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Examinations Council of Zambia — past paper

ECZ 2015 O-Level Paper 1 — Mathematics

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

G12 Titan
1.
Find the value of n, if 4n = 22 × 42.
  1. A6
  2. B4
  3. C3
  4. D2
2.
A furniture shop conducted a sale. In this sale, prices were reduced by 15%. Find the price before reduction of a table that was reduced by K120.00.
  1. AK800.00
  2. BK680.00
  3. CK920.00
  4. DK141.18
3.
Describe the region shaded in the Venn diagram using set notation.
Diagram for question 3
  1. A(A ∩ C ∩ B') ∪ (B ∩ C ∩ A')
  2. BC ∩ (A ∪ B)
  3. CA ∩ B ∩ C
  4. DC' ∩ (A ∪ B)
4.
The position vectors of the points X and Y are 3-4 and -8-1 respectively. Express XY (the vector from X to Y) as a column vector.
  1. A-113
  2. B11-3
  3. C-5-5
  4. D-11-3
5.
A fair six sided die numbered 1, 2, 3, 4, 5 and 6 is rolled. Find the probability of obtaining a prime number.
  1. A13
  2. B23
  3. C16
  4. D12
6.
If E = {first eight natural numbers} and A = {1, 4, 7}, find the set A'.
  1. A{2, 3, 5, 6, 8}
  2. B{1, 4, 7}
  3. C{2, 3, 5, 6}
  4. D{2, 4, 6, 8}
7.
Factorise 2x2 − x − 15.
  1. A(2x − 5)(x + 3)
  2. B(2x + 5)(x − 3)
  3. C(2x + 3)(x − 5)
  4. D(2x − 3)(x + 5)
8.
The diagram shows a right angled triangle in which angle ACB = 90°, AB = 15 cm and AC = 12 cm. Find the length of BC.
Diagram for question 8
  1. A9 cm
  2. B19.2 cm
  3. C3 cm
  4. D81 cm
9.
Simplify 7m − 2(3n − m) − 9n.
  1. A5m − 15n
  2. B9m − 3n
  3. C9m − 15n
  4. D5m − 3n
10.
Given that f(x) = 2x + 78 and g(x) = 3x − 66, find g(6).
  1. A2
  2. B12
  3. C2.375
  4. D1
11.
Given that f(x) = 2x + 78 and g(x) = 3x − 66, find f-1(x).
  1. A8x − 72
  2. B8x + 72
  3. C82x + 7
  4. D2x − 78
12.
Given that f(x) = 2x + 78 and g(x) = 3x − 66, find the value of x if f(x) = g(x).
  1. A7.5
  2. B−7.5
  3. C3.75
  4. D15
13.
Solve the equation 2y2 = 13y.
  1. Ay = 6.5 only
  2. By = 0 or y = 6.5
  3. Cy = 0 or y = −6.5
  4. Dy = ±6.5
14.
A circular lawn has a radius of 14 metres. Mr Kakwempa is contracted to cut the grass and charges K1.50 per every square metre of lawn cut. Find the total amount he was paid for cutting the whole lawn. (Take π to be 227)
  1. AK616.00
  2. BK924.00
  3. CK231.00
  4. DK1 232.00
15.
An aeroplane leaves a town P(33°N, 32°E) and flies due south to a town Q(12°S, 32°E). Given that it flew for 4 hours to cover the distance PQ, find the average speed of the aeroplane in km/h. (Take π to be 227 and R = 6370 km)
  1. A1 251.25 km/h
  2. B5 005 km/h
  3. C583.58 km/h
  4. D2 502.50 km/h
16.
A map of a settlement area is drawn to a scale of 1 : 40 000. If the distance between two shopping malls is 8 cm on the map, calculate the actual distance between the two shopping malls in kilometres.
  1. A3.2 km
  2. B32 km
  3. C0.32 km
  4. D5 km
17.
A map of a settlement area is drawn to a scale of 1 : 40 000. If the actual area of the settlement is 200 square kilometres, calculate the area of the settlement on the map in square centimetres.
  1. A500 cm2
  2. B125 cm2
  3. C1 250 cm2
  4. D12 500 cm2
18.
The diagram shows a regular hexagon inscribed in a circle with centre O, forming six segments between the hexagon and the circle. Which shading of segments gives the resulting shape rotational symmetry of order 3?
Diagram for question 18
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
19.
Given that P = 3-412, express P2 as a single matrix.
  1. A5-2050
  2. B91614
  3. C5-2054
  4. D6-824
20.
Given that y is proportional to x3 and that y = 250 when x = 10, find the value of the constant of variation k.
  1. Ak = 14
