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Examinations Council of Zambia — past paper

ECZ 2022 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 diagram in the answer space below.
Diagram for question 1
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
2.
Given that E={1,2,3,4,5,6,7,8,9,10},A={ Prime numbers }, B={ Multiples of 3}, list (A∪B)'.
  1. A{4,8,10}
  2. B{1,2,4,5,7,8,10}
  3. C{2,3,5,6,7,9}
  4. D{1,4,8,10}
3.
Evaluate 53 × 152.
  1. A5
  2. B125
  3. C25
  4. D15
4.
Expand and simplify (2a + 3)(3a – 4).
  1. A6a2 + 17a - 12
  2. B6a2 + a - 12
  3. C6a2 - 17a - 12
  4. D6a2 + a + 12
5.
Solve the equation 4x2 = 9x.
  1. Ax = 94
  2. Bx = 0 or x = 94
  3. Cx = 0 or x = -94
  4. Dx = 4 or x = 9
6.
Factorise completely 2ab + xy – 2ay – bx.
  1. A(2a + y)(b - x)
  2. B(2a + x)(b - y)
  3. C(2a - x)(b - y)
  4. D(2a - x)(b + y)
7.
A company declares an annual dividend of 6%. The value of each share is K25.00. Mr Mapesa has 500 shares. Find his annual dividend.
  1. AK750.00
  2. BK3 000.00
  3. CK12 500.00
  4. DK150.00
8.
For the sequence 5, 12, 19, ..., find the (a) sixth term.
  1. A40
  2. B35
  3. C42
  4. D47
9.
For the sequence 5, 12, 19, ..., find the (b) nth term.
  1. A7n - 2
  2. B5 + 7n
  3. C5n + 7
  4. D7n + 2
10.
The distance between town F and town G is 8 100 nautical miles. If a plane takes 18 hours to fly from F to G, find its average speed in knots.
  1. A8 118 knots
  2. B450 knots
  3. C90 knots
  4. D145.8 knots
11.
Town B is east of town A. When it is 11 00 hours at B, it is 07 00 hours at A. Find the difference in longitudes between the towns A and B.
  1. A240°
  2. B4°
  3. C60°
  4. D45°
12.
Given that the matrix C = 731425, find CT.
  1. A712345
  2. B731425
  3. C713245
  4. D721354
13.
Express as a single matrix 18 0-125.
  1. A840
  2. B16-39
  3. C1639
  4. D240
14.
The probability of Kasukulu waking up late is 0.3. What is the probability that she will wake up early?
  1. A0.7
  2. B1.3
  3. C0.3
  4. D0.15
15.
The following diagram shows a sector POQ of radius 6cm. Angle POQ = θ and the area of the sector is 24.2cm2. [π = 227] Find the value of θ.
Diagram for question 15
  1. A90°
  2. B77°
  3. C70°
  4. D154°
16.
On the diagram in the answer space, draw triangle Q, the image of triangle P under a reflection in the line y = -x.
Diagram for question 16
  1. A(3, 1), (3, 3) and (0, 3)
  2. B(1, -3), (3, -3) and (3, 0)
  3. C(-3, -1), (-3, -3) and (0, -3)
  4. D(-1, -3), (-3, -3) and (-3, 0)
17.
A piece of wood measures 25 cm long. Find the upper and lower limits.
  1. AUpper limit 25.5cm; Lower limit 24.5cm
  2. BUpper limit 26cm; Lower limit 24cm
  3. CUpper limit 25.25cm; Lower limit 24.75cm
  4. DUpper limit 25cm; Lower limit 24cm
18.
A piece of wood measures 25 cm long. Find the percentage error.
  1. A4%
  2. B0.50%
  3. C0.02%
  4. D2%
19.
Given that f(x) = x - 4 and h(x) = 2x + 3, find h-1(x).
  1. Ax - 23
  2. B2x - 3
  3. Cx + 32
  4. Dx - 32
20.
Given that f(x) = x - 4 and h(x) = 2x + 3, find h-1(5).
  1. A4
  2. B1
  3. C-1
  4. D11
21.
Given that f(x) = x - 4 and h(x) = 2x + 3, find hf(x).
  1. Ax - 5
  2. B2x - 5
  3. C2x - 1
  4. D2x + 5
22.
In the following diagram, P, Q and R are three points on level ground. The bearing of P from Q is 228°, angle QPR = 72° and R is due south of Q. Find the bearing of (a) Q from P.
Diagram for question 22
  1. A312°
  2. B072°
  3. C228°
  4. D048°
23.
In the following diagram, P, Q and R are three points on level ground. The bearing of P from Q is 228°, angle QPR = 72° and R is due south of Q. Find the bearing of (b) P from R.
Diagram for question 23
  1. A228°
  2. B120°
  3. C048°
  4. D300°
24.
A line passes through the points A(-2, 5) and B(0, y). Given that the gradient of line AB is -3, find the coordinates of B.
  1. A(0, -3)
  2. B(0, 1)
  3. C(0, -1)
  4. D(0, 11)
25.
