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Examinations Council of Zambia — past paper

ECZ 2019 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∪C)'∩B in the Venn diagram in the answer space.
Diagram for question 1
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
2.
Set A={ Prime numbers less than 12}. List set A .
  1. A{1,2,3,5,7,11}
  2. B{2,3,5,7,11}
  3. C{2,3,5,7,9,11}
  4. D{1,3,5,7,9,11}
3.
Evaluate (-1)0 × 23.
  1. A-8
  2. B1
  3. C8
  4. D2
4.
Solve the equation (x - 1)(2x + 5) = 0.
  1. Ax = -1 or x = 52
  2. Bx = 1 or x = -52
  3. Cx = 1 or x = 52
  4. Dx = -1 or x = -52
5.
Simplify 4x2 + 2y2 - xy - 6x2 + 2xy.
  1. A10x2 + 2y2 + xy
  2. B2x2 + 2y2 + xy
  3. C-2x2 + 2y2 - 3xy
  4. D-2x2 + 2y2 + xy
6.
Factorise completely 4ab + 6ac - 6bd - 9cd.
  1. A(2a - 3d)(2b - 3c)
  2. B(2a - 3d)(2b + 3c)
  3. C(2a + 3d)(2b + 3c)
  4. D(4a - 6d)(b + c)
7.
A company declared a dividend of K1.50 per share. Musalala has 600 shares in the company. How much will she get?
  1. AK601.50
  2. BK900.00
  3. CK400.00
  4. DK90.00
8.
Given that 17 + m + 27 + ... are consecutive terms of an Arithmetic Progression, find the arithmetic mean, m.
  1. A10
  2. B22
  3. C20
  4. D44
9.
For the sequence 11, 13, 15, ..., find the formula for the nth term.
  1. A2n + 9
  2. B2n + 11
  3. C11n + 2
  4. D2n - 9
10.
The transpose of a matrix A is (-1 4 5). Find the matrix A.
  1. A-145
  2. B-145
  3. C54-1
  4. D-154
11.
Given that (1 2 3) 1x5 = (24), find the value of x.
  1. A5
  2. B4
  3. C3
  4. D8
12.
A number is chosen at random from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Find the probability that it is a perfect square.
  1. A410
  2. B110
  3. C310
  4. D210
13.
Solve the equation 8x = 128.
  1. A73
  2. B3
  3. C7
  4. D37
14.
The diagram below shows a sector AOB. Arc AB subtends an angle of 21° at the centre O. Given that the area of the sector is 14.85 cm2, calculate the radius. [π = 227]
Diagram for question 14
  1. A9cm
  2. B14.85cm
  3. C7cm
  4. D81cm
15.
The diagram below shows the positions of towns A, B and C on the earth’s surface. (a) If it is 08 20 at A, what time is it at C?
Diagram for question 15
  1. A13 20 hours
  2. B08 20 hours
  3. C12 20 hours
  4. D03 20 hours
16.
The diagram below shows the positions of towns A, B and C on the earth’s surface. (b) A plane flies from A to B at a speed of 400 knots. How long does the journey take if AB = 4 800 nm?
Diagram for question 16
  1. A10 hours
  2. B1 920 000 hours
  3. C8 hours
  4. D12 hours
17.
The length of a piece of wire is measured as 4.5 cm. Calculate the tolerance.
  1. A0.1cm
  2. B0.5cm
  3. C0.45cm
  4. D0.05cm
18.
The length of a piece of wire is measured as 4.5 cm. Calculate the relative error.
  1. A0.05
  2. B19
  3. C9
  4. D190
19.
In the diagram below, A, B, C and D are points on the circumference of a circle, centre O. DÂT = 40°, BDC = 30° and AT is a tangent to the circle at A. Calculate (a) CBD.
Diagram for question 19
  1. A30°
  2. B60°
  3. C40°
  4. D50°
20.
In the diagram below, A, B, C and D are points on the circumference of a circle, centre O. DÂT = 40°, BDC = 30° and AT is a tangent to the circle at A. Calculate (b) BAC.
Diagram for question 20
  1. A60°
  2. B50°
  3. C30°
  4. D40°
21.
In the diagram below, A, B, C and D are points on the circumference of a circle, centre O. DÂT = 40°, BDC = 30° and AT is a tangent to the circle at A. Calculate (c) AOB.
Diagram for question 21
  1. A120°
  2. B50°
  3. C100°
  4. D80°
22.
In the diagram below, BCD is a straight line, AB = 12cm, AC = 20cm and angle ABC = 90°. Find the value of cos ACD.
Diagram for question 22
  1. A-0.6
  2. B45
  3. C-0.8
  4. D35
23.
A and B are points with coordinates (-3, 3) and (5, 9) respectively. Find the length AB.
  1. A8
  2. B14
  3. C6
  4. D10
24.
a varies directly as b and as the square of c, and a = 30 when b = 2.5 and c = 2. Find the value of k, the constant of variation.
  1. A12
  2. B10
  3. C3
  4. D30
25.
a varies directly as b and as the square of c, and a = 30 when b = 2.5 and c = 2. Find the value of a when b = 2 and c = 3.
  1. A36
  2. B27
  3. C18
  4. D54
26.
a varies directly as b and as the square of c, and a = 30 when b = 2.5 and c = 2. Find the values of c when a = 300 and b = 4.
