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POST UTME MOUNTAIN TOP UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

Solve for x in the equation $\log_{10} x^2 \$$= 4 ).$

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 2 View Details

A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?

A. 0.7

Correct B. 0.8

C. 0.9

D. 0.95

Correct Answer: B

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Question 3 View Details

The histogram below shows the distribution of exam scores for a class of 50 students. What is the mean score?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 4 View Details

Solve the quadratic equation $x^2 + 4x + 4 = 0$.

A. 0

Correct B. -2

C. -1

D. 2

Correct Answer: B

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Question 5 View Details

A circle has a radius of 4 cm. What is the area of the circle?

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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Question 6 View Details

Solve the inequality $\frac{x}{x-2} > 0$ for ( x in mathbb{R} setminus {2} ).

Correct A. $-∞, 2$ ∪ (2, ∞)

B. $-∞, 2$ ∩ (2, ∞)

C. (2, ∞)

D. $-∞, 2$

Correct Answer: A

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Question 7 View Details

Find the equation of the circle with center $3, -2 \$ ) and radius ( 4 ).

Correct A. $x-3 \$^2 + $y+2$^$2 = 16$ )

B. $x-3 \$^2 + $y+2$^$2 = 25$ )

C. $x-3 \$^2 + $y+2$^$2 = 36$ )

D. $x-3 \$^2 + $y+2$^$2 = 49$ )

Correct Answer: A

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Question 8 View Details

A sequence is defined by $a_n = 2n^2 - 3n + 1$. Find the sum of the first five terms.

Correct A. 55

B. 65

C. 75

D. 85

Correct Answer: A

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Question 9 View Details

Solve the equation $x^2 + 4x + 4 = 0$.

Correct A. $x = -2$

B. $x = 2$

C. $x = -1$

D. $x = 1$

Correct Answer: A

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Question 10 View Details

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8 cm

B. 6 cm

C. 10 cm

D. 12 cm

Correct Answer: A

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Question 11 View Details

Solve the inequality $\frac{x-2}{x+1} > 0$ for ( x in mathbb{R} ).

Correct A. $-\infty, -1 \$ cup (2, infty) )

B. $-\infty, -1 \$ cup (1, 2) )

C. $-\infty, -1 \$ cup (2, infty) cup (1, 2) )

D. $-\infty, -1 \$ cup (1, infty) )

Correct Answer: A

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Question 12 View Details

Find the volume of the solid formed by rotating the region bounded by the curves $y = x^2$ and $y = x$ about the x-axis.

A. $\frac{1}{6} \pi$

Correct B. $\frac{1}{3} \pi$

C. $\frac{1}{2} \pi$

D. $\frac{2}{3} \pi$

Correct Answer: B

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Question 13 View Details

A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 3$ with initial term $a_1 = 2$. Find the sum of the first five terms of the sequence.

A. $2 + 7 + 17 + 37 + 79$

B. $2 + 5 + 13 + 29 + 61$

Correct C. $2 + 7 + 17 + 37 + 79$

D. $2 + 5 + 13 + 29 + 61$

Correct Answer: C

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Question 14 View Details

Find the derivative of the function ( f(x) = $\frac{1}{x^2 + 1}$\)\) ) using the chain rule.

Correct A. $-\frac{2x}{x^2 + 1$ \ ^2}\)\) )

B. $\frac{2x}{x^2 + 1$ \ ^2}\)\) )

C. $-\frac{2}{x^2 + 1$ \ ^2}\)\) )

D. $\frac{2}{x^2 + 1$ \ ^2}\)\) )

Correct Answer: A

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Question 15 View Details

Solve the equation $x^3 - 6x^2 + 11x - 6 = 0$ using the rational root theorem.

A. $x = 1$

B. $x = 2$

Correct C. $x = 3$

D. $x = 6$

Correct Answer: C

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Question 16 View Details

A circle has a radius of 4 cm. Find the area of the circle.

A. ( 16pi )

B. ( 32pi )

Correct C. ( 64pi )

D. ( 128pi )

Correct Answer: C

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Question 17 View Details

Find the sum of the infinite geometric series $sum_{n = 1}^{\infty} \frac{1}{2^n}$.

Correct A. ( 1 )

B. $\frac{1}{2}$

C. $\frac{1}{4}$

D. $\frac{1}{8}$

Correct Answer: A

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Question 18 View Details

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. ( 8 )

B. ( 6 )

C. ( 4 )

D. ( 2 )

Correct Answer: A

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Question 19 View Details

Find the derivative of the function ( f(x) = \$\sin^2$ x ) using the chain rule.

A. $2\(1x$1x\)

B. $2$1x$

C. $2$1x$

D. $2\(1x$1x\)

Correct Answer: VIEW ANSWER

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Question 20 View Details

The mean of a set of numbers is 25. If the mean of a subset of these numbers is 30, and the subset has 4 more numbers than the original set, what is the mean of the original set?

A. 20

B. 22

Correct C. 24

D. 26

Correct Answer: C

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Question 21 View Details

Solve for x in the equation $x^2 + 4x + 4 = 0$.

A. 0

Correct B. -2

C. -1

D. 1

Correct Answer: B

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Question 22 View Details

Find the determinant of the matrix $\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}$.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 23 View Details

A histogram is a graphical representation of a frequency distribution. What is the name of the type of graph that is used to show the relationship between two variables?

Correct A. Scatter plot

B. Bar chart

C. Histogram

D. Pie chart

Correct Answer: A

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Question 24 View Details

If (f(x) = $2x^2 + 3x - 1$\), find $f'(x)\\((f(x) = 2x^2 + 3x - 1), find$.

Correct A. 4x + 3

B. 2x + 1

C. 3x - 2

D. $x^2 + 2x$

Correct Answer: A

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Question 25 View Details

Solve the inequality $2x - 5 > 3$.

Correct A. $x > 4$

B. $x < 4$

C. $x > 2$

D. $x < 2$

Correct Answer: A

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