Bx = 1 or x = -32
  3. Cx = 1 or x = 32
  4. Dx = -1 or x = 32
14.
The following diagram shows a regular hexagonal right pyramid. Find the number of planes of symmetry of the pyramid.
Diagram for question 14
  1. A6
  2. B1
  3. C3
  4. D12
15.
Towns A and B are on longitudes 75°W and 45°E respectively. Find the time difference between these towns.
  1. A5 hours
  2. B120 hours
  3. C8 hours
  4. D2 hours
16.
The diagram shows towns P(45°S, 75°W) and Q(0°, 75°W). An aeroplane took 4 12 hours to fly from town P to town Q. Find its average speed in knots.
Diagram for question 16
  1. A135 knots
  2. B300 knots
  3. C1200 knots
  4. D600 knots
17.
Solve 5-3x = 125.
  1. Ax = -1
  2. Bx = 3
  3. Cx = 1
  4. Dx = -3
18.
The diagram shows a sector XOY. The angle subtended at the centre is 70° and the radius is 18cm. Calculate the area of the sector XOY. [π = 227]
Diagram for question 18
  1. A99 cm2
  2. B1134 cm2
  3. C396 cm2
  4. D198 cm2
19.
The mass of a bag of mealie meal is 25.2 kg. Calculate the tolerance.
  1. A25.15 kg
  2. B0.05 kg
  3. C0.1 kg
  4. D0.5 kg
20.
The mass of a bag of mealie meal is 25.2 kg. Calculate the relative error.
  1. A1252
  2. B0.05
  3. C1504
  4. D125.2
21.
In the diagram, three points A, B and C are on level ground. The bearing of B from A is 035°, angle ABC = 90° and angle ACB = 40°. Find the bearing of (a) A from C.
Diagram for question 21
  1. A085°
  2. B265°
  3. C305°
  4. D215°
22.
In the diagram, three points A, B and C are on level ground. The bearing of B from A is 035°, angle ABC = 90° and angle ACB = 40°. Find the bearing of (b) A from B.
Diagram for question 22
  1. A145°
  2. B215°
  3. C325°
  4. D035°
23.
Given that f(x) = 3x - 52 and g(x) = x + 2, find f-1(x).
  1. A3x + 52
  2. Bx + 53
  3. C2x + 53
  4. D2x - 53
24.
Given that f(x) = 3x - 52 and g(x) = x + 2, find f-1(5).
  1. A0
  2. B152
  3. C103
  4. D5
25.
Given that f(x) = 3x - 52 and g(x) = x + 2, find fg(x).
  1. A3x + 12
  2. B3x + 52
  3. C3x - 3
  4. D3x - 12
26.
In the diagram, A, B, C and D are points on the circumference of a circle with centre O. BD = AD and angle ADB = 40°. Find (a) AOB.
Diagram for question 26
  1. A40°
  2. B140°
  3. C80°
  4. D70°
27.
In the diagram, A, B, C and D are points on the circumference of a circle with centre O. BD = AD and angle ADB = 40°. Find (b) BCD.
Diagram for question 27
  1. A80°
  2. B70°
  3. C110°
  4. D140°
28.
In the diagram, A, B, C and D are points on the circumference of a circle with centre O. BD = AD and angle ADB = 40°. Find (c) OBD.
Diagram for question 28
  1. A40°
  2. B22°
  3. C70°
  4. D20°
29.
The diagram shows triangles P and Q. Describe fully the single transformation which maps triangle P onto triangle Q.
Diagram for question 29
  1. ATranslation by -64
  2. BTranslation by 6-4
  3. CReflection in the x-axis
  4. DRotation 180° about the origin
30.
In the answer space below is an incomplete flowchart for calculating the volume (V) of a cone. Given the radius (r) and height (h) of the cone, complete the flowchart. [V = 13πr2h]
Diagram for question 30
  1. AInput r and h; V = (13) × π × r2 × h
  2. BInput r and h; V = 12 × π × r2 × h
  3. CInput V; V = πrh
  4. DInput r; V = πr2h
31.
Z varies inversely as the square of x and directly as y, and z = 6 when x = -3 and y = 27. Find the value of k, the constant of variation.
