Exam Body

Year

Subject

Paper Type

POST UTME FUTA 2024 Mathematics | Objective

Are you preparing for POST UTME FUTA exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2(x)} dx$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: A

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

Question 2

A histogram of exam scores is shown below. If the mean score is 75, and the s\tandard deviation is 10, what is the probability that a randomly selected score will be between 60 and 90?

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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

Question 3

Solve for $x$: $\tan(x) = \sqrt{3}$.

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

B. \frac{\pi}{6}

C. \frac{\pi}{2}

D. \frac{\pi}{4}

Correct Answer: A

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

Question 4

A vector $\vec{a}$ has components $a_x = 3$ and $a_y = 4$. Find the magnitude of $\vec{a}$.

A. 5

B. \sqrt{5}

Correct C. \sqrt{25}

D. \sqrt{50}

Correct Answer: C

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

Question 5

Two events $A$ and $B$ are indep\endent. If $P(A) = 0.4$ and $P(B) = 0.6$, what is the probability that both events occur?

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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

Question 6

In a certain number base $b$, the number $1011_5$ is equivalent to $3b^3 + 4b^2 + 2b + 1$ in base $10$. Find the value of $b$.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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

Question 7

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers obtained is $7$?

A. 1/6

B. 1/12

Correct C. 1/36

D. 1/18

Correct Answer: C

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

Question 8

Let $S$ be the set of all positive integers $n$ such that $n$ is a multiple of $3$ and $n$ is a power of $2$. Which of the following is the smallest element of $S$?

A. 1

B. 2

C. 4

Correct D. 8

Correct Answer: D

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

Question 9

The sequence $a_n$ is defined recursively by $a_n = 2a_{n-1} + 1$ for $n ge 2$, with $a_1 = 3$. Find the value of $a_{10}$.

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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

Question 10

The quadratic equation $x^2 + bx + c = 0$ has roots $x = 1$ and $x = -2$. Find the value of $b$.

Correct A. -3

B. -2

C. -1

D. 1

Correct Answer: A

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

Question 11

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].

Correct A. -2

B. 4

C. 6

D. 8

Correct Answer: A

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

Question 12

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

Correct A. x = \frac{-5 \pm \sqrt{5^2 - 4$ 2)\( -3 \ $}}{2(2)}

B. x = \frac{-5 \pm \sqrt{5^2 - 4(2)(3)}}{2(2)}

C. x = \frac{-5 \pm \sqrt{5^2 - 4$ 2)\( -3 \ $}}{2(2)}

D. x = \frac{-5 \pm \sqrt{5^2 - 4(2)(3)}}{2(2)}

Correct Answer: A

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

Question 13

Find the value of [ \sin(2x) \] given that [ \sin(x) = \frac{1}{2} \].

Correct A. \cos(x)

B. \sin(x)

C. \cos(2x)

D. \sin(2x)

Correct Answer: A

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

Question 14

Solve the inequality [ 2x - 5 > 3 ].

Correct A. x > \frac{8}{2}

B. x < \frac{8}{2}

C. x > \frac{8}{2}

D. x < \frac{8}{2}

Correct Answer: A

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

Question 15

Find the value of [ \cos(2x) \] given that [ \cos(x) = \frac{1}{2} \].

A. \cos(x)

B. \sin(x)

Correct C. \cos(2x)

D. \sin(2x)

Correct Answer: C

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

Question 16

Solve the equation [ x^2 + 4x + 4 = 0 ].

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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

Question 17

Find the value of [ \tan(2x) \] given that [ \tan(x) = \frac{1}{2} \].

A. \tan(x)

B. \sin(x)

C. \cos(x)

Correct D. \tan(2x)

Correct Answer: D

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

Question 18

Solve the inequality [ 3x + 2 > 7 ].

Correct A. x > \frac{5}{3}

B. x < \frac{5}{3}

C. x > \frac{5}{3}

D. x < \frac{5}{3}

Correct Answer: A

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

Question 19

Find the value of [ \sin(2x) \] given that [ \sin(x) = \frac{1}{3} \].

A. \cos(x)

B. \sin(x)

C. \cos(2x)

Correct D. \sin(2x)

Correct Answer: D

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

Question 20

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

A. 12

Correct B. 16

C. 20

D. 24

Correct Answer: B

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

Question 21

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

Correct A. 1

B. -1

C. -2

D. 2

Correct Answer: A

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

Question 22

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 23

Find the vector projection of vector →b = →(2, 3) onto vector →a = →(4, 5).

Correct A. \\u2192$ \\frac{29}{41}, \\frac{50}{41} $

B. \\u2192$ \\frac{29}{41}, -\\frac{50}{41} $

C. \\u2192$ -\\frac{29}{41}, \\frac{50}{41} $

D. \\u2192$ -\\frac{29}{41}, -\\frac{50}{41} $

Correct Answer: A

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

Question 24

Find the sum of the infinite geometric series \sum_{n=1}^\infty \frac{1}{2^n}.

A. 1

Correct B. \frac{1}{2}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: B

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

Question 25

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

Correct A. x = \frac{\pi}{2}

B. x = \frac{\pi}{4}

C. x = \\frac{3\\pi}{4}

D. x = \\frac{5\\pi}{4}

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