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POST UTME SUMMIT UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

In the number system with base 8, what is the value of the expression $5 \times 8^2 + 3 \times 8^1 + 2 \times 8^0$?

Correct A. 42

B. 48

C. 52

D. 58

Correct Answer: A

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Question 2 View Details

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

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 3 View Details

Given the vectors $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} 4 \ 5 end{pmatrix}$, find the magnitude of the vector $\\(end{pmatrix}), find the magnitude of the vector \mathbf{a} + \mathbf{b}$.

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 4 View Details

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

Correct A. $x = -2$

B. $x = -1$

C. $x = 0$

D. $x = 1$

Correct Answer: A

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Question 5 View Details

Find the value of $\(12\theta \$ ) given that 1\theta \\) = $\frac{3}{5}$\) ) and $$1\theta \$ = $\frac{4}{5}$\) ).

Correct A. $\frac{24}{25}$\)

B. $\frac{16}{25}$\)

C. $\frac{20}{25}$\)

D. $\frac{12}{25}$\)

Correct Answer: A

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Question 6 View Details

Let $S = {1, 2, 3, 4, 5}$ and $T = {2, 3, 5, 7, 11}$. Find the symmetric difference of sets S and T.

A. S \cup T

B. S \cap T

Correct C. S \triangle T

D. S \oplus T

Correct Answer: C

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Question 7 View Details

Find the sum of the first 10 terms of the geometric series $2x + 3x^2 + 4x^3 + ldots$.

A. 2x + $3x^2 + 4x^3 + ldots + 20x^{10}$

Correct B. 2x + $3x^2 + 4x^3 + ldots + 21x^{10}$

C. 2x + $3x^2 + 4x^3 + ldots + 22x^{10}$

D. 2x + $3x^2 + 4x^3 + ldots + 23x^{10}$

Correct Answer: B

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Question 8 View Details

Let $\vec{a} = egin{pmatrix} 2 \ 3 \ -1 \end{pmatrix}$ and $\vec{b} = egin{pmatrix} 1 \ -2 \ 4 \end{pmatrix}$. Find the cross product of vectors ( vec{a} ) and ( vec{b} ).

Correct A. $egin{pmatrix} 11 \ -14 \ 8 \end{pmatrix}$

B. $egin{pmatrix} 10 \ -13 \ 7 \end{pmatrix}$

C. $egin{pmatrix} 9 \ -12 \ 6 \end{pmatrix}$

D. $egin{pmatrix} 8 \ -11 \ 5 \end{pmatrix}$

Correct Answer: A

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Question 9 View Details

Solve the trigonometric equation $\sin^2 x + \cos^2 x = 1$ for ( x ) in the interval ( [0, 2pi] ).

A. $x = 0, \pi, 2\pi$

B. $x = \frac{\pi}{2}, \frac{3\pi}{2}$

Correct C. $x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}$

D. $x = \frac{\pi}{6}, \frac{5\pi}{6}, \frac{7\pi}{6}, \frac{11\pi}{6}$

Correct Answer: C

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Question 10 View Details

Find the derivative of the function ( f(x) = $x^3 - 2x^2 + 3x - 1$ ) using the power rule.

Correct A. ( f'$(x) =$$3x^2 - 4x + 3$ )

B. ( f'$(x) =$$x^2 - 2x + 1$ )

C. ( f'$(x) =$$3x^2 - 4x + 2$ )

D. ( f'$(x) =$$x^2 - 2x - 1$ )

Correct Answer: A

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Question 11 View Details

Solve for x in the equation $\tan^2 x + 2 $1x - 6 = 0$.

Correct A. $x = -2$π/3,$x =$π/3

B. $x = 2$π/3,$x = -$π/3

C. $x =$π/3,$x = -$π/3

D. $x = 2$π/3,$x =$π/3

Correct Answer: A

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Question 12 View Details

Find the value of y in the equation $y = \frac{1}{2} \left x + \frac{1}{x} right \$ ) when \$right \(x = 2$.

Correct A. $3/2$

B. $5/2$

C. $7/2$

D. $9/2$

Correct Answer: A

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Question 13 View Details

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

Correct A. $x <$$-3/2$ or $x > 1$

B. x < -1 or $x > 3$

C. $x < 1$ or $x > 3$

D. $x <$$-3/2$ or $x < 1$

Correct Answer: A

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Question 14 View Details

Find the value of x in the equation $x^3 - 6x^2 + 11x - 6 = 0$.

Correct A. $x = 1$

B. $x = 2$

C. $x = 3$

D. $x = 4$

Correct Answer: A

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Question 15 View Details

Find the value of x in the equation $x^2 + 4x + 4 = 0$.

Correct A. $x = -2$

B. $x = -1$

C. $x = 0$

D. $x = 1$

Correct Answer: A

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Question 16 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 256\pi \text{ cm}^3

B. 512\pi \text{ cm}^3

Correct C. 768\pi \text{ cm}^3

D. 1024\pi \text{ cm}^3

Correct Answer: C

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Question 17 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

Correct A. $\frac{1}{3}$\)

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

C. $\frac{2}{3}$\)

D. $\frac{4}{5}$\)

Correct Answer: A

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Question 18 View Details

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 19 View Details

Solve for x in the equation $\frac{1}{x + 2}$\) + $\frac{1}{x - 1}$\) = $\frac{3}{2}$\)

A. $x = -3$

B. $x = 2$

Correct C. $x = 4$

D. $x = 5$

Correct Answer: C

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Question 20 View Details

Find the value of sin 75^\circ in terms of \sin 15^\$sin \(75^circ$ in terms of \circ and \cos 15^\circ.

Correct A. \sin 15^\circ + \cos 15^\circ

B. \sin 15^\circ - \cos 15^\circ

C. \sin 15^\circ \cos 15^\circ

D. \cos 15^\circ - \sin 15^\circ

Correct Answer: A

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Question 21 View Details

Find the volume of the solid formed by rotating the region bounded by the curves $y = x\^2$ and $y = 4 - x\^2$ about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 22 View Details

If f(x) = $3x^2 + 2x - 5$, find the derivative of f(x) using the chain rule.

Correct A. 6x + 2

B. 6x - 2

C. $3x^2 + 2x - 5$

D. $9x^2 + 4x - 10$

Correct Answer: A

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Question 23 View Details

Solve the equation \$tan x =$$\sqrt{3}$ using the unit circle.

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

Correct B. $\frac{2\pi}{3}$\)

C. $\frac{4\pi}{3}$\)

D. $\frac{5\pi}{3}$\)

Correct Answer: B

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Question 24 View Details

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 25 View Details

Evaluate the definite integral \int_{0}^{1} $x^2$ dx.

Correct A. $\frac{1}{3}$\)

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

C. $\frac{2}{3}$\)

D. $\frac{3}{4}$\)

Correct Answer: A

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