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Examinations Council of Zambia — past paper

ECZ 2017 O-Level Paper 1 — Mathematics

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

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1.
Shade B'∩(A∩C) 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.
Given that E = {2, 4, 6, 8, 10, 12}, A = {4, 8, 12} and B = {2, 10, 12}, list A' ∩ B.
  1. A{2,10,12}
  2. B{6,12}
  3. C{2,6,10}
  4. D{2,10}
3.
Simplify 3x − (y − 2x) − 3y.
  1. Ax − 4y
  2. Bx − 2y
  3. C5x − 4y
  4. D5x − 2y
4.
Evaluate 8116−14 + 81160.
  1. A2½
  2. B1⅔
  3. C⅔
  4. D1½
5.
The gradient of the line joining the points (−2, k) and (k, −14) is 2. Calculate the value of k.
  1. A6
  2. B−10
  3. C−2
  4. D−6
6.
Factorise completely ax2y − 4ay3.
  1. Aay(x − 4y)(x + y)
  2. Bay(x − 2y)(x + 2y)
  3. Ca(x2y − 4y3)
  4. Day2(x2 − 4y)
7.
The points P and Q have coordinates (2, 4) and (−3, 1) respectively. Express PQ as a column vector.
  1. A(−5, −3)
  2. B(5, 3)
  3. C(−5, 3)
  4. D(−1, 5)
8.
Given that A = 321430 and B = 123321010, find AT.
  1. A321430
  2. B102334
  3. C430321
  4. D342310
9.
Given that A = 321430 and B = 123321010, find AB as a single matrix.
  1. A6710131415
  2. B91111131415
  3. CAB is not possible
  4. D91311141115
10.
For the sequence 25, 22, 19, 16, …, find the formula for the nth term.
  1. A28 − 3n
  2. B25 − 3n
  3. C22 − 3n
  4. D3n − 28
11.
For the sequence 25, 22, 19, 16, …, find the sum of the first 20 terms.
  1. A−140
  2. B500
  3. C−70
  4. D70
12.
Town L is on (0°, 30°W) and town K is on (0°, 60°E) as shown in the diagram. If a radio quiz is scheduled to start at 12 00 hours at L, find the time at which the people at K will be listening to the quiz.
Diagram for question 12
  1. A06 00 hrs
  2. B18 00 hrs
  3. C16 00 hrs
  4. D08 00 hrs
13.
Town L is on (0°, 30°W) and town K is on (0°, 60°E). What is the distance between L and K, in kilometres? [R = 6370 km, π = 227]
Diagram for question 13
  1. A5 005 km
  2. B20 020 km
  3. C6 370 km
  4. D10 010 km
14.
The probability that Chakupaleza will go for remedial lessons on a particular day is 710. What is the probability that she will not go for her remedial lessons on that particular day?
  1. A710
  2. B310
  3. C107
  4. D1
15.
Solve the equation 10ˣ = 0.0001.
  1. A4
  2. B−3
  3. C−4
  4. D−0.4
16.
The diagram below is a sector with centre O and radius 7cm. Angle at O is 270°. Calculate the area of the sector. [π = 227]
Diagram for question 16
  1. A38.5 cm2
  2. B154 cm2
  3. C115.5 cm2
  4. D231 cm2
17.
The functions f and g are defined by f(x) = 2x + 1 and g(x) = 5x − 1. Find g-1(x).
  1. A5x + 1
  2. Bx − 15
  3. Cx + 15
  4. D15x − 1
18.
The functions f and g are defined by f(x) = 2x + 1 and g(x) = 5x − 1. Find fg(x).
  1. A7x
  2. B10x − 1
  3. C10x + 1
  4. D10x − 2
19.
The functions f and g are defined by f(x) = 2x + 1 and g(x) = 5x − 1. Find fg(−3).
  1. A29
  2. B−29
  3. C−31
  4. D31
20.
The kite in the diagram in the answer space has coordinates (0, 0), (2, 1), (5, 0) and (2, −1). Find the coordinates of the image of the kite after a reflection in the line y = x.
Diagram for question 20
  1. A(0, 0), (1, 2), (0, 5), (−1, 2)
  2. B(0, 0), (2, 1), (5, 0), (2, −1)
  3. C(0, 0), (−2, 1), (−5, 0), (−2, −1)
  4. D(0, 0), (−1, −2), (0, −5), (1, −2)
21.
Differentiate y = ⅓x3 − 5x2 − 2x with respect to x.
  1. Ax2 − 10x
  2. Bx3 − 10x − 2
  3. C⅓x2 − 10x − 2
  4. Dx2 − 10x − 2
22.
Two boats X and Y leave port P at the same time. X travels on a bearing of 159° and Y travels on a bearing of 215° as shown in the diagram below. After sometime, X and Y are at points such that angle PYX = 41°. Find the bearing of X from Y.
Diagram for question 22
  1. A041°
  2. B056°
  3. C076°
  4. D118°
23.
Two boats X and Y leave port P at the same time. X travels on a bearing of 159° and Y travels on a bearing of 215° as shown in the diagram below. After sometime, X and Y are at points such that angle PYX = 41°. Find the bearing of P from X.
Diagram for question 23
  1. A339°
  2. B021°
  3. C159°
  4. D201°
24.
Misozi and Filamba estimated the length of a line to be 9cm and 10cm respectively. If the true length of the line was 9.6cm, find Misozi's absolute error.
  1. A0.4 cm
  2. B0.6 cm
  3. C1.6 cm
  4. D0.06 cm
25.
Misozi and Filamba estimated the length of a line to be 9cm and 10cm respectively. If the true length of the line was 9.6cm, find Filamba's percentage error.
