# Exam Questions – Second Term Examination Mathematics for SS 1

### SECTION A OBJECTIVES

Instruction: Choose the most correct from the options A – E.

1. If 32x = 27, find x.

(a)  1

(b) 1.5

(c) 4.5

(d) 18

(e) 40.5

2. If 3x = 9y, find the relationship between x and y.

(a) y = 2x

(b) y = 3x

(c) x = y²

(d) x = 2y

(e) x2 = y²

3. Simplify 161/4 x 27-1/3

(a) 6

(b) 2/3

(c) 12

(d) 4/3

(e) 32

4. If 4x = 8x – 1, find x

(a) 8

(b) 2

(c) 1

(d) 0

(e) 3

5. Find the value of n if 31 – n = 27n + 1

(a) – 2

(b) 1/2

(c) 2

(d) – 1/2

(e) 3

6. Simplify 361/2 x 641/3 x 50.

(a) 0

(b) ¾

(c) 2/3

(d) 11/2

(e) 71/2

7. Simplify (271/3)2

(a) 41/2

(b) 6

(c) 9

(d) 18

(e) 81

8. If 3y = 243, find the value of y

(a) 2

(b) 3

(c) 4

(d) 5

(e) 6

9. Simplify log2(1/32)

(a) 5

(b) 1/5

(c) -5

(d) 1

(e) 0

10. Simplify log 4 + log 25, both in base 10.

(a) 1000

(b) 100

(c) 10

(d) 1

(e) 0

11. Given that a = 2, evaluate log 8 + log 16, both base a.

(a) – 4

(b) 7

(c) 24

(d) ½

(e) 2

12. Evaluate log1/39

(a) 1

(b) 2

(c) -2

(d) 3

(e) -1

13. Evaluate log1/264

(a) 32

(b) 3

(c) 6

(d) -6

(e) -3

14. Simplify 4log 2 – 2log 4, both in base 10.

(a) 0

(b) 1

(c) 2log 2

(d) 42

(e) log2

15. If log a = 4, find a. In base 10.

(a) 0.4

(b) 40

(c) 400

(d) 1000

(e) 10000

16. Simplify log 296 – 2 log 26

(a) 2 – log 23

(b) 3 – log 23

(c) log 23 – 3

(d) log 23 – 2

(e) log 32 – 3

Use the information below to answer question 17 and 18.

17. P = {1, 2, 3, 9, ½} Q = {1, 2½, 3, 7} R = {5, 4, 2½}. Find P u Q u R.

(a) {1, 9}

(b) { ½, 1, 2, 2½, 3, 4, 5, 7, 9}

(c) {5, 4, 2½}

(d) { }

(e) {1, 2, 3, 4, 5, 7}

18. Find P n Q n R

(a) {2½}

(b) { }

(c) {1, 3, 7}

(d) {4}

(e) {5, 7, 9}

19. If P = {3, 5, 6}, Q = {4, 5, 6}, find P n Q.

(a) {3, 4}

(b) {4, 5}

(c) {5, 6}

(d) {4, 6}

(e) {3, 6}

20. If P = {3, 7, 11, 13} and Q = {2, 4, 8, 16}, which of the following is correct?

(a)  (P n Q) = {2, 3, 4, 12}

(b) n (P u Q) = 4

(c) P u Q = { }

(d) P n Q = { }

(e) n (P n Q) = 8

21. If the time is 9:00 am, what time is 5 hours time?

(a) 2 A.M.

(b) 2 P.M.

(c) 4 P.M.

(d) 4 P.M.

(e) 5 P.M.

22. A lecture ended at 6 P.M after 8 hours, what time did it start?

(a) 2 A.M.

(b) 2 A.M.

(c) 10 A.M.

(d) 10 P.M.

(e) 4 P.M.

23. In what modulus is it true that 9 + 8 = 5.

(a) Mod 10

(b) Mod 11

(c) Mod 12

(d) Mod 13

(e) Mod 14

24. Express the product of 0.0043 and 2000 in standard form.

(a) 8.3 x 10¯³

(b) 8.6 x 10¯²

(c) 8.6 x 10¹

(d) 8.6 x 10¯³

(e) 8.3 x 10¯³

25. Using log table, evaluate 5.219 x 3.867 x 15.9, leaving your answer in 1 d.p.

(a) 112.7

(b) 122.7

(c) 133.7

(d) 422.7

(e) 522.7

### THEORY

Answer all Questions in this section.

QUESTIONS 1

A. Factorize the following:

I. m² + 4m – 21

II. 2z² – 5z + 3

III. 2g² – 5g + 2

B. Solve the following equations:

I. h2 – 15h + 54 = 0

II. 2m2 – 5m + 3 = 0

III. 2m2 – 5m = 0

C. Attempt the following:

i. Find x: 2x + 4 = 0 (mod 5)

ii. Simplify: 15 – 6 (mod 4)

iii. Evaluate: 7 + 4 (mod 5)

QUESTION 2

A. Evaluate 6.3 x 105/8.1 x 103 to 3.s.f

B. Express 62/3 as a decimal correct to 3.s.f

C. Convert 3.1415926 to 5.d.p

D. Write down the number 0.0052048 correct to 3.s.f

E. Simplify and leave your answer in standard form: 0.6×32 x 0.04

QUESTION 3

A. Make x the subject of formular:

I. (x + 5)/y = 3

II. v = (1/3)πx²h

III. t = (3p/x) + s

IV. x² – a² = b

B. Evaluate (ax² + bx + c)/(mx + c), given that a = 2, x = -3, b = -2, c = 4 and m = – 1

C. Simplify the value of 2π√(l/g) , where π = 22/7, l = 98 and g = 32

QUESTION 4

Using mathematical tables, evaluate:

I. (7.143 x 821.5)/0.0014

II. (15.05 x √0.0095)/(6.95×10²)

III. √2.067/(0.0348 x 0.538)