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POST UTME OAU 2017 Mathematics | Objective

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Question 1

Determine the value of x in the equation $ \sin^2\( x \ $ + \cos^2(x) = 1 ) if $ \tan\( x \ $ = \frac{3}{4} ).

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

B. $ \frac{3pi}{4} $

C. $ \frac{5pi}{4} $

D. $ \frac{7pi}{4} $

Correct Answer: A

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Question 2

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

Correct A. ( f'(x) = \frac{-2x}{$ x^2 + 1 $^2} )

B. ( f'(x) = \frac{2x}{$ x^2 + 1 $^2} )

C. ( f'(x) = \frac{-x}{$ x^2 + 1 $^2} )

D. ( f'(x) = \frac{x}{$ x^2 + 1 $^2} )

Correct Answer: A

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Question 3

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

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

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

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

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

Correct Answer: A

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Question 4

Find the area under the curve $ y = \sin\( x \ $ ) from $ x = 0 $ to $ x = \frac{pi}{2} $.

Correct A. $ \frac{1}{2} $

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

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

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

Correct Answer: A

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Question 5

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

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

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

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

Correct D. $ \frac{5}{6} $

Correct Answer: D

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Question 6

Find the determinant of the matrix $ egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $.

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 7

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 8

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 4 $.

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 9

Solve the system of equations $ egin{cases} x + y = 2 \ x - y = 1 \end{cases} $.

A. x = 1, y = 1

B. x = 1, y = 2

Correct C. x = 2, y = 1

D. x = 2, y = 2

Correct Answer: C

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Question 10

Find the vector ( vec{a} ) such that $ vec{a} cdot vec{b} = 10 $ and $ vec{a} cdot vec{c} = 5 $, where $ vec{b} = egin{bmatrix} 2 \ 3 \end{bmatrix} $ and $ vec{c} = egin{bmatrix} 1 \ 2 \end{bmatrix} $.

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

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

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 11

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

Correct A. $ 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 12

If ( f(x) = \frac{x^2 - 4}{x + 2} ), find $ f\( -2 \ $ ).

A. ( 0 )

B. ( 2 )

C. $ -2 $

Correct D. $ \frac{0}{0} $

Correct Answer: D

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Question 13

Solve for ( x ) in the equation $ 2x^2 + 5x - 3 = 0 $.

Correct A. $ x = -3 $ or $ x = 1 $

B. $ x = -1 $ or $ x = 3 $

C. $ x = 1 $ or $ x = -3 $

D. $ x = -1 $ or $ x = -3 $

Correct Answer: A

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Question 14

Find the derivative of ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing the power rule.

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

B. ( f'(x) = x^2 - 2x + 3 )

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

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

Correct Answer: A

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Question 15

Solve the system of equations u\sing substitution: $ x + y = 4 $ and $ 2x - y = 2 $.

A. $ x = 2, y = 2 $

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

C. $ x = 1, y = 3 $

D. $ x = 2, y = 3 $

Correct Answer: B

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Question 16

Determine the sum of the infinite geometric series ∫_{n=1}^{infty} \frac{1}{2^{n-1}}

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 17

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

Correct A. $ 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 18

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

Correct A. $ -\infty, -\frac{3}{2} $ \cup $ \frac{1}{2}, \infty $

B. $ -\infty, -\frac{3}{2} $ \cup $ -\frac{1}{2}, \infty $

C. $ -\infty, -\frac{1}{2} $ \cup $ \frac{3}{2}, \infty $

D. $ -\infty, \frac{1}{2} $ \cup $ \frac{3}{2}, \infty $

Correct Answer: A

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Question 19

Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis

Correct A. \frac{32}{3}\pi

B. \frac{64}{3}\pi

C. \frac{128}{3}\pi

D. \frac{256}{3}\pi

Correct Answer: A

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Question 20

Determine the value of x in the equation \frac{x}{x+1} = \frac{2}{3}

Correct A. \frac{2}{5}

B. \frac{3}{5}

C. \frac{4}{5}

D. \frac{5}{6}

Correct Answer: A

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Question 21

Find the value of $\frac{d}{dx}\left$ \frac{1}{x^2}\right $$.

Correct A. -\frac{2}{x^3}

B. \frac{2}{x^3}

C. -\frac{1}{x^3}

D. \frac{1}{x^3}

Correct Answer: A

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Question 22

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

Correct A. $ -\infty,-1)\cup\( 5,\infty \ $

B. $ -\infty,1)\cup\( 5,\infty \ $

C. $ -\infty,1)\cup\( 2,5 \ $

D. $ -\infty,5)\cup\( 2,\infty \ $

Correct Answer: A

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Question 23

Find the equation of the \tangent line to the curve $y=x^2-4x+3$ at the point $$ 1,-2 $$.

Correct A. y=-2x+1

B. y=-2x-1

C. y=2x-1

D. y=2x+1

Correct Answer: A

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Question 24

Solve the system of equations $\begin{cases} x+y=4\ x-y=2\end{cases}$.

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 25

Find the value of $\frac{d}{dx}\left$ \frac{x^2}{x^2+1}\right $$.

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

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

C. \frac{2x^3}{$ x^2+1 $^2}

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

Correct Answer: A

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