Exam Body

Year

Subject

Paper Type

POST UTME ESUT 2017 Mathematics | Objective

Are you preparing for POST UTME ESUT 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 determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

A. -120

B. 120

Correct C. 0

D. -60

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2

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

Correct A. \( x \leq -1 \) or \( x \geq \frac{3}{2} \)

B. \( x \geq -1 \) or \( x \leq \frac{3}{2} \)

C. \( x \leq -1 \) or \( x \geq -\frac{3}{2} \)

D. \( x \geq -1 \) or \( x \leq -\frac{3}{2} \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3

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

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4

Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \).

Correct A. \( x = \frac{3}{2}, y = \frac{1}{2} \)

B. \( x = \frac{1}{2}, y = \frac{3}{2} \)

C. \( x = 1, y = 1 \)

D. \( x = 2, y = 0 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5

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 = 9 \)

D. \( x - 3 \)^2 + \( y - 2 \)^2 = 9 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6

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

A. 24πcm³

Correct B. 48πcm³

C. 96πcm³

D. 192πcm³

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7

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

Correct A. \( -∞, -1 \) ∪ [3, ∞)

B. \( -∞, -3 \) ∪ [1, ∞)

C. \( -∞, -3 \) ∪ \( -1, ∞ \)

D. \( -∞, 3 \) ∪ [1, ∞)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8

Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...

A. 1040

Correct B. 1080

C. 1120

D. 1160

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9

Solve the system of equations x + y = 4 and x - 2y = -3.

Correct A. (1, 3)

B. (3, 1)

C. \( -1, -3 \)

D. \( 3, -1 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10

Find the area of the triangle with vertices (2, 3), (4, 5), and (6, 7).

A. 9

Correct B. 10

C. 11

D. 12

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11

Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).

Correct A. \( x^2 + y^2 - 12x - 16y + 40 = 0 \)

B. \( x^2 + y^2 - 10x - 12y + 20 = 0 \)

C. \( x^2 + y^2 - 14x - 20y + 60 = 0 \)

D. \( x^2 + y^2 - 12x - 14y + 30 = 0 \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12

Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).

Correct A. \( x in \( -infty, -3 \ \) cup (3, infty) )

B. \( x in \( -infty, -3 \ \) cup (3, infty) cup {0} )

C. \( x in \( -infty, -3 \ \) cup (3, infty) cup {0, 2} )

D. \( x in \( -infty, -3 \ \) cup (3, infty) cup {0, 2, 4} )

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \( \frac{1}{4} \)

B. \( \frac{1}{5} \)

Correct C. \( \frac{3}{8} \)

D. \( \frac{1}{2} \)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14

Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.

A. \( \frac{4}{3} pi \)

B. \( \frac{8}{3} pi \)

Correct C. \( \frac{16}{3} pi \)

D. \( \frac{32}{3} pi \)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. \( -1 \)

B. ( 0 )

C. ( 1 )

D. ( 2 )

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 5.5 \cdot 10^6

B. 1.6 \cdot 10^7

Correct C. 3.2 \cdot 10^7

D. 6.3 \cdot 10^7

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17

Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0.

A. \left\( -\infty, -1 \right \) \cup \left\( 1, \infty \right \)

B. \left\( -\infty, -3 \right \) \cup \left\( 1, \infty \right \)

Correct C. \left\( -\infty, -3 \right \) \cup \left\( -1, 1 \right \) \cup \left\( 1, \infty \right \)

D. \left\( -\infty, -3 \right \) \cup \left\( 1, \infty \right \)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18

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

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19

Solve the system of equations \begin{align*} x + y &= 2 \ x - y &= 1 \end{align*}.

Correct A. \left\( 1, 1 \right \)

B. \left\( 1, -1 \right \)

C. \left\( -1, 1 \right \)

D. \left\( -1, -1 \right \)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20

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

Correct A. 3x^2 - 4x + 1

B. 3x^2 - 4x - 1

C. 3x^2 + 4x - 1

D. 3x^2 - 4x + 2

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2 \cdot \frac{3^{10} - 1}{3 - 1}

B. 2 \cdot \frac{3^{11} - 1}{3 - 1}

C. 2 \cdot \frac{3^{12} - 1}{3 - 1}

D. 2 \cdot \frac{3^{13} - 1}{3 - 1}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22

Solve the system of equations u\sing matrices: \begin{align*} x + y + z &= 6, \ x + 2y + 3z &= 11, \ x + 3y + 6z &= 16. \end{align*}

A. \begin{bmatrix} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 3 & 6 \end{bmatrix}

B. \begin{bmatrix} 1 & 2 & 3 \ 1 & 3 & 6 \ 1 & 6 & 11 \end{bmatrix}

Correct C. \begin{bmatrix} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 3 & 6 \end{bmatrix}^{-1}

D. \begin{bmatrix} 1 & 2 & 3 \ 1 & 3 & 6 \ 1 & 6 & 11 \end{bmatrix}^{-1}

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?

A. \frac{1}{3}

Correct B. \frac{1}{4}

C. \frac{1}{6}

D. \frac{1}{12}

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25

Find the magnitude of the vector \begin{bmatrix} 3 \ 4 \end{bmatrix}.

Correct A. \sqrt{25}

B. \sqrt{26}

C. \sqrt{27}

D. \sqrt{28}

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support