1.Â The expression ax^2 + bx takes the value 6 when x = 1 and 10 when x = 2. Find its values when x = 5

A. 10

B. 12

C. 6

D. -10

**ANSWER: A (10)**

2. The indefinite integral of xe^x, for any real constant is

A. C

B. x + e^x + C

C. x^2 + e^x + C

D. e^x(x-1) + C

**ANSWER: D ( e^x(x-1) + C )**

3. A cone has a base radius of 4 cm and a height of 3 cm. The area of its curved surface is

A. 12 pi cm^2

B. 20 pi cm^2

C. 24 pi cm^2

D. 251 pi cm^2

**ANSWER: B (20 pi cm^2)**

4. The sum of the first five terms 0f the series 4+2+1â€¦ is

A. 12

B. -12

C. -6

D. 31/4

**ANSWER: D (31/4)**

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5. If aâˆš5 + b âˆš2 is the square root of 95-30âˆš10, the values of a and b are, respectively

A. 5, 2

B. 2, -5

C. -5, 3

D. 3, -5

**ANSWER: D (3, -5)**

6. Factorise completely 8p + 125py^3

A. (2p+5y^2)(4+25py)

B. (2+5y)(4-10y+25y^2)

C. (2p+5yx-10py+25y^2)

D. (2+5y)(4+10y+25y^2)

**ANSWER: B**Â **(2+5y)(4-10y+25y^2)**

7. Two fair dice are rolled. What is the probability that both show up the same number of point?

A. 1/36

B. 7/36

C. 1/2

D. 1/6

**ANSWER: D (1/6)**

8. A bag contains 5 yellow balls, 6 green balls and 9 black balls. A ball is drawn from the bag. What is the probability that it is black or yellow ball

A. 37/160

B. 133/400

C.Â 7/10

D. 133/800

**ANSWER: C (7/10)**

9. If x = 1 is the root of the equation x^3 -2x^2- 5x +6, find the other roots

A. -3 and 2

B. 2 and 2

C. 3 and -2

D. 1 and 3

**ANSWER: C (3 and -2)**

10. If 27^x = 9^(x-y), then the formula connecting x and y is

A. x+2y = 0

B. x-2y = 0

C. x^2+2y^2 = 0

D. x+2y = 1

**ANSWER: A ( x+2y = 0 )**

11. The expression px^3+2qx^2+24 has x-1 and x+2 as factors. The values of p and q are respectively?

A. -6, -9

B. -2, 1

C. -2, -1

D. 0, 1

**ANSWER: A ( -6, -9 )**

12. The expression a^3+b^3 is equal to

A. (a^2+b)(a-ab+b^2)

B. (a+b)(a^2-ab+b^2)

C. (a-b)(a^2-ab+b)

D. (a-b)(a^2+ab+b^2)

**ANSWER: B (a+b)(a^2-ab+b^2)**

13. The interior angles of a pentagon are: 180 degrees, 118 degrees, 78 degrees, 84 degrees, and x. The value of x is?

A. 75 degrees

B. 80 degrees

C. 120 degrees

D. 134 degrees

**ANSWER: B (80 degrees)**

14. Find the value of k which makes the expression y^2+2(k+1)y+k+3 perfect square

A. -1, 1

B.Â 2, -2

C. 1, -2

D. -1, 2

**ANSWER: C (-2 or 1)**

15. Two brothers, Peter and Paul owned a business in which the ratio of shares is 5:3 respectively. Paul later sold 1/3 of his shares to Peter 15, 000 naira. Find the total value of the business.

A. 12000 naira

B. 1200 naira

C. 120000 naira

D. 1200000000 naira

**ANSWER: C (120,000 naira)**

16 Express, correct to three significant figures, 0.003597.

A.Â 0.359

B. 0.004

C. 0.00360

D. 0.00359

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17. Evaluate:Â (0.064)^-1/3

A. 5/2

B. 2/5

C. -2/5

D. -5/2

18. Solve: Â y+1/2 â€“ 2y-1/3 = 4

A. y = 19

B. y = -19

C. y = -29

D. y = 29

19. Musa borrows #10.00 at 2% per month interest and repays #8.00 after 4 months. However much does he still owe?

A. #10.80

B. #10.67

C. #2.80

C. #2.67

20. If 3 gallons of spirit containing 20% water is added to 5gallons of another spirit containing 15% water, what percentage of the mixture is water?

A. 24/5%

B. 167/8%

C. 181/8%

D. 187/8%

21. What is the product of 27/5 â€“ (3)3 and (1/5)?

A. 5

B. 3

C. 1

D. 1/25

22. Simplify 2log2/5 â€“ log72/125 + log9

A. 1 â€“ 4log 3

B. â€“1 + 2log3

C. â€“1 +5log2

D. 1-2log2

23. A car travels from Calabar to Enugu, a distance of pkm with an average speed of ukm per hour and continues to Benin, a distance of qkm, with an average speed of wkm per hour. Find its average speed from Calabar to Benin.

A. (p+q)/(up+wq)

B.Â u+w

C. uw(p+q)/(wp+uq)

D. (wp+uq)/(u+wq)

24. If w varies inversely as uv/u + v and is equal to 8 when u = 2 and v = 6, find a relationship between u, v, w.

A. upw = 16(u + t)

B. 16ur = 3w(u + t)

C. upw = 12(u + t)

D. 12upw = u + r

25. If g(x = x2 + 3x ) find g(x + 1) â€“ g(x)

A. (x + 2)

B. 2(x + 2)

C. (2x + 1)

D. (x + 4)

26. Factorize m3 â€“ m2 â€“ m + 2

A. (m2 + 1)(m â€“ 2)

B. (m + 1)(m + 1)(m + 2)

C. (m + 1)(m + 1)(m â€“ 2)

D. (m2 + 2)(m â€“ 1)

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27**.**Â The angles of a quadrilateral are 5xÂ â€“Â 30, 4x + 60, 60 â€“ x and 3x + 61. find the smallest of these angles.

A. 5x â€“ 30

B. 4x + 60

C. 60 â€“ x

D. 3x + 61

28. What is the nth term of the sequence 2, 6, 12, 20,â€¦?

A. 4n â€“ 2

B. 2(3n â€“ 1)

C. n2 + n

D. n2 + 3n +2

29. If the binary operation * is defined by m*n = mn + m + n for any real number m and n, find the identity element under this operation.

A. e = 1

B. e = -1

C. e = -2

D. e = 0

30**.**Â Each of the interior angles of a regular polygon is 1400. How many sides has the polygon?

A. 9

B. 8

C. 7

D. 5

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