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Examinations Council of Zambia — past paper

ECZ 2022 O-Level Paper 1 — Mathematics

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

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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 the universal set E={1,3,5,7,9,11},X={1,5,9} and Y={3,9,11}, list X∩Y'.
  1. A{1,5}
  2. B{1,9}
  3. C{5,7}
  4. D{3,11}
3.
Evaluate 32-2.
  1. A49
  2. B94
  3. C-0.44
  4. D-2.25
4.
Factorise completely 2ax + 4ay - 3bx - 6by.
  1. A(2a - 3b)(x + 2y)
  2. B(2a - 3b)(x - 2y)
  3. C(2a + 3b)(x + 2y)
  4. D(2a + 3b)(x - 2y)
5.
Simplify 3(4x - 5) + 2.
  1. A4x - 13
  2. B12x + 17
  3. C12x - 13
  4. D12x - 15
6.
Solve the equation 4y2 - 8y = 0.
  1. Ay = 0 or y = -2
  2. By = 0 or y = 2
  3. Cy = 2 only
  4. Dy = -2 or y = 2
7.
A company declared a dividend of K2.75 per share. A businessman invested 560 shares in the company. How much dividend did he get?
  1. AK1 400.00
  2. BK562.75
  3. CK1 540.00
  4. DK203.64
8.
Given that 2, -1, -4 ... are consecutive terms of an Arithmetic progression, find the (a) common difference, d,
  1. A-5
  2. B3
  3. C-2
  4. D-3
9.
Given that 2, -1, -4 ... are consecutive terms of an Arithmetic progression, find the (b) formula for the nth term.
  1. A5 - 3n
  2. B2 - 3n
  3. C5 + 3n
  4. D2 + 3n
10.
The probability that a boy will be late for school on any particular day is x. Find, in terms of x, the probability that he will not be late for school.
  1. A1 + x
  2. Bx
  3. Cx - 1
  4. D1 - x
11.
The vector RS = -45. Given that the coordinates of the point S are (1, 2), find the coordinates of the point R.
  1. A(5, -3)
  2. B(-3, 7)
  3. C(3, -5)
  4. D(-5, 3)
12.
The matrix M = 1527 and the matrix N = 0120. Find (a) MT,
  1. A1527
  2. B7251
  3. C1257
  4. D5172
13.
The matrix M = 1527 and the matrix N = 0120. Find (b) NM.
  1. A27210
  2. B10272
  3. C0540
  4. D15414
14.
The diagram shows two triangles A and B. Describe fully the single transformation which maps triangle A onto triangle B.
Diagram for question 14
  1. ATranslation by 01
  2. BReflection in the line y = 2
  3. CReflection in the x-axis
  4. DRotation 180° about (2, 2)
15.
In the following diagram, points A and B lie on latitude 60°S while point C is on latitude 30°N. (a) The local time at A is 10 00 hours when it is 13 00 hours at B. Find the difference in longitudes between A and B.
Diagram for question 15
  1. A45°
  2. B90°
  3. C30°
  4. D3°
16.
In the following diagram, points A and B lie on latitude 60°S while point C is on latitude 30°N. (b) A plane flew from B to C at a speed of 600 knots. How long did the plane take?
Diagram for question 16
  1. A6 hours
  2. B90 hours
  3. C9 hours
  4. D4.5 hours
17.
Find the gradient of the line passing through the points A(4, -6) and B(2, 4).
  1. A15
  2. B-0.2
  3. C5
  4. D-5
18.
Solve the equation 2x3 = 16.
  1. Ax = 4
  2. Bx = 2
  3. Cx = 8
  4. Dx = 16
19.
In the following diagram, AB and AC are tangents to the circle, centre O. AC and BE produced, meet at D and angle BAC = 54°. Calculate angle (a) ACB.
Diagram for question 19
  1. A27°
  2. B90°
  3. C63°
  4. D54°
20.
In the following diagram, AB and AC are tangents to the circle, centre O. AC and BE produced, meet at D and angle BAC = 54°. Calculate angle (b) CBD.
Diagram for question 20
  1. A90°
  2. B54°
  3. C63°
  4. D27°
21.
In the following diagram, AB and AC are tangents to the circle, centre O. AC and BE produced, meet at D and angle BAC = 54°. Calculate angle (c) CDB.
Diagram for question 21
  1. A54°
  2. B63°
  3. C36°
  4. D27°
22.
The mass of a loaf of bread is 702.1 g, correct to 1 decimal place. Find the lower limit of the mass.
  1. A702.0g
  2. B701.6g
  3. C702.15g
  4. D702.05g
23.
The mass of a loaf of bread is 702.1 g, correct to 1 decimal place. Find the relative error in the mass of the loaf.
  1. A114042
  2. B0.05
  3. C11404.2
  4. D121
24.
Two similar solids P and Q have volumes 80cm3 and 270cm3 respectively. The height of the smaller solid is 8cm. Find the height of the larger solid.
  1. A27cm
  2. B12cm
  3. C18cm
  4. D8cm
25.
In the diagram, FGH is a straight line, FG = 8cm, EG = 10cm and angle EFG = 90°. Find the value of sin EGH.
Diagram for question 25
  1. A53
  2. B35
  3. C45
  4. D-0.6
26.
