Mathematics 2006 Objective — Question 1
In set theory, an empty set is represented with
- A. ∅
- B. {}
- C. {.}
- D. ∅ and {}Correct
Explanation
Both the symbol ∅ and the notation {} are valid representations of the empty set.
Post-UTME Mathematics 2006 Objective Past Questions
All 10 questions from the Post-UTME Screening (Post-UTME) Mathematics 2006 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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Mathematics 2006 Objective — Question 2
The value of sin300° is
- A. √3/2
- B. ½
- C. -½
- D. -√3/2Correct
Explanation
sin300°=-sin(360°-300°)=-sin60°=-√3/2.
Mathematics 2006 Objective — Question 3
The 2nd and 5th terms of a geometric progression are 24 and 81 respectively, find the common ratio.
- A. 2/3
- B. 3/2Correct
- C. 5/2
- D. 7/2
Explanation
ar=24, ar⁴=81; dividing gives r³=27/8, so r=3/2.
Mathematics 2006 Objective — Question 4
The percentage score of 10 students in a test are 12, 56, 42, 21, 25, 18, 10, 53, 42, 24. What is the median score?
- A. 25.4
- B. 27.6
- C. 263
- D. 27.5
Explanation
Sorted: 10,12,18,21,24,25,42,42,53,56. Median=(24+25)/2=24.5.
Mathematics 2006 Objective — Question 5
Multiply x²+x+1 by x²-x+1
- A. x⁴+3x²+x+1
- B. x⁴+x²+1Correct
- C. x⁴+4x²-6x
- D. x⁴-6x²-4x+1
Explanation
(x²+x+1)(x²-x+1) = (x²+1)²-x² = x⁴+2x²+1-x² = x⁴+x²+1.
Mathematics 2006 Objective — Question 6
The sum of the roots of a quadratic is 5/2 and the product of the roots is 4. Find the quadratic equation.
- A. 2x²+5x+8=0
- B. 2x²-5x+8=0Correct
- C. 2x²ox+5=0
- D. 2x²+8x-5=0
Explanation
x²-(sum)x+(product)=0 gives x²-(5/2)x+4=0; multiplying by 2: 2x²-5x+8=0.
Mathematics 2006 Objective — Question 7
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; x=2 is a maximum, with y(2)=12-8=4.
Mathematics 2006 Objective — Question 8
Find the derivative of the function y=-2x²(2x-1) at the point x=-1 (figures partly unclear in the source)
- A. -6
- B. -4
- C. 4Correct
- D. 6
Explanation
The source's own worked solution computes a value of -16 at x=-1, which does not match any of the listed options — this looks like an error somewhere in the original question or key. The letter given by the source is C.
Mathematics 2006 Objective — Question 9
Simplify cos²x(sec²x-tan²x) (figures partly unclear in the source)
- A. 2
- B. 4
- C. -1
- D. 1Correct
Explanation
Using the identity sec²x-tan²x=1, this simplifies to cos²x×1=cos²x; the source's key marks option D, though this only equals a constant 1 if x=0.
Mathematics 2006 Objective — Question 10
If 52(base n) - 24(base n) = 25(base n), then n is
- A. 4
- B. 7Correct
- C. 11
- D. 5
Explanation
(5n+2)-(2n+4)=(2n+5) gives 3n-2=2n+5, so n=7.
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