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Examinations Council of Zambia — past paper

ECZ 2018 GCE 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 region in the Venn diagram below.
Diagram for question 1
  1. AA∪B
  2. B(A∪B)∩C′
  3. CC∩(A∪B)
  4. DA∩B∩C′
2.
Given that E={1,2,3,4,5,6,7,8},A={1,2,3,4} and B={2,3,4,5,6}, list (A∪B)'.
  1. A{1,7,8}
  2. B{1,2,3,4,5,6}
  3. C{5,6,7,8}
  4. D{7,8}
3.
Simplify 4(x + 2y) − (3x − 8y).
  1. Ax + 16y
  2. Bx
  3. C7x + 16y
  4. Dx − 16y
4.
Evaluate 2723.
  1. A18
  2. B3
  3. C9
  4. D81
5.
A straight line passing through A(3, 2) and B(5, y) has gradient −2. Find the value of y.
  1. A−6
  2. B−2
  3. C6
  4. D2
6.
Factorise completely 5x2 − 5.
  1. A5(x2 − 1)
  2. B(5x − 5)(x + 1)
  3. C5(x − 1)2
  4. D5(x − 1)(x + 1)
7.
Given that C = 5-121 and D = 1-2, express CD as a single matrix.
  1. A[3; 0]
  2. B[7; 0]
  3. C[7; 4]
  4. D[3; 4]
8.
The first three terms in an arithmetic progression are 5, 7 and 9. Find the common difference.
  1. A5
  2. B4
  3. C−2
  4. D2
9.
The first three terms in an arithmetic progression are 5, 7 and 9. Find the sum of the first 12 terms.
  1. A192
  2. B27
  3. C384
  4. D96
10.
In a game, the probability of a player losing is 0.3. What is the probability of the player winning the game?
  1. A0.3
  2. B0.7
  3. C0.4
  4. D1
11.
The coordinates of B and C are (2, 5) and (4, −3) respectively. If M is the mid-point of BC, what is the position vector of M?
  1. A[6; 2]
  2. B[1; −4]
  3. C[3; −1]
  4. D[3; 1]
12.
The scale of a map is 1 : 20 000. The actual area of residential plots is 60 km2. Calculate the area of residential plots on the map in square centimetres.
  1. A15 cm2
  2. B1500 cm2
  3. C150 cm2
  4. D3000 cm2
13.
The difference in longitude between town A and town B is 105°. B is west of A. A family at A was watching a football match at 16 00 hours. At what time did a family at B watch the same match?
  1. A23 00 hours
  2. B11 00 hours
  3. C09 00 hours
  4. D07 00 hours
14.
The distance between P and Q is 3 600 nautical miles. If an aeroplane flies from P to Q at 600 knots, how long will it take?
  1. A6 hours
  2. B60 hours
  3. C6 minutes
  4. D12 hours
15.
The transpose of a matrix P is 134251301. Write down the matrix P.
  1. A[1 2 3; 3 5 0; 4 1 1]
  2. B[1 3 4; 2 5 1; 3 0 1]
  3. C[3 0 1; 2 5 1; 1 3 4]
  4. D[4 3 1; 1 5 2; 1 0 3]
16.
Solve the equation 22x − 1 = 16−2x.
  1. Ax = −16
  2. Bx = 110
  3. Cx = 12
  4. Dx = −110
17.
The diagram below shows a sector AOB of a circle with centre O and radius 7 cm. The area of the sector is 25⅔ cm2. [π = 227] Calculate AÔB.
Diagram for question 17
  1. A30°
  2. B120°
  3. C60°
  4. D45°
18.
Ngiwezi invested K14 500.00 in a business firm. The condition was that if she left her shares in the firm for 12 months, a profit of 5% would be added to her shares. How much will she get at the end of 12 months?
  1. AK725.00
  2. BK15 950.00
  3. CK13 775.00
  4. DK15 225.00
19.