y varies directly as the square of x and inversely as z, and y = 2 when x = 4 and z = 24. Find the value of k, the constant of variation.
  1. A6
  2. B24
  3. C3
  4. D13
27.
y varies directly as the square of x and inversely as z, and y = 2 when x = 4 and z = 24. Find the value of y when x = 9 and z = 27.
  1. A27
  2. B9
  3. C3
  4. D1
28.
y varies directly as the square of x and inversely as z, and y = 2 when x = 4 and z = 24. Find the values of x when y = 8 and z = 6.
  1. Ax = 4 only
  2. Bx = 4 or x = -4
  3. Cx = 16 or x = -16
  4. Dx = 2 or x = -2
29.
The diagram below shows a regular triangular prism. Describe the symmetry of the prism.
Diagram for question 29
  1. ARotational symmetry of order 6 about the axis shown
  2. BRotational symmetry of order 2 about the axis shown
  3. CRotational symmetry of order 3 about the axis shown
  4. DNo rotational symmetry
30.
In the answer space below is an incomplete program written in pseudocode for calculating the curved surface area (A) of a cone with base radius (r) and slant height (s). Complete the program. (A = πrs)
Diagram for question 30
  1. AEnter A; r = Aπs
  2. BEnter r and s; A = π*r*s
  3. CEnter r and h; A = π*r2*h
  4. DEnter r and s; A = 2π*r*s
31.
ABC is a straight line. The coordinates of the points A and B are (2, 1) and (-6, 5) respectively. Given that B is the midpoint of AC, find the coordinates of C.
  1. A(10, -3)
  2. B(-4, 6)
  3. C(-14, 9)
  4. D(-8, 4)
32.
In the diagram, AOB is a sector of a circle, centre O. Angle AOB = 72° and the radius is 14cm. Calculate the area of the sector. [π = 227]
Diagram for question 32
  1. A61.6cm2
  2. B246.4cm2
  3. C616cm2
  4. D123.2cm2
33.
Given that f(x) = 3x + 1 and g(x) = 4x - 1, find f-1(x).
  1. Ax - 13
  2. Bx + 13
  3. Cx - 31
  4. D3x - 1
34.
Given that f(x) = 3x + 1 and g(x) = 4x - 1, find f-1(-5).
  1. A2
  2. B-1.33
  3. C-16
  4. D-2
35.
Given that f(x) = 3x + 1 and g(x) = 4x - 1, find fg(x).
  1. A12x + 2
  2. B12x - 2
  3. C7x
  4. D12x - 1
36.
In the following diagram, angle BAC is 46° and AC = BC. B is due east of A. Calculate the bearing of (a) A from C.
Diagram for question 36
  1. A316°
  2. B044°
  3. C136°
  4. D224°
37.
In the following diagram, angle BAC is 46° and AC = BC. B is due east of A. Calculate the bearing of (b) C from B.
Diagram for question 37
  1. A316°
  2. B136°
  3. C224°
  4. D046°
38.
Write the four inequalities that define the unshaded region R in the diagram below.
Diagram for question 38
  1. Ax ≥ -2; x ≤ 4; y ≥ 2; y ≤ -3x4 + 6
  2. Bx ≥ -2; x ≥ 4; y ≥ 2; y ≤ -3x4 + 6
  3. Cx ≥ -2; x ≤ 4; y ≤ 2; y ≤ -3x4 + 6
  4. Dx ≤ -2; x ≤ 4; y ≥ 2; y ≤ -3x4 + 6
39.
Given that y = 2x2 - 4x + 3, find dydx.
  1. A2x - 4
  2. B4x + 4
  3. C4x - 1
  4. D4x - 4
40.
The sketch shows the graph of y = x2 - 2x - 8. Find the coordinates of (i) A and B.
Diagram for question 40
  1. AA(-2, 0), B(4, 0)
  2. BA(0, -2), B(0, 4)
  3. CA(2, 0), B(-4, 0)
  4. DA(-4, 0), B(2, 0)
41.
The sketch shows the graph of y = x2 - 2x - 8. Find the coordinates of (ii) the minimum point on the graph.
Diagram for question 41
  1. A(-1, -9)
  2. B(1, -9)
  3. C(1, 9)
  4. D(3, -9)
42.
The diagram below is the speed-time graph of an object. The object starts from rest and accelerates uniformly for 2 seconds until it reaches a speed of 10m/s. It then travels at this speed for 8 seconds and finally decelerates to rest after 5 seconds. Find the (a) retardation of the object in the last 5 seconds.
Diagram for question 42
  1. A10m/s2
  2. B12 m/s2
  3. C2m/s2
  4. D5m/s2
43.
The diagram below is the speed-time graph of an object. The object starts from rest and accelerates uniformly for 2 seconds until it reaches a speed of 10m/s. It then travels at this speed for 8 seconds and finally decelerates to rest after 5 seconds. Find the (b) distance travelled in the first 10 seconds.
Diagram for question 43
  1. A80m
  2. B90m
  3. C50m
  4. D100m
44.
The diagram below is the speed-time graph of an object. The object starts from rest and accelerates uniformly for 2 seconds until it reaches a speed of 10m/s. It then travels at this speed for 8 seconds and finally decelerates to rest after 5 seconds. Find the (c) average speed of the object for the whole journey.
Diagram for question 44
  1. A9015 m/s
  2. B8m/s
  3. C10m/s
  4. D233 m/s