  1. Ac = 5 or c = -5
  2. Bc = 10 or c = -10
  3. Cc = 25 or c = -25
  4. Dc = 5 only
27.
Find ∫(3x2 + 8x - 5) dx.
  1. Ax3 + 8x2 - 5x + C
  2. Bx3 + 4x2 - 5x + C
  3. C6x + 8 + C
  4. D3x3 + 4x2 - 5x + C
28.
The diagram below shows two triangles A and B. Describe fully the single transformation which maps triangle A onto triangle B.
Diagram for question 28
  1. AReflection in the y-axis
  2. BTranslation by 6-2
  3. CRotation through 180° about (0, 2)
  4. DTranslation by -62
29.
In the diagram below, A, B and C are three points on level ground. The bearing of B from A is 062° and angle ABC = 128°. C is due east of A. Find the bearing of (a) C from B.
Diagram for question 29
  1. A114°
  2. B128°
  3. C062°
  4. D242°
30.
In the diagram below, A, B and C are three points on level ground. The bearing of B from A is 062° and angle ABC = 128°. C is due east of A. Find the bearing of (b) A from C.
Diagram for question 30
  1. A270°
  2. B062°
  3. C090°
  4. D114°
31.
The diagram below shows a plane figure made up of congruent semi circles. Angle AOB = 90°. Describe fully the symmetry of the figure.
Diagram for question 31
  1. ARotational symmetry of order 3 about O
  2. BLine symmetry only
  3. CRotational symmetry of order 2 about O
  4. DRotational symmetry of order 4 about O
32.
In the answer space below is an incomplete program written in pseudocode for calculating the volume V of a cuboid, given the length, l, base, b, and the height, h. Complete the program by filling in the blank spaces with appropriate statements.
Diagram for question 32
  1. AEnter V; l = Vb*h
  2. BEnter l, b and h; V = l + b + h
  3. CEnter l and b; V = l*b
  4. DEnter l, b and h; V = l*b*h
33.
The functions f and g are defined by f(x) = 2x - 3 and g(x) = 3x. Find f-1(x).
  1. Ax + 32
  2. Bx + 23
  3. C2x + 3
  4. Dx - 32
34.
The functions f and g are defined by f(x) = 2x - 3 and g(x) = 3x. Find gf(x).
  1. A6x - 9
  2. B2x - 9
  3. C6x - 3
  4. D5x - 3
35.
The functions f and g are defined by f(x) = 2x - 3 and g(x) = 3x. Find gf(2).
  1. A3
  2. B6
  3. C9
  4. D1
36.
In the diagram below, A is the point (0, 4) and B is the point (2, 0) and O is the origin. Find the equation of a straight line through O which is parallel to the line AB.
Diagram for question 36
  1. Ay = -2x
  2. By = -2x + 4
  3. Cy = -12x
  4. Dy = 2x
37.
The heights of two similar cylinders are 4 cm and 6 cm. If the volume of the smaller cylinder is 48 cm3, find the volume of the larger cylinder.
  1. A108cm3
  2. B324cm3
  3. C162cm3
  4. D72cm3
38.
Write down the three inequalities that define the unshaded region R, on the diagram below.
Diagram for question 38
  1. Ay ≥ 6; y > x - 2; y ≥ -3x + 6
  2. By ≤ 6; y < x - 2; y ≥ -3x + 6
  3. Cy ≤ 6; y > x - 2; y ≥ -3x + 6
  4. Dy ≤ 6; y > x - 2; y ≤ -3x + 6
39.
M is the point (0, 5) and MN = -34. Find ON.
  1. A09
  2. B-39
  3. C31
  4. D-34
40.
The sketch shown below represents the graph of the curve y = x2 - 4x + 3, passing through the points A, B and C. Find the (i) coordinates of the points B and C,
Diagram for question 40
  1. AB(-1, 0), C(-3, 0)
  2. BB(1, 0), C(3, 0)
  3. CB(3, 0), C(1, 0)
  4. DB(0, 1), C(0, 3)
41.
The sketch shown below represents the graph of the curve y = x2 - 4x + 3, passing through the points A, B and C. Find the (ii) minimum value of y.
Diagram for question 41
  1. A2
  2. B-1
  3. C3
  4. D1
42.
The diagram below is the speed time graph of a car. The car starts from rest and accelerates uniformly at 2 m/s2 for t seconds until it reaches a speed of 16 m/s. It then travels at 16 m/s for 40 seconds, after which it comes to rest in a further 10 seconds. Find the (a) value of t.
Diagram for question 42
  1. A4 seconds
  2. B16 seconds
  3. C8 seconds
  4. D32 seconds
43.
The diagram below is the speed time graph of a car. The car starts from rest and accelerates uniformly at 2 m/s2 for t seconds until it reaches a speed of 16 m/s. It then travels at 16 m/s for 40 seconds, after which it comes to rest in a further 10 seconds. Find the (b) distance travelled in the last 50 seconds.
Diagram for question 43
  1. A80m
  2. B800m
  3. C640m
  4. D720m
44.
The diagram below is the speed time graph of a car. The car starts from rest and accelerates uniformly at 2 m/s2 for t seconds until it reaches a speed of 16 m/s. It then travels at 16 m/s for 40 seconds, after which it comes to rest in a further 10 seconds. Find the (c) speed of the car when t = 53 seconds.
Diagram for question 44
  1. A16m/s
  2. B5m/s
  3. C8m/s
  4. D0m/s