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Examinations Council of Zambia — past paper

ECZ 2012 O-Level Paper 1 — Mathematics

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

G12 Titan
1.
Simplify 3x - 7(2x - 5).
  1. A35 - 11x
  2. B35 + 11x
  3. C-11x - 35
  4. D5 - 11x
2.
Given that A = 1-345 and B = 93-126, find A - (13)B.
  1. A-8-6163
  2. B-2-403
  3. C-2-483
  4. D4-207
3.
Factorise completely 4 - 16x2.
  1. A4(1 - 4x2)
  2. B4(1 - 2x)(1 + 2x)
  3. C4(1 - 2x)2
  4. D16(1 - x)(1 + x)
4.
Mr Hambwiimbwi planned to employ 20 men to build his house in 7 days. On the day work was to start, he reduced the number of men so that the work would now be completed in 28 days, working at the same rate. How many men were needed for the work?
  1. A80
  2. B35
  3. C15
  4. D5
5.
Find the gradient of the straight line with equation 4x + 2y = 9.
  1. A-2
  2. B2
  3. C-4
  4. D92
6.
The diagram shows a squared floor tile with centre O. Describe fully the rotational symmetry, about O, of this floor tile.
Diagram for question 6
  1. ARotational symmetry of order 2
  2. BRotational symmetry of order 4
  3. CNo rotational symmetry, order 1
  4. DRotational symmetry of order 8
7.
In the diagram, A, B and C are points on the circumference of a circle with centre O. AT and TB are tangents to the circle, angle CAO = 30° and angle CBO = 29°. Calculate angle ACB.
Diagram for question 7
  1. A30°
  2. B29°
  3. C59°
  4. D118°
8.
In the diagram, AT and TB are tangents to the circle at A and B, angle CAO = 30° and angle CBO = 29°. Calculate angle ATB.
Diagram for question 8
  1. A118°
  2. B59°
  3. C121°
  4. D62°
9.
Given that vector a = -86, find the magnitude of a.
  1. A10
  2. B2
  3. C14
  4. D100
10.
The diagram shows two circles with the same centre O. The radius of the smaller circle is 5 cm and that of the larger is 15 cm. Chord AB is 7 cm and angle ABO = angle DCO = 40°. Calculate the length of the chord CD.
Diagram for question 10
  1. A14 cm
  2. B21 cm
  3. C23 cm
  4. D7 cm
11.
Given that E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, list the subset A = {x : x is a factor of 55}.
  1. A{1, 5, 11, 55}
  2. B{5, 11}
  3. C{1, 5, 11}
  4. D{1, 11}
12.
Given that E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, list the subset B = {x : (12)x ≥ 5 12}.
  1. A{11}
  2. B{12}
  3. C{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
  4. D{11, 12}
13.
In the diagram, BCD is a straight line, AB = 6 cm, BD = 13 cm, angle ACD = 135° and angle ABC = 90°. Calculate the length of CD.
Diagram for question 13
  1. A7 cm
  2. B6 cm
  3. C13 cm
  4. D19 cm
14.
Using the same diagram, calculate the area of triangle ACD.
Diagram for question 14
  1. A39 cm2
  2. B21 cm2
  3. C18 cm2
  4. D42 cm2
15.
A pack of eleven identical cards is labelled 1 to 11. The cards are shuffled and placed upside down. If a card is picked at random from the pack, what is the probability that it is a prime numbered card?
  1. A411
  2. B611
  3. C511
  4. D510
16.
In the diagram, AC = 10 cm, BC = 5 cm and angle ACB = 60°. Given that sin 60 = 0.866, cos 60 = 0.5 and tan 60 = 1.73, calculate the value of (AB)2.
