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Examinations Council of Zambia — past paper

ECZ 2021 O-Level 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 part 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.
It is given that the universal set E={ first 8 whole numbers } and A={ even numbers }. List set A.
  1. A{2,4,6,8}
  2. B{1,3,5,7}
  3. C{0,2,4,6}
  4. D{0,2,4,6,8}
3.
Simplify 2y - 3(x - 4) - y.
  1. A3y - 3x + 12
  2. By - 3x + 12
  3. Cy + 3x + 12
  4. Dy - 3x - 12
4.
Evaluate -32 + 32.
  1. A0
  2. B18
  3. C-18
  4. D9
5.
Solve the equation (2x - 5)(x + 3) = 0
  1. Ax = 5 or x = -3
  2. Bx = 52 or x = -3
  3. Cx = 52 or x = 3
  4. Dx = -52 or x = 3
6.
Find the equation of a straight line passing through the points (3, 4) and (7, 12).
  1. Ay = 2x + 2
  2. By = 4x - 8
  3. Cy = x + 1
  4. Dy = 2x - 2
7.
Factorise completely 3x3 - 12xy2.
  1. A3x(x - 2y)(x + 2y)
  2. B3(x - 2y)(x + 2y)
  3. Cx(3x - 12y2)
  4. D3x(x2 - 4y2)
8.
Matrix M = -234-2. Find the transpose of M.
  1. A4-2-23
  2. B-243-2
  3. C3-2-24
  4. D-234-2
9.
Matrix P = 2-103 and Q = -13. Find PQ.
  1. A-59
  2. B-2-309
  3. C13
  4. D5-9
10.
A certain company sells shares at K1.30 per share. A businesswoman had K9 100.00 to buy shares. How many shares did she get?
  1. A700 shares
  2. B11 830 shares
  3. C9 100 shares
  4. D7 000 shares
11.
The third and fourth terms of an Arithmetic progression are 6 and 3 respectively. Find the (a) first term.
  1. A-3
  2. B9
  3. C12
  4. D15
12.
The third and fourth terms of an Arithmetic progression are 6 and 3 respectively. Find the (b) formula for the nth term.
  1. A12 - 3n
  2. B15 - 3n
  3. C12 + 3n
  4. D15 + 3n
13.
The probability of getting a black button from a box is 29. Find the probability of getting a button which is not black.
  1. A119
  2. B79
  3. C29
  4. D19
14.
The diagram below shows a sector AOB with centre at O and radius 21cm. The angle subtended at the centre is θ and the area of the sector is 462cm2. Calculate the value of θ. [π = 227]
Diagram for question 14
  1. A240°
  2. B90°
  3. C120°
  4. D60°
15.
The positions of three towns A, B and C on the earth’s surface are shown in the diagram below. (a) A plane flying a distance of 4 500 nautical miles directly from town A to B takes 5 hours. Find the speed of the plane in knots.
Diagram for question 15
  1. A900 knots
  2. B4 500 knots
  3. C22 500 knots
  4. D90 knots
16.
The positions of three towns A, B and C on the earth’s surface are shown in the diagram below. (b) If town C is 5 hours ahead of town A, find the longitude marked X.
Diagram for question 16
  1. A25°E
  2. B75°E
  3. C50°E
  4. D50°W
17.
A learner measured the length of a line to be 2.2 cm. The actual length of the line is 2 cm. Find the absolute error in the learner's measurement.
  1. A0.2cm
  2. B2.2cm
  3. C10cm
  4. D0.1cm
18.
A learner measured the length of a line to be 2.2 cm. The actual length of the line is 2 cm. Find the percentage error in the learner's measurement.
  1. A110%
  2. B20%
  3. C10%
  4. D0.10%
19.
The points A, B, C and D are on the circumference of a circle centre O, such that angle AOC = 126°. AO is parallel to DC and angle OCB = 33°. Find (a) ADC.
Diagram for question 19
  1. A63°
  2. B126°
  3. C117°
  4. D54°
20.
The points A, B, C and D are on the circumference of a circle centre O, such that angle AOC = 126°. AO is parallel to DC and angle OCB = 33°. Find (b) OCD.
Diagram for question 20
  1. A126°
  2. B72°
  3. C63°
  4. D54°
21.
The points A, B, C and D are on the circumference of a circle centre O, such that angle AOC = 126°. AO is parallel to DC and angle OCB = 33°. Find (c) BAO.
Diagram for question 21
  1. A30°
  2. B27°
  3. C33°
  4. D57°
22.
The diagram below shows three points J, K and L on level ground. K is due east of J, angle LJK = 70° and angle JKL = 30°. Calculate the bearing of (a) K from L,
Diagram for question 22
  1. A340°
  2. B060°
  3. C030°
  4. D240°
23.
The diagram below shows three points J, K and L on level ground. K is due east of J, angle LJK = 70° and angle JKL = 30°. Calculate the bearing of (b) J from L.
Diagram for question 23
  1. A060°
  2. B020°
  3. C160°
  4. D340°
24.
Find the equation of a straight line which is perpendicular to the line 2y - x = 3 and passing through the point (-4, 1).
