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POST UTME VERITAS UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

Find the area under the curve $y = \frac{1}{2}x^2 + 3x - 2$ from $x = 0$ to $x = 4$.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 2 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. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 3 View Details

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

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

B. $$1x$

C. $$1x$

D. $\cos^2 x$

Correct Answer: A

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Question 4 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

Correct A. $x < -1$ or $x > \frac{3}{2}$

B. $x < -1$ or $x < \frac{3}{2}$

C. $x > -1$ or $x < \frac{3}{2}$

D. $x > -1$ or $x > \frac{3}{2}$

Correct Answer: A

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Question 5 View Details

A polynomial function has a degree of 4 and has roots at $x = -2, 1, 3$. Find the polynomial function.

Correct A. $x^4 + 6x^3 - 3x^2 - 18x + 18$

B. $x^4 + 6x^3 - 3x^2 + 18x - 18$

C. $x^4 - 6x^3 - 3x^2 + 18x + 18$

D. $x^4 - 6x^3 + 3x^2 - 18x - 18$

Correct Answer: A

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Question 6 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 7 View Details

Find the value of $\frac{1}{2} \times 3 \times 4$ without using a calculator.

A. 3

B. 6

Correct C. 12

D. 24

Correct Answer: C

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Question 8 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

Correct A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, 3$ ∪ (4, ∞)

C. $-∞, -3$ ∪ (1, ∞)

D. $-∞, 1$ ∪ (3, ∞)

Correct Answer: A

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Question 9 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

Correct A. $y = 2x - 1$

B. $y = 2x + 1$

C. $y = x + 2$

D. $y = x - 2$

Correct Answer: A

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Question 10 View Details

Solve the system of equations $x + y = 4$ and $x - y = 2$.

Correct A. $x = 3$, $y = 1$

B. $x = 1$, $y = 3$

C. $x = 2$, $y = 2$

D. $x = 4$, $y = 0$

Correct Answer: A

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Question 11 View Details

Find the area under the curve $y = 2x\^2 + 3x - 1$ from $x = 0$ to $x = 2$.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 12 View Details

Solve the inequality \$(2x^2 + 5x - 3$$> 0.$\)

Correct A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, -3$ ∪ (1, ∞)

C. $-∞, 1$ ∪ (3, ∞)

D. $-∞, -3$ ∪ (1, ∞)

Correct Answer: A

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Question 13 View Details

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

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

B. $x - 3$^2 + $y - 2$^$2 = 16$

C. $x + 2$^2 + $y + 3$^$2 = 16$

D. $x - 2$^2 + $y + 3$^$2 = 16$

Correct Answer: A

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Question 14 View Details

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

Correct A. $x = -2$

B. $x = -1$

C. $x = 1$

D. $x = 2$

Correct Answer: A

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Question 15 View Details

Find the value of x in the equation $2^x$ + \$(3^x$$= 5$\$)^x$.

A. $x = 2$

Correct B. $x = 3$

C. $x = 4$

D. $x = 5$

Correct Answer: B

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Question 16 View Details

Let $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix}$. Find the projection of ( mathbf{b} ) onto ( mathbf{a} ).

Correct A. \begin{pmatrix} 1.6 \ 2.4 \end{pmatrix}

B. \begin{pmatrix} 0.8 \ 1.2 \end{pmatrix}

C. \begin{pmatrix} 2.4 \ 3.6 \end{pmatrix}

D. \begin{pmatrix} 3.2 \ 4.8 \end{pmatrix}

Correct Answer: A

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Question 17 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 18 View Details

A random experiment has two independent events, A and B, with probabilities 0.4 and 0.6, respectively. Find the probability that at least one of the events occurs.

A. 0.8

Correct B. 0.9

C. 0.7

D. 0.5

Correct Answer: B

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Question 19 View Details

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

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

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

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

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

Correct Answer: C

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Question 20 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. Find the z-score of a score of 70.

A. 0.5

Correct B. 1

C. 1.5

D. 2

Correct Answer: B

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Question 21 View Details

Determine the value of $\sum_{n = 1}^{\infty} \frac{1}{n^2}$ using the properties of infinite geometric series.

Correct A. $\frac{\pi^2}{6}$

B. $\frac{\pi^2}{12}$

C. $\frac{\pi^2}{24}$

D. $\frac{\pi^2}{48}$

Correct Answer: A

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Question 22 View Details

Solve the system of linear equations using matrices: $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}$

Correct A. $\begin{bmatrix} 1 \ 2 \end{bmatrix}$

B. $\begin{bmatrix} 2 \ 1 \end{bmatrix}$

C. $\begin{bmatrix} -1 \ 1 \end{bmatrix}$

D. $\begin{bmatrix} 1 \ -1 \end{bmatrix}$

Correct Answer: A

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Question 23 View Details

Find the equation of the circle with center $\left \frac{3}{2}, \frac{5}{4} \right$\) and radius $\frac{5}{4}$.

Correct A. $\left x - \frac{3}{2} \right$^2 + \left$y - \frac{5}{4} \right$\$(^2$ =\)\left$\frac{5}{4} \right$^2\)

B. $\left x - \frac{5}{4} \right$^2 + \left$y - \frac{3}{2} \right$\$(^2$ =\)\left$\frac{5}{4} \right$^2\)

C. $\left x - \frac{3}{2} \right$^2 + \left$y - \frac{5}{4} \right$\$(^2$ =\)\left$\frac{3}{2} \right$^2\)

D. $\left x - \frac{5}{4} \right$^2 + \left$y - \frac{3}{2} \right$\$(^2$ =\)\left$\frac{3}{2} \right$^2\)

Correct Answer: A

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Question 24 View Details

A histogram represents the distribution of exam scores with a mean of 70 and a standard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 60 and 80.

Correct A. 0.68

B. 0.84

C. 0.95

D. 0.99

Correct Answer: A

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Question 25 View Details

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

Correct A. $x = -2$

B. $x = -3$

C. $x = 2$

D. $x = 3$

Correct Answer: A

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