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POST UTME SKYLINE 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. $\frac{1}{2}$

B. ( 3 )

C. ( 4 )

Correct D. ( 6 )

Correct Answer: D

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Question 2 View Details

Solve for ( x ) in the equation $2^x + 3^x = 5^x$.

Correct A. $x = 1$

B. $x = 2$

C. $x = 3$

D. $x = 4$

Correct Answer: A

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Question 3 View Details

Find the value of $\log_{10} 1000 \$ ).

A. ( 3 )

Correct B. ( 4 )

C. ( 5 )

D. ( 6 )

Correct Answer: B

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Question 4 View Details

Solve the inequality $x^2 - 4x - 5 > 0$.

Correct A. $x < -1$ or $x > 5$

B. $x < 1$ or $x > 5$

C. $x < -1$ or $x < 5$

D. $x < 1$ or $x > 5$

Correct Answer: A

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Question 5 View Details

Find the value of $\(12\theta \$ ) given that 1\$theta =$$\frac{1}{2}$\) and $$1\theta = \frac{\sqrt{3}}{2}$.

Correct A. $\frac{\sqrt{3}}{2}$

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

C. $\frac{\sqrt{5}}{2}$

D. $\frac{1}{\sqrt{2}}$

Correct Answer: A

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Question 6 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 48\pi

B. 64\pi

Correct C. 80\pi

D. 96\pi

Correct Answer: C

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Question 7 View Details

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

Correct A. $x - 1$, x - 2\)$x - 3$

B. $x - 1$, x - 2\)$x - 4$

C. $x - 1$, x - 3\)$x - 4$

D. $x - 2$, x - 3\)$x - 4$

Correct Answer: A

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Question 8 View Details

Find the magnitude of the vector $\vec{a} = 3\hat{i} + 4\hat{j}$ and the angle it makes with the positive x-axis.

A. $\sqrt{5}$

Correct B. $\sqrt{10}$

C. $\sqrt{20}$

D. $\sqrt{25}$

Correct Answer: B

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Question 9 View Details

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

Correct A. 0, $\frac{\pi}{2}$\), \pi, $\frac{3\pi}{2}$\)

B. $\frac{\pi}{4}$\), $\frac{3\pi}{4}$\), $\frac{5\pi}{4}$\), $\frac{7\pi}{4}$\)

C. $\frac{\pi}{6}$\), $\frac{\pi}{3}$\), $\frac{2\pi}{3}$\), $\frac{5\pi}{6}$\)

D. $\frac{\pi}{8}$\), $\frac{3\pi}{8}$\), $\frac{5\pi}{8}$\), $\frac{7\pi}{8}$\)

Correct Answer: A

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Question 10 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 11 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x\^2$, $y = 0$, and $x = 2$ 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 12 View Details

A binary operation ast on the set of integers is defined as a \ast $b = ab + 1\\(ast on the set of integers is defined as a ast$. Find the value of 2 \ast 3.

A. 7

Correct B. 9

C. 11

D. 13

Correct Answer: B

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Question 13 View Details

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

A. 64

B. 128

Correct C. 192

D. 256

Correct Answer: C

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Question 14 View Details

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 123

B. 124

C. 125

Correct D. 126

Correct Answer: D

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Question 15 View Details

Find the derivative of the function f(x) = $2x^3 - 5x^2 + 3x - 1$.

A. $6x^2 - 10x + 3$

B. $12x^2 - 20x + 6$

Correct C. $24x^2 - 40x + 12$

D. $48x^2 - 80x + 24$

Correct Answer: C

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Question 16 View Details

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

Correct A. \boxed{ x + 2 ^2 + y - $3 ^2 = 16$}

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

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

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

Correct Answer: A

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Question 17 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its surface area.

Correct A. $2(6)(4) + 2(6)(3) + 2(4)(3) =$$48 + 36 + 24 = 108$

B. $2(6)(4) + 2(6)(3) + 2(4)(3) =$$48 + 36 + 24 = 108$

C. $2(6)(4) + 2(6)(3) + 2(4)(3) =$$48 + 36 + 24 = 108$

D. $2(6)(4) + 2(6)(3) + 2(4)(3) =$$48 + 36 + 24 = 108$

Correct Answer: A

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Question 18 View Details

Simplify the expression: $\frac{2x^2 + 5x - 3}{x + 3}$\)\)

Correct A. $\frac{2x^2 + 5x - 3}{x + 3}$\)\$) = 2x - 1$

B. $\frac{2x^2 + 5x - 3}{x + 3}$\)\$) = 2x + 1$

C. $\frac{2x^2 + 5x - 3}{x + 3}$\)\$) = x - 1$

D. $\frac{2x^2 + 5x - 3}{x + 3}$\)\$) = x + 1$

Correct Answer: A

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Question 19 View Details

Find the derivative of the function:$f(x) =$$3x^2 + 2x - 5$

Correct A. f'$(x) = 6x + 2$

B. f'$(x) = 6x - 2$

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

D. f'$(x) =$$3x^2 - 2$

Correct Answer: A

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Question 20 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 21 View Details

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

Correct A. $y = 1x + 1$

B. $y = 1x - 1$

C. $y = -1x + 1$

D. $y = -1x - 1$

Correct Answer: A

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Question 22 View Details

A circle has a radius of 4 cm and a center at (0, 0). Find the equation of the circle.

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

B. $x^2$ + \$(y^2$$= 4$\)

C. $x^2$ - \$(y^2$$= 16$\)

D. $x^2$ - \$(y^2$$= 4$\)

Correct Answer: A

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Question 23 View Details

Find the volume of the rectangular prism with length 6 cm, width 4 cm, and height 3 cm.

A. $6(4)(3) = 72$

B. $6(4)(3) = 64$

C. $6(4)(3) = 80$

D. $6(4)(3) = 96$

Correct Answer: VIEW ANSWER

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Question 24 View Details

In a circle with center $O$, a chord $AB$ is drawn such that $OA = 3$ and $OB = 4$. If (M\) is the midpoint of $AB\\((M) is the midpoint of$, find the area of $\triangle OMA$.

Correct A. 12

B. 16

C. 20

D. 24

Correct Answer: A

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Question 25 View Details

Let (f(x) = $\frac{\(x^2+1}{x$^2-1}\)\). Find the value of \$(f(x) = frac{x^2+1}{x^2-1}\(f^{-1}(2)$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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