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Examinations Council of Zambia — past paper

ECZ 2016 O-Level Paper 1 — Mathematics

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

G12 Titan
1.
Given that E={a,b,c,d,e,f,g,h},A={a,b,c,d} and B={b,c,d,e,f}, list (A∪B)'.
  1. A{g,h}
  2. B{a,b,c,d,e,f}
  3. C{e,f,g,h}
  4. D{a,g,h}
2.
Use set notation to describe the shaded region in the diagram below.
Diagram for question 2
  1. AP∩Q∩R
  2. B(P∪R)∩Q
  3. C(P∩R)∪Q
  4. D(P∪Q)∩R
3.
Evaluate 823.
  1. A4
  2. B2
  3. C16⁄3
  4. D64
4.
Simplify 3(a + 5) − a(a − 2).
  1. Aa2 + 5a + 15
  2. B15 + 5a − a2
  3. C15 + a − a2
  4. D15 + 3a − a2
5.
The diagram below shows a right pyramid with a square base ABCD and apex P. How many planes of symmetry has the pyramid?
Diagram for question 5
  1. A2
  2. B1
  3. C4
  4. D8
6.
Express −12−35−24231 as a single matrix.
  1. A6−3
  2. B−6−3
  3. C−145
  4. D−63
7.
On the diagram in the answer space, OP = p and OQ = q. Given that OR = p + q, express OR as a column vector.
Diagram for question 7
  1. A(11, 3)
  2. B(11, 7)
  3. C(−7, 7)
  4. D(7, −7)
8.
The first and second terms of an arithmetic progression are 100 and 95, respectively. Find the tenth term.
  1. A50
  2. B55
  3. C45
  4. D145
9.
The first and second terms of an arithmetic progression are 100 and 95, respectively. Find the sum of the first ten terms. [Sn = n2(2a + (n − 1)d)]
  1. A700
  2. B550
  3. C775
  4. D1000
10.
There are 45 green and red marbles in a bag. Given that the probability of choosing a green marble is 2⁄5, calculate the number of green marbles in the bag.
  1. A27
  2. B9
  3. C90
  4. D18
11.
The base areas of two containers that are geometrically similar are 80 cm2 and 180 cm2, respectively. If the capacity of the larger container is 54 litres, calculate the capacity of the smaller one.
  1. A16 litres
  2. B24 litres
  3. C36 litres
  4. D12 litres
12.
Mogadishu and Kinshasa are on longitudes 45°E and 15°E respectively. If it is 11 30 hours in Mogadishu, what time is it in Kinshasa?
  1. A13 30 hours
  2. B09 30 hours
  3. C10 30 hours
  4. D07 30 hours
13.
What is the shortest distance over the Earth’s surface between A(32°N, 8°W) and B(40°N, 172°E)? [R = 6370 km, π = 22⁄7]
  1. A6 006 km
  2. B16 016 km
  3. C12 012 km
  4. D5 720 km
14.
The length of a wire is 5.2 cm, correct to 1 decimal place. What is its maximum possible length?
  1. A5.3 cm
  2. B5.15 cm
  3. C5.2 cm
  4. D5.25 cm
15.
The dividend due on 1 000 shares at the end of a financial year is K2 250.00. If the annual dividend rate is 3% of the share value, calculate the value of each share.
  1. AK75.00
  2. BK7.50
  3. CK67.50
  4. DK750.00
16.
Find the gradient of the straight line whose equation is 3y + x = 5.
  1. A3
  2. B−1⁄3
  3. C−3
  4. D1⁄3
17.
Triangle P has vertices (−4, 0), (−4, 1) and (−2, 1). It is mapped onto triangle Q by a reflection in the line y = −x. State the coordinates of triangle Q.
Diagram for question 17
  1. A(4, 0), (4, 1), (2, 1)
  2. B(0, −4), (1, −4), (1, −2)
  3. C(0, 4), (−1, 4), (−1, 2)
  4. D(0, 4), (1, 4), (1, 2)
18.
Factorise completely km − 6ln + 3kn − 2lm.
  1. A(k + 2l)(m − 3n)
  2. B(k − 2l)(m − 3n)
  3. C(k + 2l)(m + 3n)
  4. D(k − 2l)(m + 3n)
19.
In the diagram below, MN is an arc of a circle whose centre is O and radius 21 cm. Given that ∠MON = 120°, calculate the area of the sector MON. [Take π to be 22⁄7]
Diagram for question 19
  1. A462 cm2
  2. B231 cm2
  3. C1386 cm2
  4. D154 cm2
20.
Find the transpose of the matrix B = 4−125.
  1. A4−125
  2. B42−15
  3. C5−124
  4. D−1452
21.
Find the percentage error of the mass of a bag of sugar that weighs 10.00 kg, correct to 2 decimal places.
  1. A0.5%
  2. B0.005%
  3. C0.05%
  4. D0.1%
22.
Find the equation of the straight line passing through (−4, 4) and is perpendicular to the straight line whose equation is y + x⁄7 = 1.
  1. Ay = −1⁄7 x + 32
  2. By = 7x − 24
  3. Cy = −7x + 32