The diagram below shows a circle with a tangent RWS. The points V, W, X and Y are on the circle such that XŶW = 44°, VŴY = 54° and SŴV = 39°. Calculate RŴX.
Diagram for question 19
  1. A39°
  2. B54°
  3. C43°
  4. D44°
20.
The diagram below shows a circle with a tangent RWS. The points V, W, X and Y are on the circle such that XŶW = 44°, VŴY = 54° and SŴV = 39°. Calculate XṼW.
Diagram for question 20
  1. A54°
  2. B44°
  3. C39°
  4. D88°
21.
The diagram below shows a circle with a tangent RWS. The points V, W, X and Y are on the circle such that XŶW = 44°, VŴY = 54° and SŴV = 39°. Calculate YX̂W.
Diagram for question 21
  1. A88°
  2. B93°
  3. C98°
  4. D83°
22.
The ratio of the heights of two containers that are geometrically similar is 2 : 3. If the surface area of the smaller container is 80 cm2, find the surface area of the larger container.
  1. A120 cm2
  2. B270 cm2
  3. C180 cm2
  4. D360 cm2
23.
In the diagram, triangle ABC has vertices A(1, 3), B(1, 1) and C(4, 1). It is mapped onto triangle STU with vertices S(−4, −6), T(−4, −4) and U(−1, −4) by a combined transformation. Name the two transformations that map triangle ABC onto triangle STU.
Diagram for question 23
  1. AA reflection in the x-axis followed by a translation by [−5; −3]
  2. BA rotation of 180° about the origin followed by a translation by [−3; −5]
  3. CA reflection in the y-axis followed by a translation by [−5; −3]
  4. DA rotation of 90° clockwise about the origin followed by a translation by [−5; −3]
24.
Two variables x and y have the following corresponding values: when x = 2, y = 20; when x = 3, y = 40; when x = a, y = 104. Given that y varies directly as (x2 + 1), find the constant of variation, k.
  1. A4
  2. B5
  3. C20
  4. D14
25.
Two variables x and y are such that y varies directly as (x2 + 1), and when x = 2, y = 20. Find the equation connecting y and x.
  1. Ay = 4x2
  2. By = 4(x2 + 1)
  3. Cy = 4x2 + 1
  4. Dy = x2 + 4
26.
Two variables x and y are such that y = 4(x2 + 1). Given that y = 104 when x = a, find the values of a.
  1. A5
  2. B25
  3. C±6
  4. D±5
27.
Given that f(x) = 8x, find f-1(x).
  1. A8x
  2. B−8x
  3. Cx8
  4. D18x
28.
Given that f(x) = 8x and g(x) = 3x − 24, find an expression for fg(x).
  1. A6x − 4
  2. B24x − 24
  3. C6x − 2
  4. D3x − 232
29.
Given that f(x) = 8x and g(x) = 3x − 24, find the value of x for which fg(x) = 20.
  1. A83
  2. B24
  3. C4
  4. D3
30.
In the diagram below, a cyclist starts from town W and cycles on a bearing of 216° to town P. She then leaves town P and cycles on a bearing of 296° to Z. Z is west of W. Calculate PŴZ.
Diagram for question 30
  1. A44°
  2. B36°
  3. C64°
  4. D54°
31.
In the diagram below, a cyclist starts from town W and cycles on a bearing of 216° to town P. She then leaves town P and cycles on a bearing of 296° to Z. Z is west of W. Calculate WṖZ.
Diagram for question 31
  1. A90°
  2. B116°
  3. C100°
  4. D80°
32.
The diagram shows a regular hexagonal prism. State the number of planes of symmetry.
Diagram for question 32
  1. A6
  2. B7
  3. C8
  4. D12
33.
A piece of timber measures 5.25 cm long. Calculate the relative error of the measurement.
  1. A1105
  2. B1525
  3. C11050
  4. D12100
34.