  1. A12
  2. B54
  3. C18
  4. D2
32.
Z varies inversely as the square of x and directly as y, and z = 6 when x = -3 and y = 27. Find the value of z when y = -6 and x = -2.
  1. A12
  2. B-12
  3. C3
  4. D-3
33.
Z varies inversely as the square of x and directly as y, and z = 6 when x = -3 and y = 27. Find the values of x when y = 8 and z = 1.
  1. Ax = 4 or x = -4
  2. Bx = 8 or x = -8
  3. Cx = 4
  4. Dx = 16 or x = -16
34.
Paul invests K50 000.00 in a government bond at 9% simple interest per annum. How much will the bond be worth after 3 years?
  1. AK13 500.00
  2. BK59 000.00
  3. CK63 500.00
  4. DK65 000.00
35.
Two cylindrical tins are geometrically similar. The radius of the base of the smaller tin is 6cm and that of the bigger tin is 9cm. Given that the volume of the bigger tin is 108cm3, find the volume of the smaller tin.
  1. A32 cm3
  2. B36 cm3
  3. C48 cm3
  4. D72 cm3
36.
The diagram shows a right angled triangle ABC. BC is produced to D. AC = 13cm and cos BAC = 1213. Find the value of tan ACD.
Diagram for question 36
  1. A125
  2. B-0.416666667
  3. C512
  4. D-2.4
37.
Find the equation of a straight line passing through the point (-2, 3) and is parallel to the straight line whose equation is 2y - 3x = 5.
  1. A3y - 2x = 12
  2. B2y - 3x = 5
  3. C2y + 3x = 12
  4. D2y - 3x = 12
38.
Write three inequalities that define the unshaded region R in the diagram below.
Diagram for question 38
  1. Ay ≥ 1; y < 2x; y ≥ -x + 6
  2. By ≥ 1; y > 2x; y ≤ -x + 6
  3. Cy ≥ 1; y < 2x; y ≤ -x + 6
  4. Dy ≤ 1; y < 2x; y ≤ -x + 6
39.
Integrate 3x2 − 5x + 9x3 with respect to x.
  1. Ax3 − 5x22 + 92x2 + c
  2. Bx3 − 5x22 − 92x2 + c
  3. C6x − 5 − 27x4 + c
  4. Dx3 − 5x22 − 3x2 + c
40.
The diagram shows the graph of the function y = x2 + 2x − 15. The curve cuts the x-axis at A and B and the y-axis at C. Find the coordinates of B and C.
Diagram for question 40
  1. AB(3, 0) and C(0, −15)
  2. BB(−5, 0) and C(0, −15)
  3. CB(3, 0) and C(0, 15)
  4. DB(5, 0) and C(0, −15)
41.
The diagram shows the graph of the function y = x2 + 2x − 15. The curve cuts the x-axis at A and B and the y-axis at C. Find the minimum value of y.
Diagram for question 41
  1. A−15
  2. B−1
  3. C−17
  4. D−16
42.
The following diagram is a speed-time graph of a car. The car starts from rest and accelerates uniformly at 3 m/s2 for 4 seconds until it reaches a speed of v m/s. It then travels at this constant speed for 8 seconds. It finally comes to rest after t seconds. Find the value of v.
Diagram for question 42
  1. A7 m/s
  2. B12 m/s
  3. C48 m/s
  4. D3 m/s
43.
The following diagram is a speed-time graph of a car. The car starts from rest and accelerates uniformly at 3 m/s2 for 4 seconds until it reaches a speed of v m/s. It then travels at this constant speed for 8 seconds. It finally comes to rest after t seconds. Find the average speed for the first 12 seconds.
Diagram for question 43
  1. A12 m/s
  2. B8 m/s
  3. C10 m/s
  4. D6 m/s
44.
The following diagram is a speed-time graph of a car. The car starts from rest and accelerates uniformly at 3 m/s2 for 4 seconds until it reaches a speed of v m/s. It then travels at this constant speed for 8 seconds. It finally comes to rest after t seconds. Find the value of t, if the speed at t = 14 is 4 m/s.
Diagram for question 44
  1. A14
  2. B16
  3. C18
  4. D15