  1. Ay = -2x - 7
  2. By = -12x - 1
  3. Cy = 12x + 3
  4. Dy = 2x + 9
25.
In the answer space below is an incomplete flowchart for calculating the curved surface area (A) of a cylinder with radius (r) and height (h). Complete the flowchart.
Diagram for question 25
  1. AInput r and h; A = 2*π*r*h
  2. BInput r and h; A = π*r2*h
  3. CInput A; r = A2*π*h
  4. DInput r; A = 2*π*r
26.
The figure below shows a parallelogram with centre O. Describe fully the symmetry of the parallelogram about the centre O.
Diagram for question 26
  1. ARotational symmetry of order 2 about O
  2. BRotational symmetry of order 4 about O
  3. CLine symmetry through O
  4. DNo symmetry about O
27.
The diagram below shows triangle A which is mapped onto triangle B by a single transformation P. Describe fully the transformation P.
Diagram for question 27
  1. ATranslation by 44
  2. BRotation through 90° about (12, 0)
  3. CReflection in the x-axis
  4. DReflection in the line y = -x
28.
It is given that y varies directly as 2x and inversely as z2, and y = 4 when x = 8 and z = 2. Find the value of k, the constant of variation.
  1. A2
  2. B4
  3. C12
  4. D1
29.
It is given that y varies directly as 2x and inversely as z2, and y = 4 when x = 8 and z = 2. Find the value of y when x = 27 and z = 3.
  1. A9
  2. B18
  3. C3
  4. D6
30.
It is given that y varies directly as 2x and inversely as z2, and y = 4 when x = 8 and z = 2. Find the values of z when x = 24 and y = 3.
  1. Az = 4 or z = -4
  2. Bz = 16 or z = -16
  3. Cz = 2 or z = -2
  4. Dz = 4 only
31.
Find ∫(6x2 - 2x + 7) dx.
  1. A2x3 - 2x2 + 7x + C
  2. B12x - 2 + C
  3. C6x3 - x2 + 7x + C
  4. D2x3 - x2 + 7x + C
32.
The areas of two similar cylinders are 64cm2 and 36cm2 respectively. If the height of the larger cylinder is 30cm, find the height of the smaller cylinder.
  1. A20cm
  2. B40cm
  3. C15cm
  4. D22.5cm
33.
In the diagram below, AB = 3cm, BC = 4cm, AD = 13cm and ABC = ACD = 90°. Calculate the value of tan DAC.
Diagram for question 33
  1. A34
  2. B125
  3. C512
  4. D43
34.
A is the point (1, 2) and B is the point (-2, 5). Find AB as a column vector.
  1. A1-2
  2. B-33
  3. C-17
  4. D3-3
35.
Write three inequalities that define the unshaded region R, on the diagram below.
Diagram for question 35
  1. Ax ≥ 2; y ≤ x - 2; 2x + 3y ≤ 24
  2. Bx ≤ 2; y ≥ x - 2; 2x + 3y ≤ 24
  3. Cx ≥ 2; y ≥ x - 2; 2x + 3y ≤ 24
  4. Dx ≥ 2; y ≥ x - 2; 2x + 3y ≥ 24
36.
Given that √2 = 2x, find the value of x.
  1. A2
  2. B-0.5
  3. C12
  4. D1
37.
The diagram below shows the graph of y = (-x + 2)(x - 5). The graph cuts the x-axis at A and B. Find the (i) coordinates of the points A and B.
Diagram for question 37
  1. AA(5, 0), B(2, 0)
  2. BA(0, 2), B(0, 5)
  3. CA(2, 0), B(5, 0)
  4. DA(-2, 0), B(5, 0)
38.
The diagram below shows the graph of y = (-x + 2)(x - 5). The graph cuts the x-axis at A and B. Find the (ii) maximum value of y.
Diagram for question 38
  1. A4
  2. B92
  3. C94
  4. D-2.25
39.
The diagram below shows the speed-time graph of a moving object. (a) Find the acceleration of the object when t = 3.
Diagram for question 39
  1. A4m/s2
  2. B20m/s2
  3. C5m/s2
  4. D3m/s2
40.
The diagram below shows the speed-time graph of a moving object. (b) Given that the object decelerates at 2m/s2, find the value of t,
Diagram for question 40
  1. A17 seconds
  2. B22 seconds
  3. C20 seconds
  4. D12 seconds
41.
The diagram below shows the speed-time graph of a moving object. (c) Calculate the average speed of the object in the first 10 seconds of the journey.
Diagram for question 41
  1. A18m/s
  2. B24m/s
  3. C19m/s
  4. D14m/s
42.
The functions f and g are defined by f(x) = x + 92 and g(x) = x − 2. Find f-1(x).
  1. Ax − 92
  2. B2x + 9
  3. C2x − 9
  4. Dx2 − 9
43.
The functions f and g are defined by f(x) = x + 92 and g(x) = x − 2. Find fg(x).
  1. Ax + 52
  2. Bx + 72
  3. Cx + 7
  4. Dx + 112
44.
The functions f and g are defined by f(x) = x + 92 and g(x) = x − 2. Find fg(−5).
  1. A0
  2. B2
  3. C−1
  4. D1