Third Term Examination
Class : SSS 2
Subject : Mathematics
Duration : 2 Hours.
Section A : Objective Questions
Instruction : Attempt all the questions. Solve and choose from the alternatives lettered a – d.
1. The probability that a student will pass his exam is 1/3. What is the probability that he will fail his exam? (a) 1/2 (b) 1 (c) 2/3 (d) 3/2
2. A fair dice is tossed once, what is the probability of throwing a even number? (a) 5/6 (b) 1/5 (c) 1/2 (d) 1/6
3. A bearing of 320° expressed as a compass bearing is ________. (a) N50° W (b) N40°W (c) N50°E (d) N40°E
4. The average age of 25 girls is 10 years, if one girl, aged 12years and 4months joins the group, find correct to one decimal place, the new average age of the group. (a) 10.1 years (b) 9.3 years (c) 8.7 years (d) 8.3 years
5. In what quadrant is cotangent and Cosec of an angle negative? (a) first (b) second (c) third (d) fourth
6. The ages of Tunde and Ola are in the ratio 1 : 2. If the ratio of Ola’s age to Musa is 4 : 5, what is the ratio of Tunde’s age to Musa age? (a) 1 : 4 (b) 1 : 5 (c) 2 : 5 (d) 5 : 2
7. Given that 150° is an angle in the second quadrant; then cos will be ______. (a) positive (b) negative (c) zero (d) can not be determined
8. A bag contain 14 identical balls. 4 of the balls are red, 2 white, 3 green and 5 blue. A ball is chosen at random. What is the probability that is not red? (a) 5/7 (b) 3/7 (c) 5/14 (d) 3/14
9. Convert the bearing 153° at a point A to a bearing with specified direction. (a) N63°W (b) S63°W (c) S27°W (d) S27°E
10. Which of the following is not a measure of dispersion? (a) mode (b) mean deviation (c) range (d) Standard deviation
11. The bearing of X from Y is 104°, what is the bearing of Y from X? (a) 014° (b) 076° (c) 256° (d) 284°
12. Express the true bearing of 210°as a compass bearing. (a) S30°W (b) S30°E (c) S60°E (d) S60°W
The table shows the age of students in a club. Use it to answer 13 and 14.
Age (years): 13 14 15 16 17
Frequency : 10 24 8 5 3
13. How many students are in the club? (a) 50 (b) 55 (c) 60 (d) 65
14. Find the median age. (a) 13 (b) 14 (c) 15 (d) 16
15. Point X and Y are 20km north and 9km of point O respectively, calculate, correct to the nearest degree, the bearing of Y from X. (a) 114° (b) 154° (c) 204° (d) 336°
16. Find the mean of the whole numbers between 5 and 20 inclusive which are divisible by 2 or 3. (a) 13.2 (b) 12.8 (c) 12.0 (d) 11.2
17. Find the sum of the median and the range of these numbers : 6, 2, 4, 3, 8, 4, 2. (a) 12 (b) 10 (c) 8 (d) 6
18. Find the mean deviation of 1, 2, 3, 4 and 5. (a) 1.2 (b) 1.5 (c) 2.0 (d) 3.0
19. The tangent of which angle gives the same result as Tan (- 238°) (a) 58° (b) – 122° (c) 238° (d) 302°
20. The line drawn from the center of a circle to bisect it is called __________. (a) arc (b) radius (c) diameter (d) chord
21. A chord of a radius 26cm is 10cm from the center of the circle. Calculate the length of the chord. (a) 16cm (b) 32cm (c) 48cm (d) 55.76cm
22. Which of these angles has it cosecant and cotangent function to be negative? (a) 67° (b) 178.65° (c) 191.21° (d) 354.34°
23. Two bottles are drawn with replacement from a crate containing 8 coke, 12 fanta and 4 sprite bottles. What is the probability that the first is coke and the second is not coke? (a) 1/12 (b) 1/6 (c) 2/9 (d) 2/8
24. The mean of 4, 8, 6, p, and q is 6. Find the mean of p + 1 and q – 3. (a) 5 (b) 6 (c) 7.(d) 8
25. Calculate the variance of 2, 3, 3, 4, 5, 5, 5, 7, 7 and 9. (a) 2.2 (b) 3.4 (c) 4.0 (d) 4.2
26. Obtain the range of the following numbers: 1.57, 2.66, 12.08, – 3.45, 10.26 and – 0.72. (a) 8.63 (b) 15.53 (c) – 15.53 (d) – 8.63
27. A letter is chosen at random from the word “WRESTLEMANIA”. What is the word that it is in the word “MANTLE” or in the word “WASTE”? (a) 4/5 (b) 3/5 (c) 2/5 (d) 1/5
28. A fair coin is tossed four times, what is the probability of obtaining at least one head? (a) 1/2 (b) 1/4 (c) 13/16 (d) 15/16
Use the diagram below to answer questions 29 to 33.