Diagram for question 16
  1. A125
  2. B175
  3. C25
  4. D75
17.
Given that f(x) = 3x - 52, find f(-9).
  1. A-16
  2. B16
  3. C-11
  4. D-32
18.
Given that f(x) = 3x - 52, find f-1(x).
  1. A3x - 52
  2. B2x + 53
  3. C2x - 53
  4. D23x - 5
19.
Given that f(x) = 3x - 52 and g(x) = x - 46, find the value of x for which f(x) = 3g(x).
  1. A2
  2. B-12
  3. C12
  4. D1
20.
Given that y varies directly as x and z, and that y = 9 when x = 6 and z = 12, find k, the constant of variation.
  1. A9
  2. B12
  3. C13
  4. D3
21.
y varies directly as x and as z, with constant k = 3 (so y = 3xz). Find the value of y when x = 4 and z = 3.
  1. A36
  2. B12
  3. C6
  4. D108
22.
y varies directly as x and as z, with constant k = 3 (so y = 3xz). Find the value of x when y = 4 12 and z = 5.
  1. A30
  2. B0.3
  3. C3
  4. D1.5
23.
Solve the equation x2 - 4x = 0.
  1. Ax = 4
  2. Bx = 0 or x = -4
  3. Cx = 0 or x = 4
  4. Dx = 2
24.
In the diagram, PQR is parallel to TS, QUT is a straight line, angle QRU = 30°, angle TSU = 20° and angle SUT = 97°. Calculate angle PQT.
Diagram for question 24
  1. A97°
  2. B30°
  3. C117°
  4. D63°
25.
Using the same diagram, calculate angle RUS.
Diagram for question 25
  1. A50°
  2. B33°
  3. C83°
  4. D47°
26.
Triangle A has vertices (1, 3), (3, 3) and (3, 5). It is transformed by a shear with invariant line y = 2 and shear factor -2. What are the vertices of the image B?
Diagram for question 26
  1. A(3, 3), (5, 3), (7, 5)
  2. B(-1, 3), (1, 3), (-3, 5)
  3. C(1, 1), (3, 1), (3, 3)
  4. D(-1, 3), (1, 3), (3, 5)
27.
A plane flew north from town A (28 S, 20 E) to town B (32 N, 20 E) in 9 hours. Find the speed of the plane in knots.
  1. A3600 knots
  2. B40 knots
  3. C400 knots
  4. D240 knots
28.
A region R is defined by y ≤ x, x + y ≤ 4 and y ≥ 0. Which of these points lies inside region R?
Diagram for question 28
  1. A(1, 3)
  2. B(3, 2)
  3. C(-1, 2)
  4. D(2, 1)
29.
Evaluate 21613.
  1. A72
  2. B6
  3. C8
  4. D648
30.
The speed-time graph shows a van which starts from rest and accelerates uniformly for 8 seconds until it reaches a speed of 6 m/s. Find the acceleration of the van during the first 8 seconds.
Diagram for question 30
  1. A0.75 m/s2
  2. B1.33 m/s2
  3. C48 m/s2
  4. D6 m/s2
31.
Using the same speed-time graph, find the distance travelled by the van in 20 seconds.
Diagram for question 31
  1. A120 m
  2. B72 m
  3. C96 m
  4. D24 m
32.
The car starts from the same place as the van but 4 seconds later, and accelerates uniformly until it overtakes the van. Given that overtaking occurs when the van has been travelling for 20 seconds, calculate the speed of the car at this instant.
Diagram for question 32
  1. A6 m/s
  2. B9.6 m/s
  3. C24 m/s
  4. D12 m/s
33.
A map is drawn to a scale of 1 : 50 000. Two camps are 7 cm apart on the map. Find the actual distance between them, in kilometres.
  1. A35 km
  2. B3.5 km
  3. C0.35 km
  4. D350 km
34.
A map is drawn to a scale of 1 : 50 000. The actual area of a game park is 25 square kilometres. Calculate its area on the map, in square centimetres.
  1. A50 cm2
  2. B12.5 cm2
  3. C100 cm2
  4. D500 cm2