Two cylinders A and B are geometrically similar and the ratio of their heights is m : 4 respectively. Given that the areas of A and B are 144cm2 and 256cm2 respectively, find the value of m.
  1. A12
  2. B916
  3. C4
  4. D3
26.
The diagram below shows a square based right pyramid with an axis AB. Describe fully the symmetry of the pyramid.
Diagram for question 26
  1. ARotational symmetry of order 4 about axis AB
  2. BNo rotational symmetry
  3. CRotational symmetry of order 2 about axis AB
  4. DRotational symmetry of order 4 about a base edge
27.
In the following diagram, A, B, C and D are points on the circumference of the circle, centre O. BD is the diameter, AD = AC and angle BDC = 22°. Find (a) BAC.
Diagram for question 27
  1. A68°
  2. B44°
  3. C90°
  4. D22°
28.
In the following diagram, A, B, C and D are points on the circumference of the circle, centre O. BD is the diameter, AD = AC and angle BDC = 22°. Find (b) CBD.
Diagram for question 28
  1. A22°
  2. B68°
  3. C90°
  4. D112°
29.
In the following diagram, A, B, C and D are points on the circumference of the circle, centre O. BD is the diameter, AD = AC and angle BDC = 22°. Find (c) ACO.
Diagram for question 29
  1. A68°
  2. B34°
  3. C22°
  4. D56°
30.
y varies directly as x and inversely as the square of z, and y = 8 when x = 4 and z = 1. Find the value of k, the constant of variation.
  1. A2
  2. B8
  3. C12
  4. D32
31.
y varies directly as x and inversely as the square of z, and y = 8 when x = 4 and z = 1. Find the value of y when x = 9 and z = 3.
  1. A6
  2. B2
  3. C18
  4. D54
32.
y varies directly as x and inversely as the square of z, and y = 8 when x = 4 and z = 1. Find the values of z when y = 3 and x = 54.
  1. Az = 3 or z = -3
  2. Bz = 6
  3. Cz = 36 or z = -36
  4. Dz = 6 or z = -6
33.
Solve the equation x13 = 9.
  1. Ax = 3
  2. Bx = 729
  3. Cx = 27
  4. Dx = 81
34.
In the answer space below is an incomplete flowchart for calculating the height (h) of a cylinder given its volume (v) and radius (r). Complete the flowchart.
Diagram for question 34
  1. AInput h and r; v = πr2h
  2. BInput v and h; r = vπh
  3. CInput v and r; h = vπr2
  4. DInput v and r; h = v2πr
35.
Points A and B have coordinates (2, -3) and (7, 9) respectively. Find the length AB.
  1. A13 units
  2. B17 units
  3. C12 units
  4. D25 units
36.
Given that y = 4x3 – 3x2 + 5x, find dydx.
  1. A12x3 - 6x2 + 5
  2. B4x2 - 6x + 5
  3. C12x2 - 3x + 5
  4. D12x2 - 6x + 5
37.
Write down the three inequalities that define the unshaded region R on the diagram below.
Diagram for question 37
  1. Ax ≤ 7; y ≥ x; y ≥ x + 23
  2. Bx ≥ 7; y ≤ x; y ≥ x + 23
  3. Cx ≤ 7; y ≤ x; y ≥ x + 23
  4. Dx ≤ 7; y ≤ x; y ≤ x + 23
38.
The components of the vectors OA and OB are 23 and 42 respectively. Write down BA as a column vector.
  1. A-6-5
  2. B2-1
  3. C65
  4. D-21
39.
The diagram shows the sketch of the graph of y = 3 - 2x - x2 passing through A, B and C. Find the (i) coordinates of the points A and C.
Diagram for question 39
  1. AA(-3, 0) and C(-1, 0)
  2. BA(0, -3) and C(0, 1)
  3. CA(-3, 0) and C(1, 0)
  4. DA(-1, 0) and C(3, 0)
40.
The diagram shows the sketch of the graph of y = 3 - 2x - x2 passing through A, B and C. Find the (ii) turning point of the graph.
Diagram for question 40
  1. A(-1, 4)
  2. B(1, 4)
  3. C(-1, -4)
  4. D(1, -4)
41.
The following diagram is the speed time graph of a car. (a) Calculate the acceleration of the car during the first 5 seconds.
Diagram for question 41
  1. A5 m/s2
  2. B100 m/s2
  3. C4 m/s2
  4. D20 m/s2
42.
The following diagram is the speed time graph of a car. (b) Find the value of t, given that the total distance travelled was 550m.
Diagram for question 42
  1. A55 seconds
  2. B40 seconds
  3. C35 seconds
  4. D30 seconds
43.
The following diagram is the speed time graph of a car. (c) Calculate the average speed for the whole journey.
Diagram for question 43
  1. A20 m/s
  2. B11 m/s
  3. C15 m/s
  4. D1107 m/s
44.
In the diagram, ABC is a straight line. Angle BCD = 90° and tan AB̂D = −34. Calculate the length of BD.
Diagram for question 44
  1. A3 units
  2. B4 units
  3. C5 units
  4. D7 units