  1. A4.00%
  2. B0.42%
  3. C96%
  4. D4.17%
26.
It is given that t = kv2, where k is the constant of variation. v1b5t436a Use the information given in the table to find the value of k.
  1. A4
  2. B2
  3. C16
  4. D¼
27.
It is given that t = kv2, where k is the constant of variation. v1b5t436a Use the information given in the table to find the value of a.
  1. A20
  2. B40
  3. C100
  4. D400
28.
It is given that t = kv2, where k is the constant of variation. v1b5t436a Use the information given in the table to find the values of b.
  1. A3
  2. B±3
  3. C9
  4. D±9
29.
In the diagram below, A, B, C, D, E and F are points on the circumference of a circle. Angle FBD = 70° and angle AEF = 20°. Explain why AD is the diameter.
Diagram for question 29
  1. ABecause AD passes through the centre by inspection
  2. BBecause AD is the longest chord in the diagram
  3. CBecause angle AFD = 70° − 20° = 50°, doubling to 100°
  4. DBecause angle ACD = angle ACF + angle FCD = 20° + 70° = 90°, and a 90° inscribed angle stands on a diameter
30.
In the diagram below, A, B, C, D, E and F are points on the circumference of a circle. Angle FBD = 70° and angle AEF = 20°. Find angle ACF.
Diagram for question 30
  1. A20°
  2. B70°
  3. C40°
  4. D90°
31.
In the diagram below, A, B, C, D, E and F are points on the circumference of a circle. Angle FBD = 70° and angle AEF = 20°. Given that AD is a diameter, find angle DEF.
Diagram for question 31
  1. A70°
  2. B90°
  3. C110°
  4. D160°
32.
It is given that triangle PQR below is right angled at R. QR = 4cm and tan(angle QPR) = 43. Find sin(angle PQR).
Diagram for question 32
  1. A45
  2. B35
  3. C43
  4. D34
33.
The ratio of the surface areas of two cubes is 16:25. What is the volume of the smaller cube, if the volume of the bigger cube is 500cm3?
  1. A320 cm3
  2. B400 cm3
  3. C200 cm3
  4. D256 cm3
34.
A businessman bought 300 company shares at K60.00. The nominal price was K30.00. How much does he pay for the shares?
  1. AK18 000
  2. BK9 000
  3. CK90 000
  4. DK4 500
35.
The equation of a straight line L is given by 2y = 4x − 5. Find the equation of the line passing through (−2, 3) and perpendicular to line L.
  1. Ay = 2x + 7
  2. By = −½x + 1
  3. Cy = −½x + 2
  4. Dy = −½x − 1
36.
The diagram below shows a cone with apex V and radius r. How many planes of symmetry has the cone?
Diagram for question 36
  1. A1
  2. B2
  3. C4
  4. DInfinitely many
37.
The diagram below is an incomplete program flow chart to calculate the curved surface area, S, of a cone with base radius r and slant height l. The chart runs Begin → [input box] → [process box] → Output S → End. Which statements correctly complete the blank symbols?
Diagram for question 37
  1. AInput S; then r = πSl
  2. BInput r, l; then S = πrl
  3. CInput r, l; then S = πr2
  4. DInput r, l, S; then Output r
38.
Write down the four inequalities that define the unshaded region R, on the diagram below.
Diagram for question 38
  1. Ax > 1, x ≤ 5, y ≤ 6, y ≥ x − 2
  2. Bx > −1, x ≤ 4, y ≤ 6, y < x − 2
  3. Cx > −1, x ≤ 4, y ≤ 6, y > x − 2
  4. Dx < −1, x ≥ 4, y ≥ 6, y < x − 2
39.
If y = (1 − 2x)(1 + x) − 2, find the values of x for which y = −2.
  1. Ax = ½ or x = −1
  2. Bx = −½ or x = 1
  3. Cx = 2 or x = −1
  4. Dx = ½ or x = 1
40.
The sketch shown below represents a section of the curve y = x(x − 2). Find the coordinates of the points where the curve cuts the x-axis.
Diagram for question 40
  1. A(0, 0) and (−2, 0)
  2. B(2, 0) and (−2, 0)
  3. C(0, 0) and (0, 2)
  4. D(0, 0) and (2, 0)
41.
The sketch shown below represents a section of the curve y = x(x − 2). What is the minimum value of the function?
Diagram for question 41
  1. A0
  2. B−1
  3. C1
  4. D−2
42.
The diagram below shows a speed-time graph of a car journey. Find the acceleration during the first 5 seconds.
Diagram for question 42
  1. A6 m/s2
  2. B5 m/s2
  3. C30 m/s2
  4. D150 m/s2
43.
The diagram below shows a speed-time graph of a car journey. If the total distance travelled was 825m, find the value of T.
Diagram for question 43
  1. A30 s
  2. B40 s
  3. C45 s
  4. D55 s
44.
The diagram below shows a speed-time graph of a car journey. If the total distance travelled was 825m, find the average speed for the whole journey.
Diagram for question 44
  1. A30 m/s
  2. B15 m/s
  3. C20 m/s
  4. D18⅓ m/s (≈18.3)