Second Term Examination Mathematics SS 2 Second Term Lesson Notes

SECOND TERM EXAMINATION

Subject: Mathematics
Class: SS2
Time: 2 Hours

PART A: Objective Questions (Answer all questions)

1. Calculate the standard deviation of the following distribution: 2,3,4,4,5,6
   (a) 1.29 (b) 1.35 (c) 2.04 (d) 2.50

2. Which of the following is not a measure of dispersion?
   (a) Mode (b) Range (c) Standard deviation (d) Mean deviation

3. A plane flies 90 km on a bearing of 030°, then flies 150 km due east. How far east of the starting point is the plane?
   (a) 120 km (b) 165 km (c) 195 km (d) 240 km

4. A town P is 150 km from town Q in the direction 50°. What is the bearing of Q from P?
   (a) 50° (b) 130° (c) 230° (d) 270°

5. The bearing of two points Q and R from a point P are 30° and 120° respectively. If |PQ| = 12 m and |PR| = 5 m, find the distance |QR|
   (a) 13 m (b) 11 m (c) 9 m (d) 7 m

6. Which of the following is equivalent to S 50° W?
   (a) 40° (b) 130° (c) 220° (d) 230°

7. A group of numbers are written in ascending order as (X-2), 8, (5+X), 12, (X+14). Find the range of the numbers.
   (a) 12 (b) 14 (c) 16 (d) 20

8. A fair die is rolled once. What is the probability of obtaining 4 or 6?
   (a) 1/12 (b) 1/6 (c) 1/3 (d) 1/2

9. What is the probability of having an odd number in a single toss of a fair die?
   (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3

10. A number is chosen at random from the set [2,4,6,……18,20]. Find the probability that it is either a factor of 18 or a multiple of 5.
    (a) 1/2 (b) 3/5 (c) 2/6 (d) 1/3

11. What is the probability of throwing a number greater than 2 with a single die?
    (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3

12. The mean heights of three groups of students consisting of 20, 16, and 14 students are 1.67 m, 1.50 m, and 1.40 m respectively. Find the mean height of all the students.
    (a) 1.52 m (b) 1.53 m (c) 1.54 m (d) 1.55 m

13. Solve the inequality -2(13+X) ≥ 9+5X.
    (a) X ≥ -5 (b) X ≤ -5 (c) X ≥ 5 (d) X ≤ 5

14. Solve 3(1 – X) ≤ 3.
    (a) X ≤ -1 (b) X ≥ -2 (c) X ≤ 1 (d) X ≥ -3

15. Three balls are drawn one after the other with replacement from a bag containing 5 red, 9 white, and 4 blue balls. What is the probability of drawing one red, one white, and one blue?
    (a) 5/102 (b) 5/136 (c) 5/162 (d) 5/200

16. A tree is 8 km due south of a building. Kofi is standing 8 km west of the tree. How far is Kofi from the building?
    (a) 4 km (b) 8 km (c) 8√2 km (d) 16 km

17. Find the bearing of Kofi from the building.
    (a) 315° (b) 270° (c) 225° (d) 135°

18. Esther was facing S 20° W and turned 90° clockwise. What direction is she facing now?
    (a) N 70° W (b) S 70° E (c) N 20° W (d) S 20° E

19. Calculate the variance of the numbers 5,11,13,14,17.
    (a) 5.3 (b) 7.3 (c) 8.0 (d) 10.3

20. Find the mean deviation of 2,3,5,6.
    (a) 1.0 (b) 1.2 (c) 1.4 (d) 1.5

21. What is the mean of 1,3,4,8,8,4,7?
    (a) 4 (b) 5 (c) 6 (d) 7

22. The probabilities that John and James pass an examination are 3/4 and 3/5 respectively. Find the probability of both failing the examination.
    (a) 1/10 (b) 3/10 (c) 9/20 (d) 11/20

23. A point X is on the bearing 342° from a point Y. What is the bearing of Y from X?
    (a) 342° (b) 252° (c) 198° (d) 162°

24. There are M boys and 12 girls in a class. What is the probability of selecting a girl at random?
    (a) M/12 (b) 12/M (c) 12/(M+12) (d) 12/(M+12)

25. If 2X + 5 ≤ 1 and X – 4 < 1, what is the range of values of X?
    (a) X ≤ -2 (b) X ≤ -1 (c) X ≥ 3 (d) X ≤ 3

PART B: Theory Questions (Answer question 1 and any other 3 questions)

1. The table below shows the hourly wages of 50 workers in a factory.

   82	132	199	248	300	89	145	200	249	324
   94	152	206	255	334	96	156	214	263	348
   98	158	220	265	369	108	163	221	270	381
   114	176	232	270	401	120	178	235	280	440
   125	185	206	288	477	128	189	247	294	485

   (a) Construct a frequency distribution table using class intervals #0 – #49, #50 – #99, … #450 – #499.
   (b) Calculate:
   i. Mean
   ii. Mean deviation
   iii. Variance
   iv. Standard deviation

2. An airplane flies from A to B on a bearing 350° for 1.25 hours at 600 km/hr, then from B to C on a bearing 130° for 1.5 hours at 400 km/hr. Calculate:
   (a) Distance from C to A
   (b) Bearing of C from A

3. Solve 4y – 7 ≤ 3y and 3y ≤ 5y + 8. Express the solution in the form a ≤ y ≤ b.

4. Find the inverse and determinant of the matrix:

   [3124]\begin{bmatrix} 3 & 1 \\ 2 & 4 \end{bmatrix}[32​14​]