29. The line OD is a ___________ to the circle. (a) secant (b) tangent (c) radius (d) chord
30. The point D on the circle is called ______. (a) the mid point (b) center (c) perfection (d) point of tangency
31. The angle formed by line OD and DM is _________. (a) an obtuse angle (b) an acute angle (c) zero degrees (d) 90 degrees
32. The line AB is a ___________. (a) tangent (b) chord (c) secant (d) diameter
33. Calculate the length of a chord which is at the distance 12cm from the centre of a circle. (a) 5cm (b) 6cm (c) 12cm (d) – 3cm
34. A number is selected at random from the set y = (18, 19, 20,…, 28, 29). Find the probability that the number is prime. (a) 1/4 (b) 3/11 (c) 1/2 (d) 3/4
35. Find the upper quartile of 2, 4, 5, 7, 8, 9, 10. (a) 10 (b) 9 (c) 8 (d) 7
Section B: Theory
Instruction : Answer all questions from this section.
1. An aeroplane leaves an airport A and flies on a bearing 035° for 3/2 Hours at 600km/h to an airport B. It then flies on a bearing 130° for 3/2 Hours at 400km/h to an airport C. Calculate the :
(a) distance from C to A.
(b) Bearing of C from A.
2. Draw a histogram and a frequency polygon of the frequency distribution shown below:
Find : (i.) the modal class (ii.) the mean (iii.) the median
3. If x is an acute angle, and tan x = 3/4, evaluate (cos x – sin x) / (cos x + sin x)
4. Two fair dice are thrown together once. Find the probability that the sum of the outcome is :
i.) a prime number ii.) a total of 7
iii.) at most 5
Section C
Instruction: Answer any three questions from this section.
5. A box contains 15 balls, six of which are red, five are black and four are white. Three balls are drawn one after the other without replacement. Find the probability of choosing all three balls of different colours
6. The third term of a geometric progression (G. P) is 360 and sixth term is 1215. Find the: (a) Common Ratio (b) First term (c) Sum of the first four terms.
7. The frequency distribution of weight of 100 participants in a high jump competition is shown below
(a) Construct the commulative frequency table.
(b) Draw the commulative frequency curve
(c) From the curve, estimate the : (i.) median; (ii.) Semi inter-quartile range; (iii.) Probability that a particular chosen at random weight at least 60kg.
8. When twice a certain number y is subtracted from, the result is at least 16.
(i.) Write an inequality to represent this statement.
(ii.) Solve the inequality
(iii.) Given that y is an integer, what is the greatest possible value of y which satisfies the inequality.
9. A point X is on bearing of 065° and at distance 57m from a point Y. Another point Z is 84m from X and on a bearing of 145° from Y. Find:
(a) The bearing of Z from X, correct to the nearest degree.
(b) The distance of Z from Y, correct to three significant figures.
10. The cost of 12kg of apples and 24kg of oranges is #43, 200. The cost of 24kg of apples and 12kg of oranges cost #36, 000. Find the cost of
(i.) Apples per kg; (ii.) Oranges per kg
(iii.) 3kg of apples and 2kg of oranges.