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POST UTME ELIZADE UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = x\^2\), the x-axis, and the line \$(y = x^2\(x = 2$ about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 2 View Details

Solve the system of equations: \begin{align*} x + y + z &= 6 \ 2x + 2y + 3z &= 12 \ 3x + 2y + z &= 9 \end{align*}

Correct A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}

B. \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}

C. \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}

D. \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}

Correct Answer: A

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Question 3 View Details

Find the area under the curve $y = x\^3 - 6x^2 + 9x + 2$ from $x = 0$ to $x = 4$.

A. 128

B. 192

Correct C. 256

D. 320

Correct Answer: C

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Question 4 View Details

Solve the inequality: $\frac{x + 1}{x - 2}$\$) > 0.$

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

B. $-\infty, 2$ \cup $2, \infty$

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

D. $-\infty, 2$ \cup $2, \infty$

Correct Answer: A

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Question 5 View Details

Find the surface area of the solid formed by revolving the region bounded by the curve (y = x\^2\), the x-axis, and the line \$(y = x^2\(x = 2$ about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 6 View Details

In the coordinate plane, the equation of a circle is given by $x - h \$^2 + $y - k$^$2 = r\^2$ ). If the center of the circle is at ( (h,$k) = (2$, 3) ) and the radius is 4, what is the equation of the circle?

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

B. $x - 2 \$^2 + $y - 3$^$2 = 32$ )

C. $x - 2 \$^2 + $y - 3$^$2 = 64$ )

D. $x - 2 \$^2 + $y - 3$^$2 = 256$ )

Correct Answer: A

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Question 7 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 5 terms of the sequence.

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

B. 2 + 5 + 13 + 29 + 61

C. 2 + 7 + 17 + 37 + 83

D. 2 + 5 + 13 + 29 + 67

Correct Answer: A

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Question 8 View Details

In a geometric progression, the first term is 2 and the common ratio is 3. Find the sum of the first 5 terms of the progression.

Correct A. 2 + 6 + 18 + 54 + 162

B. 2 + 6 + 18 + 54 + 162

C. 2 + 6 + 18 + 54 + 162

D. 2 + 6 + 18 + 54 + 162

Correct Answer: A

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Question 9 View Details

A set of 5 numbers has a mean of 10 and a median of 12. If the largest number is 18, what is the sum of the remaining 3 numbers?

Correct A. 30 + 12 + 18

B. 30 + 12 + 18

C. 30 + 12 + 18

D. 30 + 12 + 18

Correct Answer: A

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Question 10 View Details

A circle has a radius of 5 units and passes through the points ( (0, 0) ) and ( (3, 4) ). Find the equation of the circle.

Correct A. $x - 1 \$^2 + $y - 4$^$2 = 25$ )

B. $x + 1 \$^2 + $y - 4$^$2 = 25$ )

C. $x - 1 \$^2 + $y + 4$^$2 = 25$ )

D. $x + 1 \$^2 + $y + 4$^$2 = 25$ )

Correct Answer: A

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Question 11 View Details

In the diagram below, the graph of $y = \frac{1}{2} $12x$ is shown. What is the amplitude of the function?

A. 1

Correct B. 0.5

C. 2

D. 3

Correct Answer: B

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Question 12 View Details

A random variable X has a probability distribution given by

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 13 View Details

The area under the curve $y = x^2$ from $x = 0$ to $x = 2$ is given by

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 14 View Details

The determinant of the matrix $\begin{bmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{bmatrix}$ is

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 15 View Details

The probability of independent events A and B occurring is given by

A. P(A) + P(B)

Correct B. P(A) \cdot P(B)

C. P(A) - P(B)

D. $P(A) / P(B)$

Correct Answer: B

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Question 16 View Details

Find the value of $\int_{0}^{\frac{\pi}{2}} \frac{\sin^2 x}{\cos^2 x + 2} dx$.

Correct A. $\frac{\pi}{4}$\)

B. $\frac{\pi}{2}$\)

C. $\frac{\pi}{3}$\)

D. $\frac{\pi}{6}$\)

Correct Answer: A

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Question 17 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?

A. 0.68

Correct B. 0.80

C. 0.90

D. 0.95

Correct Answer: B

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Question 18 View Details

Solve the inequality $\frac{x^2 - 4}{x^2 - 9} > 0$.

Correct A. $-\infty, -3$ \cup $3, \infty$

B. $-3, 3$

C. $-\infty, -3$ \cup (0, 3)

D. $-\infty, 0$ \cup $3, \infty$

Correct Answer: A

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Question 19 View Details

Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.

Correct A. $\frac{\pi}{4}$\)

B. $\frac{\pi}{2}$\)

C. $\frac{\pi}{3}$\)

D. $\frac{\pi}{6}$\)

Correct Answer: A

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Question 20 View Details

A quadratic equation has roots $\alpha$ and $beta$. If $\\(beta). If \alpha + \beta = -2$ and $\alpha \beta = 3$, find the equation of the quadratic.

Correct A. \$(x^2 + 2x + 3$$= 0$\)

B. \$(x^2 - 2x + 3$$= 0$\)

C. \$(x^2 + 4x + 3$$= 0$\)

D. \$(x^2 - 4x + 3$$= 0$\)

Correct Answer: A

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Question 21 View Details

Determine the mean of the following set of numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the mean is increased by 2, what is the new mean?

A. 24

Correct B. 26

C. 28

D. 30

Correct Answer: B

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Question 22 View Details

Solve the quadratic equation: $x^2 + 5x + 6 = 0$.

A. -2

Correct B. -3

C. -1

D. 1

Correct Answer: B

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Question 23 View Details

Find the sum of the first 10 terms of the arithmetic progression: 2, 5, 8, 11, ...

A. 55

B. 60

Correct C. 65

D. 70

Correct Answer: C

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Question 24 View Details

In the diagram below, ( O ) is the center of the circle, and ( AB ) is a chord. If $OA = 6$ cm and $OB = 8$ cm, find the length of ( AB ).

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 25 View Details

A vector ( mathbf{a} ) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of ( mathbf{a} ).

Correct A. (4, 3)

B. (3, 4)

C. (5, 5)

D. (6, 6)

Correct Answer: A

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