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POST UTME FUTA 2023 Mathematics | Objective

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Question 1 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 2 View Details

A particle moves in a straight line with an initial velocity of 5 $(m/s$\). If it decelerates uniformly at a rate of 2 $m/s\\((m/s). If it decelerates uniformly at a rate of 2 \^2$, find its velocity after 4 seconds.

A. 3 $m/s$

Correct B. 4 $m/s$

C. 5 $m/s$

D. 6 $m/s$

Correct Answer: B

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Question 3 View Details

Find the value of x in the quadratic equation $x^2 + 4x + 4 = 0$.

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 4 View Details

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. $\frac{1}{5}$\)

D. $\frac{1}{6}$\)

Correct Answer: B

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Question 5 View Details

Solve the system of equations $x + y = 2$ and $x - y = 1$.

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

B. $x = 1$, $y = 2$

C. $x = 2$, $y = 1$

D. $x = 2$, $y = 2$

Correct Answer: A

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Question 6 View Details

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

A. 12π cm³

Correct B. 24π cm³

C. 36π cm³

D. 48π cm³

Correct Answer: B

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Question 7 View Details

Solve the inequality $x^2 + 4x - 5 > 0$.

A. $-∞, -5$ ∪ (1, ∞)

Correct B. $-∞, -5$ ∪ (1, ∞)

C. $-∞, -5$ \cup $-1, ∞$\)

D. $-∞, -5$ ∪ (1, ∞)

Correct Answer: B

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Question 8 View Details

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

Correct A. $\frac{2x x^2 + 1$ \ - $2x^3}{$ $x^2 + 1$ ^2}\)\) )

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

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

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

Correct Answer: A

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Question 9 View Details

Evaluate the definite integral $int_0^1 x^2 $1x dx$.

A. $\left[ -x^2 \(1x + 2$1x $1x dx \right]_$0^1$\)

B. $\left[ -x^2 \(1x + 2$1x $1x dx \right]_$0^1$\)

C. $\left[ -x^2 \(1x + 2x$1x + 2 $1x \right]_$0^1$\)

Correct D. $\left[ -x^2 \(1x + 2x$1x + 2 $1x \right]_$0^1$\)

Correct Answer: D

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Question 10 View Details

Solve the equation $$12x = \frac{1}{2}$.

A. $x = \frac{\pi}{12} + \frac{k \pi}{2}$

B. $x = \frac{\pi}{12} + \frac{k \pi}{2}$

C. $x = \frac{\pi}{6} + \frac{k \pi}{2}$

Correct D. $x = \frac{\pi}{6} + \frac{k \pi}{2}$

Correct Answer: D

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Question 11 View Details

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

Correct A. $x =$$\frac{\pi}{4}$\)

B. $x =$\$\frac{3\pi}{4}$\)

C. $x =$\$\frac{5\pi}{4}$\)

D. $x =$\$\frac{7\pi}{4}$\)

Correct Answer: A

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Question 12 View Details

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

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 13 View Details

Solve the quadratic equation $x^2 + 5x + 6 = 0$ using the quadratic formula.

A. $x = -2$

Correct B. $x = -3$

C. $x = -1$

D. $x = 1$

Correct Answer: B

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Question 14 View Details

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

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 15 View Details

Solve the inequality $x^2 - 4x + 4 > 0$ using algebraic manipulation.

A. $x < 0$

B. $x > 0$

Correct C. $x < 2$

D. $x > 2$

Correct Answer: C

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Question 16 View Details

Find the value of ( x ) in the equation $$1x = \frac{1}{2}$ using trigonometric identities.

Correct A. $x =$$\frac{\pi}{6}$\)

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

C. $x =$$\frac{\pi}{3}$\)

D. $x =$$\frac{\pi}{2}$\)

Correct Answer: A

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Question 17 View Details

Solve the system of equations $x + y = 2$ and $x - y = 1$ using algebraic manipulation.

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

B. $x = 1$,$y = -1$

C. $x = -1$, $y = 1$

D. $x = -1$,$y = -1$

Correct Answer: A

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Question 18 View Details

Find the area under the curve $y = x^3$ from $x = 0$ to $x = 2$ using integration.

A. 8

B. 16

Correct C. 32

D. 64

Correct Answer: C

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Question 19 View Details

Solve the inequality $x^2 + 2x - 3 > 0$ using algebraic manipulation.

A. $x < -3$

B. $x > -3$

Correct C. $x < 1$

D. $x > 1$

Correct Answer: C

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Question 20 View Details

Find the equation of the circle passing through the points (2, 3), (4, 1), and $-1, 2$.

Correct A. \left$x - 1 \right$^2 + \left$y - 2 \right$^$2 = 13$

B. \left$x + 1 \right$^2 + \left$y - 2 \right$^$2 = 13$

C. \left$x - 1 \right$^2 + \left$y + 2 \right$^$2 = 13$

D. \left$x + 1 \right$^2 + \left$y + 2 \right$^$2 = 13$

Correct Answer: A

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Question 21 View Details

A rectangular box has dimensions 3 cm, 4 cm, and 5 cm. Find the volume of the box.

A. 60 $cm^3$

B. 80 $cm^3$

Correct C. 100 $cm^3$

D. 120 $cm^3$

Correct Answer: C

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Question 22 View Details

Solve the equation \$tan x =$$\sqrt{3}$ \sin x.

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

Correct B. $\frac{\pi}{3}$\)

C. $\frac{\pi}{2}$\)

D. $\frac{\pi}{6}$\)

Correct Answer: B

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Question 23 View Details

Find the equation of the line passing through the points (2, 3) and (4, 1).

Correct A. $y = -$$\frac{1}{2}$\) x + 5

B. $y =$$\frac{1}{2}$\) x + 3

C. $y = -2x + 7$

D. $y = 2x - 1$

Correct Answer: A

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Question 24 View Details

A polynomial function f(x) has zeros at x = -2, $x = 1$, and $x = 3$. Write the function in factored form.

Correct A. $f(x) =$$x + 2$, x - 1\)$x - 3$

B. $f(x) =$$x - 2$, x + 1\)$x - 3$

C. $f(x) =$$x + 2$, x + 1\)$x - 3$

D. $f(x) =$$x - 2$, x - 1\)$x + 3$

Correct Answer: A

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Question 25 View Details

Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}.

A. 10

Correct B. 12

C. 15

D. 20

Correct Answer: B

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