Mathematics First Term Examination for SSS1, 2025

Objective ( Attempt all questions 20 marks)

1. Evaluate (17 + 13) mod 9

2. If A = {2, 4, 6, 8, 10} and B = { 1, 2, 3, 4, 5}, find A n B

3. If n(M) = 18, n(N) = 23 and n (M n N) = 10, find n(M u N)

4. Two sets are disjoint if

5. What is the logarithm of 39.73 ?

6. If 0.000725 = 7.25 × 10^n, find the value of n.

7. Simplify 125^⅓ × 49^ -½ × 5⁰

8. The sum of 11011two , 11111two and 10000two is equal to 10m10n0 two. Find the values of m and n

9. Solve 2^× = 0.25

10. Find the number whose logarithm to base 10 is 2.3482

11. If 300base x = 75ten, find x

12. Simplify (t³)²

13. Simplify 8^(p - 2) × 8^(2 - p)

14. Solve Log(base 8)X = 2

15. If it is December now, what month will it be 19 months from now?

16. Evaluate Log( base 3) 81

17. Given that 3^(t - 2) = 1, find t

18. P= { x: -5 < x < 2}, find the cardinality of P

19. What is the characteristics of logarithm of 4893?

20. Write 38 in its simplest form in mod 7

Subjective ( Attempt all questions)

21. Find the value of 7^( x - 5 ) = Log 10 base 10

22. Simplify (¼) ^ -1½

23. Find the least value of x in 3x = 4 ( mod 5)

24. Change 0.0438 to standard form

25. Given that the universal set £ = { 1, 2, 3, 4}, P = { 2, 3} and Q = { 2, 4}. Find (P n Q)'

26. If n (A) = 6, n(B) = 5 and n(A u B) = 9, find n(A n B)

27. Given that T= { x : - 2 < x < or equal to 9} where x is an integer. List all the elements of T.

28. Draw a Venn diagram and shade the region of AnBnC

29. Evaluate 16 × 3 mod 5

30. If 3^(x + 1) = 9⁴, find x

Theory ( Attempt any four questions)

1). 48 people went to a restaurant, 20 of them ate yam while 18 ate beans. If 11 ate yam and beans, how many ate neither yam nor beans?

2. Express 413 base 7 in base 5

3. Given that 312 base four + 52 base x = 96 base 10, find x

4a. Simplify (- c)² × c⁴ ÷ ( - c)⁵ 4b. If 9 raised to power x = 27 × 3 raised to power (1 - x), find the value of x + 1

5. Given that the universal set is £= { 1, 2,3, 4,5,.....,10}, A= {1,2,5,7} and B = { 1, 3, 6, 7} . Find the following: (a) A' (b) A' n A (c) A u B (d) A n B (e) ( A n B)'

6. Use logarithm table to evaluate (36.84 × 2.95) ÷ 18.52