Integrate 3x4 − 4x-3 with respect to x.
  1. A(35)x5 + 2x2 + c
  2. B(35)x5 − 2x2 + c
  3. C(35)x2 − 2x2 + c
  4. D12x3 + 12x-4 + c
35.
Solve the equation (2x − 1)2 = 25.
  1. Ax = 3 only
  2. Bx = −2 or x = 3
  3. Cx = −3 or x = 2
  4. Dx = 13 or x = −12
36.
Find the equation of a line which is parallel to 2x + y = 3 passing through (−2, 3).
  1. Ay = −2x + 1
  2. By = 2x + 7
  3. Cy = −2x − 1
  4. Dy = −½x + 2
37.
In triangle XYZ, the side opposite angle X is x = YZ, the side opposite Y is y = XZ, and the side opposite Z is z = XY. A flow chart computes cos X: Begin → [input] → [process] → Output cos X → End. Which statements correctly complete the input and process boxes?
Diagram for question 37
  1. AEnter x, y, z; cos X = y2 + z2 + x22yz
  2. BEnter x, y, z; cos X = y2 + z2 − x22yz
  3. CEnter x, y, z; cos X = x2 + z2 − y22xz
  4. DEnter y, z; cos X = y2 + z2 − x2yz
38.
In the diagram, R is the unshaded region bounded by three lines: the line through (0, 0) and (5, 5); the line through (0, 2) and (8, 0); and the line through (5, 5) and (8, 0). Write three inequalities which describe the region R.
Diagram for question 38
  1. Ay ≤ x, y ≥ −¼x + 2, y ≤ −⁵⁄₃x + ⁴⁰⁄₃
  2. By ≥ x, y ≤ −¼x + 2, y ≥ −⁵⁄₃x + ⁴⁰⁄₃
  3. Cy ≤ x, y ≥ −¼x + 2, y ≤ −⅓x + 8
  4. Dy ≤ x, y ≤ −¼x + 2, y ≤ −⁵⁄₃x + ⁴⁰⁄₃
39.
Given a right-angled triangle XYZ where ∠Z is 90° and sin X = 45, find the value of cos X.
  1. A45
  2. B34
  3. C35
  4. D43
40.
The diagram below shows a sketch of a graph which meets the x-axis at −4 and 2. Find the equation of the graph.
Diagram for question 40
  1. Ay = x2 + 2x − 8
  2. By = x2 − 2x − 8
  3. Cy = −x2 − 2x + 8
  4. Dy = x2 + 2x + 8
41.
The diagram shows a sketch of the parabola y = x2 + 2x − 8, which meets the x-axis at −4 and 2. Find the coordinates of the turning point.
Diagram for question 41
  1. A(−1, −5)
  2. B(1, −9)
  3. C(−1, −9)
  4. D(−2, −8)
42.
The speed-time graph shows a particle which started from rest and accelerated uniformly for 10 seconds to a speed V. It then travelled at constant speed for 20 seconds and then decelerated to rest at time t. Find the speed V the particle reached if its acceleration was 2 m/s2 in the first 10 seconds.
Diagram for question 42
  1. A5 m/s
  2. B20 m/s
  3. C2 m/s
  4. D40 m/s
43.
The speed-time graph shows a particle which accelerated uniformly from rest to 20 m/s in 10 seconds, travelled at 20 m/s for 20 seconds, then decelerated to rest at time t. Given that the total distance covered was 750 m, find the value of t.
Diagram for question 43
  1. A50
  2. B65
  3. C45
  4. D55
44.
The speed-time graph shows a particle which accelerated uniformly from rest to 20 m/s in 10 seconds, travelled at 20 m/s for 20 seconds, then decelerated uniformly to rest at t = 55 seconds. What was the speed at 40 seconds?
Diagram for question 44
  1. A8 m/s
  2. B12 m/s
  3. C16 m/s
  4. D10 m/s