Mathematics 2010 Objective — Question 1
Simplify (225^½ + 85⁰) × 256^(-¼)
- A. 2
- B. 4Correct
- C. -2
- D. -4
Explanation
225^½=15; 85⁰=1 (anything to the power 0 is 1); 256^(-¼)=1/4. So (15+1)×¼ = 16×¼ = 4.
Post-UTME Mathematics 2010 Objective Past Questions
All 10 questions from the Post-UTME Screening (Post-UTME) Mathematics 2010 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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Mathematics 2010 Objective — Question 2
In how many ways can 3 boys and 2 girls sit in a row, if just the two girls are to sit together?
- A. 120
- B. 24
- C. 48Correct
- D. 36
Explanation
Treat the 2 girls as one block: 4 units arrange in 4!=24 ways; the 2 girls within their block arrange in 2!=2 ways. Total=24×2=48.
Mathematics 2010 Objective — Question 3
The probability of an event P is ¾ while that of another event Q is 1/6. If the probability of both P and Q is 1/12, what is the probability of either P or Q?
- A. 1/96
- B. 1/8
- C. 5/6Correct
- D. 11/12
Explanation
P(P∪Q)=P(P)+P(Q)-P(P∩Q) = 3/4+1/6-1/12 = 9/12+2/12-1/12 = 10/12 = 5/6.
Mathematics 2010 Objective — Question 4
What is the value of x satisfying the equation 4^(2x) ÷ 4^x = ... (figures partly unclear in the source)
- A. -2
- B. 1/7Correct
- C. ½
- D. 2
Explanation
The precise original equation was not fully legible in the source scan; option B (x=-1/2, matching the source's own worked solution) is the answer given by the key.
Mathematics 2010 Objective — Question 5
The weight of 30 new-born babies are given as: 6,9,5,7,6,7,5,8,9,5,7,5,8,7,8,7,5,6,5,7,6,9,9,7,8,8,7,8,9,8. The mode is
- A. 6
- B. 5
- C. 8
- D. 7Correct
Explanation
7 is the most frequently occurring value in the data set.
Mathematics 2010 Objective — Question 6
On each market day, Mrs. Bassey walks to the market from her home at a steady speed. This journey normally takes her 2 hours. By increasing her usual speed, she can save 20 minutes. Find her usual speed in km/hr.
- A. 1⅔
- B. 2
- C. 5Correct
- D. 6
Explanation
Following the source's worked solution (which used a specific distance figure not fully legible here), the usual speed works out to 5km/hr.
Mathematics 2010 Objective — Question 7
Factorize the following expression: 2x²+x-15
- A. (2x+5)(x-3)
- B. (2x-5)(x+3)Correct
- C. (2x-5)(x-3)
- D. (2x-3)(x+5)
Explanation
2x²+x-15 = 2x²+6x-5x-15 = 2x(x+3)-5(x+3) = (2x-5)(x+3).
Mathematics 2010 Objective — Question 8
Simplify (log√27)/log81
- A. 1/6
- B. 3/8Correct
- C. ½
- D. ¾
Explanation
(½log27)/log81 = (½×3log3)/(4log3) = (3/2)/4 = 3/8.
Mathematics 2010 Objective — Question 9
Determine the maximum value of y=3x²-x³
- A. 0
- B. 2
- C. 4Correct
- D. 6
Explanation
dy/dx=6x-3x²=0 gives x=0 or x=2; the second derivative test shows x=2 is a maximum. y(2)=3(4)-8=4.
Mathematics 2010 Objective — Question 10
What are the integral values of x which satisfy the inequality -1<3-2x≤5?
- A. 2, 10, -1
- B. -1, 0, 1, 2
- C. -1, 0, 1Correct
- D. 0, 1, 2
Explanation
Splitting the compound inequality: 3-2x>-1 gives x<2; 3-2x≤5 gives x≥-1. So -1≤x<2, with integer values -1, 0, 1.
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