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POST UTME EKSU 2017 Mathematics | Objective

Are you preparing for POST UTME EKSU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

D. \( \frac{1}{2} \times 4^2 + 3 \times \frac{4^2}{2} - 2 \times 4 \)

Correct Answer: A

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Question 2

Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.

Correct A. \( x = \frac{-5 pm \sqrt{25 + 24}}{4} \)

B. \( x = \frac{-5 pm \sqrt{25 - 24}}{4} \)

C. \( x = \frac{-5 pm \sqrt{25 + 12}}{4} \)

D. \( x = \frac{-5 pm \sqrt{25 - 12}}{4} \)

Correct Answer: A

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Question 3

Find the derivative of the function \( y = \sin^2 x \) u\sing the chain rule.

Correct A. \( y' = 2 \sin x \cos x \)

B. \( y' = \sin x \cos x \)

C. \( y' = 2 \cos x \)

D. \( y' = \sin x \)

Correct Answer: A

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Question 4

A vector ( vec{a} ) has magnitude 5 and direction \( 30^circ \) from the positive x-axis. Find the vector ( vec{a} ) in component form.

Correct A. \( vec{a} = 5 \cos 30^circ hat{i} + 5 \sin 30^circ hat{j} \)

B. \( vec{a} = 5 \sin 30^circ hat{i} + 5 \cos 30^circ hat{j} \)

C. \( vec{a} = 5 \cos 30^circ hat{j} + 5 \sin 30^circ hat{i} \)

D. \( vec{a} = 5 \sin 30^circ hat{j} + 5 \cos 30^circ hat{i} \)

Correct Answer: A

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Question 5

A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).

Correct A. \( 2 ast 3 = 2^2 + 3^2 = 13 \)

B. \( 2 ast 3 = 2^2 - 3^2 = -5 \)

C. \( 2 ast 3 = 2^2 + 3^2 + 2 \times 2 \times 3 = 25 \)

D. \( 2 ast 3 = 2^2 + 3^2 - 2 \times 2 \times 3 = 1 \)

Correct Answer: A

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Question 6

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 7

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).

Correct A. -2

B. -3

C. -1

D. 1

Correct Answer: A

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Question 8

Find the value of \( \log_{10} \( x^2 \ \) ) if \( x = 10 \).

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 9

A histogram is a graphical representation of the distribution of a set of data. What is the primary purpose of a histogram?

A. To show the mean of a data set

B. To show the median of a data set

Correct C. To show the distribution of a data set

D. To show the s\tandard deviation of a data set

Correct Answer: C

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Question 10

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

Correct A. \( x > -1 \) or \( x < 3 \)

B. \( x > 1 \) or \( x < -3 \)

C. \( x > 3 \) or \( x < -1 \)

D. \( x > -3 \) or \( x < 1 \)

Correct Answer: A

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Question 11

Find the value of 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

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

A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

Correct C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 1 \) ∪ (3, ∞)

Correct Answer: C

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Question 13

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 14

Solve the system of equations \( egin{cases} x + y = 4 \ 2x - y = 3 \end{cases} \).

Correct A. (1, 3)

B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: A

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Question 15

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

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 16

Find the equation of the line pas\sing through the points (2,3) and (4,5) in the vector form \( vec{r} = vec{a} + tvec{b} \), where (vec{a}) is the position vector of the point (2,3) and (vec{b}) is a direction vector of the line.

Correct A. \( vec{r} = egin{pmatrix} 2 \ 3 \end{pmatrix} + t egin{pmatrix} 2 \ 2 \end{pmatrix} \)

B. \( vec{r} = egin{pmatrix} 2 \ 3 \end{pmatrix} + t egin{pmatrix} 1 \ 1 \end{pmatrix} \)

C. \( vec{r} = egin{pmatrix} 2 \ 3 \end{pmatrix} + t egin{pmatrix} 2 \ -1 \end{pmatrix} \)

D. \( vec{r} = egin{pmatrix} 2 \ 3 \end{pmatrix} + t egin{pmatrix} 1 \ 2 \end{pmatrix} \)

Correct Answer: A

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Question 17

Solve the system of equations \( egin{cases} x + y + z = 6 \ 2x + 3y + z = 12 \ x + 2y + 3z = 8 \end{cases} \) u\sing the method of elimination.

Correct A. \( egin{cases} x = 2 \ y = 1 \ z = 3 \end{cases} \)

B. \( egin{cases} x = 1 \ y = 2 \ z = 3 \end{cases} \)

C. \( egin{cases} x = 3 \ y = 2 \ z = 1 \end{cases} \)

D. \( egin{cases} x = 2 \ y = 3 \ z = 1 \end{cases} \)

Correct Answer: A

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Question 18

Find the equation of the circle with center at (2,3) and radius 4 in the form \( x - h \ \)^2 + \( y - k \)^2 = r^2).

Correct A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )

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

D. \( x - 3 \ \)^2 + \( y - 3 \)^2 = 16 )

Correct Answer: A

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Question 19

A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.

Correct A. ( 24 )

B. ( 26 )

C. ( 28 )

D. ( 30 )

Correct Answer: A

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Question 20

A random experiment has 3 possible outcomes: A, B, and C. If the probability of outcome A is 0.4, the probability of outcome B is 0.3, and the probability of outcome C is 0.3, find the probability that outcome A occurs.

Correct A. ( 0.4 )

B. ( 0.3 )

C. ( 0.2 )

D. ( 0.1 )

Correct Answer: A

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Question 21

Solve the inequality \( |x - 2| > 3 \).

Correct A. \( x < -1 \text{ or } x > 5 \)

B. \( x < 1 \text{ or } x > 5 \)

C. \( x < -1 \text{ or } x > 2 \)

D. \( x < 1 \text{ or } x > 2 \)

Correct Answer: A

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Question 22

Find the value of (x) in the equation \( 2^x = 16 \).

A. ( 2 )

Correct B. ( 3 )

C. ( 4 )

D. ( 5 )

Correct Answer: B

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Question 23

A set of 4 numbers has a mean of 12 and a range of 8. If the largest number is 18, find the sum of the remaining 3 numbers.

Correct A. ( 36 )

B. ( 38 )

C. ( 40 )

D. ( 42 )

Correct Answer: A

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Question 24

Find the equation of the circle with center at ((2,3)) and radius (5).

Correct A. \( x^2 + y^2 - 4x + 6y + 9 = 0 \)

B. \( x^2 + y^2 + 4x - 6y + 9 = 0 \)

C. \( x^2 + y^2 - 4x - 6y + 9 = 0 \)

D. \( x^2 + y^2 + 4x + 6y + 9 = 0 \)

Correct Answer: A

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Question 25

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

Correct A. \( x = 10^4 \)

B. \( x = 10^2 \)

C. \( x = 10^8 \)

D. \( x = 10^6 \)

Correct Answer: A

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