  2. Bk = 4
  3. Ck = 25
  4. Dk = 2.5
21.
y is proportional to x3 with constant of variation k = 14, so y = (14)x3. Find y when x = 4.
  1. A16
  2. B1
  3. C100
  4. D64
22.
y is proportional to x3 with constant of variation k = 14, so y = (14)x3. Find x when y = 54.
  1. Ax = 6
  2. Bx = 216
  3. Cx = 13.5
  4. Dx = 3
23.
In the triangle shown, PQ = QR, angle QPR = (3x + 31)° and angle QRP = (91 − 2x)°. Find the size of angle PQR.
Diagram for question 23
  1. A46°
  2. B67°
  3. C12°
  4. D44°
24.
In the diagram, triangle ABC with A(1, 5), B(1, 2) and C(2, 2) is mapped onto triangle A₁B₁C₁ with A₁(5, 4), B₁(5, 1) and C₁(4, 1) by transformation X followed by transformation Y. Describe fully the transformations X and Y.
Diagram for question 24
  1. AX: reflection in the line x = 3; Y: translation 0-1
  2. BX: translation 4-1; Y: no further transformation
  3. CX: reflection in the line y = 3; Y: translation 0-1
  4. DX: rotation of 180° about (3, 3); Y: translation 0-1
25.
Which sketch shows the graph of y + x2 = 0?
  1. AOption A
  2. BOption B
  3. COption C
  4. DOption D
26.
In the diagram, A, B, C and D are points on the circumference of a circle with centre O. ADE and BCE are straight lines, angle CED = 28° and angle BCA = 43°. Find angle CDE.
Diagram for question 26
  1. A62°
  2. B28°
  3. C90°
  4. D47°
27.
In the diagram, A, B, C and D are points on the circumference of a circle with centre O. ADE and BCE are straight lines, angle CED = 28° and angle BCA = 43°. Find angle CDB.
Diagram for question 27
  1. A75°
  2. B43°
  3. C15°
  4. D105°
28.
In the diagram, A, B, C and D are points on the circumference of a circle with centre O. ADE and BCE are straight lines, angle CED = 28° and angle BCA = 43°. Find angle DAC.
Diagram for question 28
  1. A15°
  2. B28°
  3. C43°
  4. D62°
29.
In the XOY plane shown, the unshaded region R is bounded by straight lines AB, AC and OB, where A(−2, 12), B(2, 12) and C(2, 0). Write three inequalities that define the region R.
Diagram for question 29
  1. Ay ≤ 12, y ≥ 6x, y ≥ −3x + 6
  2. By < 12, y > 6x, y > −3x + 6
  3. Cy ≤ 12, y ≤ 6x, y ≥ −3x + 6
  4. Dy ≥ 12, y ≤ 6x, y ≤ −3x + 6
30.
A sum of money is shared among Satala, Sichale and Sichambo in the ratio 7 : 5 : 4 respectively. If Satala got K140 000.00, how much was the total sum of money?
  1. AK320 000.00
  2. BK448 000.00
  3. CK160 000.00
  4. DK280 000.00
31.
A sum of money is shared among Satala, Sichale and Sichambo in the ratio 7 : 5 : 4 respectively. If Satala got K140 000.00, how much did Sichambo get?
  1. AK80 000.00
  2. BK100 000.00
  3. CK140 000.00
  4. DK56 000.00
32.
Two cylindrical mugs are geometrically similar. The smaller mug has diameter 8 cm and holds 125 cm3 of a liquid. If the larger mug holds 1000 cm3 of a liquid, find its diameter.
  1. A16 cm
  2. B64 cm
  3. C24 cm
  4. D12 cm
33.
In the diagram, BCD is a straight line, AB = 12 cm, AC = 13 cm and angle ABC = 90°. Find, as a fraction, cos angle ACD.
Diagram for question 33
  1. A−513
  2. B513
  3. C−1213
  4. D1213
34.
The figure shows the speed–time graphs of cars driven by Sulanji and Lumbwa. Find the acceleration of Sulanji's car during the first 10 seconds.
Diagram for question 34
  1. A3 m/s2
  2. B30 m/s2
  3. C13 m/s2
  4. D300 m/s2
35.
From the speed–time graphs shown, calculate how far Lumbwa's car travelled before coming to rest.
Diagram for question 35
  1. A500 m
  2. B1 000 m
  3. C450 m
  4. D250 m
36.
From the speed–time graphs shown, what is Sulanji's acceleration between the 25th and 30th seconds?
Diagram for question 36
  1. A−6 m/s2
  2. B6 m/s2
  3. C−1.2 m/s2
  4. D−7.5 m/s2