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POST UTME BSU 2019 Mathematics | Objective

Are you preparing for POST UTME BSU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the value of $\frac{d}{dx} \left$ \frac{1}{x^2} \right $$ u\sing the quotient rule.

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 2

Solve the equation $\log_2 $ x^2 $ = 4$ for $x$.

A. 2

B. 4

Correct C. 8

D. 16

Correct Answer: C

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Question 3

A histogram of exam scores is shown below. If the mean score is 75, what is the value of $k$?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 4

Solve the equation $\sin^2 x + \cos^2 x = 1$ for $x$.

A. 0

B. \frac{\pi}{2}

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

D. \frac{3\pi}{4}

Correct Answer: C

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Question 5

A circle with center $C$ and radius $r$ is shown below. If the area of the circle is $\pi r^2$, what is the value of $r$?

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 6

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

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 7

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 8

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

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 9

Solve the system of equations x + y = 4 and xy = 6.

Correct A. (1, 3)

B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: A

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Question 10

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

Correct A. 32\pi

B. 64\pi

C. 128\pi

D. 256\pi

Correct Answer: A

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Question 11

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

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 12

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

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 13

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 14

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 - 3 $^2 + $ y + 2 $^2 = 16

Correct Answer: A

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Question 15

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 16

Solve the inequality $ \frac{x-2}{x+1} > 0 $ for $ x in \( -infty, -1 \ $ cup $ -1, 2 $ cup (2, infty) ).

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

B. $ x > -1 $ and $ x < 2 $

C. $ x < -1 $ and $ x > 2 $

D. $ x > -1 $ or $ x < 2 $

Correct Answer: A

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Question 17

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. $ x-3 \ $^2 + $ y-4 $^2 = 25 )

B. $ x-4 \ $^2 + $ y-3 $^2 = 25 )

C. $ x-5 \ $^2 + $ y-3 $^2 = 25 )

D. $ x-3 \ $^2 + $ y-5 $^2 = 25 )

Correct Answer: A

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Question 18

Solve the system of equations $ egin{cases} x + y = 3 \ x - y = 1 \end{cases} $.

Correct A. $ x = 2, y = 1 $

B. $ x = 1, y = 2 $

C. $ x = 2, y = 2 $

D. $ x = 1, y = 1 $

Correct Answer: A

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Question 19

Find the vector ( mathbf{a} ) such that $ mathbf{a} cdot mathbf{b} = 10 $ and $ mathbf{a} cdot mathbf{c} = 5 $, where $ mathbf{b} = egin{pmatrix} 2 \ 3 \end{pmatrix} $ and $ mathbf{c} = egin{pmatrix} 1 \ 4 \end{pmatrix} $.

Correct A. $ egin{pmatrix} 5 \ 2 \end{pmatrix} $

B. $ egin{pmatrix} 2 \ 5 \end{pmatrix} $

C. $ egin{pmatrix} 3 \ 4 \end{pmatrix} $

D. $ egin{pmatrix} 4 \ 3 \end{pmatrix} $

Correct Answer: A

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Question 20

Solve the \logarithmic equation $ \log_2 \( x^2 + 1 \ $ = 3 ).

Correct A. $ x = 7 $

B. $ x = -7 $

C. $ x = 3 $

D. $ x = -3 $

Correct Answer: A

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Question 21

Solve the system of linear equations u\sing matrices: [ egin{array}{ccc|c} 2 & 1 & -1 & 3 \ 1 & -1 & 2 & 0 \ 3 & -2 & 1 & 5 \end{array} ]. Find the value of x.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 22

A binary operation $ * $ on the set of integers is defined as: [ a * b = a^2 + b^2 ]. Find the value of $ 5 * 6 $.

Correct A. 37

B. 40

C. 41

D. 42

Correct Answer: A

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Question 23

A quadratic equation is given by: [ x^2 + 4x + 4 = 0 ]. Find the value of x.

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 24

A probability experiment consists of two indep\endent events A and B. The probability of event A occurring is 0.4 and the probability of event B occurring is 0.6. Find the probability of both events occurring.

Correct A. 0.24

B. 0.26

C. 0.28

D. 0.30

Correct Answer: A

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Question 25

A matrix is given by: [ \begin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix} \]. Find the determinant of the matrix.

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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