  4. Dy = 7x + 32
23.
The diagram below shows an equilateral triangle ABC. A is due North of B and CN is parallel to BA. Find BĈN.
Diagram for question 23
  1. A120°
  2. B60°
  3. C30°
  4. D150°
24.
For the same equilateral triangle (A due North of B), find the bearing of C from A.
Diagram for question 24
  1. A060°
  2. B120°
  3. C240°
  4. D300°
25.
Given that f(x) = (5x + 4)⁄5, find f⁻¹(x).
  1. A5⁄(5x + 4)
  2. B(5x + 4)⁄5
  3. C(5x − 4)⁄5
  4. D(x − 4)⁄5
26.
Using f(x) = (5x + 4)⁄5, find f⁻¹(−2).
  1. A−6⁄5
  2. B14⁄5
  3. C−2
  4. D−14⁄5
27.
Given f(x) = (5x + 4)⁄5 and g(x) = x − 1, find fg(x) in its simplest form.
  1. A(5x − 1)⁄5
  2. B(5x + 3)⁄5
  3. C(5x − 1)
  4. D(x + 3)⁄5
28.
Evaluate 50 + 51.
  1. A10
  2. B6
  3. C1
  4. D5
29.
In the answer space below is an incomplete simple program pseudocode for calculating and outputting the volume of a cylinder V, given the base radius r and the height h. Which statements complete the blank spaces?
Diagram for question 29
  1. AEnter V ; V = πrh
  2. BEnter r, h ; V = 2πrh
  3. CEnter r, h ; V = πr2h
  4. DEnter r, h, V ; V = πr2
30.
Find ∫(6x2 − 5) dx.
  1. A12x + c
  2. B2x3 − 5
  3. C6x3 − 5x + c
  4. D2x3 − 5x + c
31.
The diagram below shows triangle PQR in which PQ = 12 cm, QR = 10 cm and ∠PQR = 150°. Calculate the area of triangle PQR.
Diagram for question 31
  1. A30 cm2
  2. B60 cm2
  3. C120 cm2
  4. D52 cm2
32.
In the diagram below, PR is a diameter of a circle with centre O. Q and S are points on the circumference. The tangent to the circle at the point P meets QS produced at T, ∠PQS = 26° and ∠QPR = 42°. Calculate PR̂S.
Diagram for question 32
  1. A64°
  2. B26°
  3. C48°
  4. D42°
33.
For the same circle (PR a diameter, ∠QPR = 42°), calculate PRQ.
Diagram for question 33
  1. A42°
  2. B58°
  3. C48°
  4. D90°
34.
For the same circle (tangent at P meets QS produced at T, ∠PQS = 26°, ∠QPR = 42°), calculate PTQ.
Diagram for question 34
  1. A32°
  2. B26°
  3. C42°
  4. D22°
35.
It is given that w varies directly as the square of x and inversely as y. Write an expression for w, in terms of x, y and a constant k.
  1. Aw = kx²⁄y
  2. Bw = ky⁄x²
  3. Cw = kx2y
  4. Dw = kxy2
36.
It is given that w = kx²⁄y. If x = −6, y = 12 and w = 15, find k.
  1. A3
  2. B5
  3. C45
  4. D1⁄5
37.
Using w = 5x²⁄y, find the value of y when x = 8 and w = 20.
  1. A160
  2. B4
  3. C16
  4. D32
38.
On the XOY plane below, region R is unshaded. Write the four inequalities that define the region R.
Diagram for question 38
  1. Ax ≤ 2, y ≤ 3, y ≥ 7, x + y > 12
  2. Bx ≥ 2, y ≥ 3, y ≤ 7, x + y > 12
  3. Cx ≥ 3, y ≥ 2, y ≤ 7, x + y < 12
  4. Dx ≥ 2, y ≥ 3, y ≤ 7, x + y < 12
39.
Solve the equation x2 = 3x.
  1. Ax = 0 or x = 3
  2. Bx = 3 only
  3. Cx = −3 or x = 3
  4. Dx = 0 or x = −3
40.
The diagram below shows a sketch of the graph of y = 3 − 2x − x2, passing through P, Q and R. Find the equation of the axis of symmetry of the graph.
Diagram for question 40
  1. Ax = 1
  2. Bx = −1
  3. Cx = 3
  4. Dx = −2
41.
For the graph y = 3 − 2x − x2, find the coordinates of the turning point.
Diagram for question 41
  1. A(1, 0)
  2. B(−1, 6)
  3. C(−1, 4)
  4. D(−1, −4)
42.
The diagram below is the speed-time graph of a particle. The particle accelerates uniformly from a speed of v m/s to a speed of 5v m/s in 20 seconds. Find an expression in terms of v, for acceleration.
Diagram for question 42
  1. A4v m/s2
  2. Bv⁄4 m/s²
  3. C5v m/s2
  4. Dv⁄5 m/s²
43.
The diagram below is the speed-time graph of a particle, which accelerates uniformly from a speed of v m/s to a speed of 5v m/s in 20 seconds. The distance travelled by the object from 0 seconds to 20 seconds is 80m. Find the value of v.
Diagram for question 43
  1. A4⁄3 m/s
  2. B4 m/s
  3. C8⁄3 m/s
  4. D2⁄3 m/s
44.
For the same motion (start speed v = 4⁄3 m/s, acceleration v⁄5), find the speed at t = 15 seconds.
Diagram for question 44
  1. A4 m/s
  2. B16⁄3 m/s
  3. C20⁄3 m/s
  4. D3 m/s