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POST UTME KSU 2024 Mathematics | Objective

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Question 1 View Details

Let ( f(x) = $\frac{1}{1 + \sin^2$ x}\)\) ). Find ( f'(x) ) using the chain rule.

Correct A. $f'(x) = \frac{-2 \(1x$1x}{1 + \$sin^2$ x ^2}\)

B. $f'(x) = \frac{2 \(1x$1x}{1 + \$sin^2$ x ^2}\)

C. $f'(x) = \frac{$1x}{1 + \sin^2 x ^2}$

D. $f'(x) = \frac{$1x}{1 + \sin^2 x ^2}$

Correct Answer: A

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Question 2 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?

A. P(\text{multiple of 3} = $\frac{1}{3}$\$(text{multiple of 3} =$

Correct B. P(\text{multiple of 3} = $\frac{2}{6}$\$(text{multiple of 3} =$

C. P(\text{multiple of 3} = $\frac{1}{2}$\$(text{multiple of 3} =$

D. P(\text{multiple of 3} = $\frac{3}{6}$\$(text{multiple of 3} =$

Correct Answer: B

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Question 3 View Details

Solve the inequality $2x^2 - 5x - 3 > 0$.

Correct A. $x < -1$\text{ or }$x >$$\frac{3}{2}$\)

B. $x < -1$\text{ or }$x <$$\frac{3}{2}$\)

C. $x > -1$\text{ or }$x >$$\frac{3}{2}$\)

D. $x < -1$\text{ and }$x >$$\frac{3}{2}$\)

Correct Answer: A

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Question 4 View Details

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

Correct A. $10$

B. $-10$

C. $20$

D. $-20$

Correct Answer: A

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Question 5 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. $A = 16\pi \text{cm}^2$

B. $A = 32\pi \text{cm}^2$

C. $A = 64\pi \text{cm}^2$

D. $A = 128\pi \text{cm}^2$

Correct Answer: A

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Question 6 View Details

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 7 View Details

Solve for ( x ) in the equation $2^x + 3^x = 5^x$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 8 View Details

Find the value of $\log_{10} x^2 \$ ) given that $\log_{10} x = 2$.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 9 View Details

A particle moves in a straight line with a velocity ( v(t) = 2t + 5 ) $(m/s$\). Find the displacement of the particle from $t = 0\\((m/s). Find the displacement of the particle from$ to $t = 3$ seconds.

A. 21

B. 25

Correct C. 30

D. 35

Correct Answer: C

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Question 10 View Details

Solve the system of equations: $x + y = 4$ and $xy = 5$.

Correct A. 1, 3

B. 2, 2

C. 3, 1

D. 4, 0

Correct Answer: A

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Question 11 View Details

Let ( X ) and ( Y ) be independent random variables with probability density functions $f_X x \$ = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ) and $f_Y y \$ = egin{cases} $3y^2$ & 0 leq y leq 1 \ 0 & text{otherwise} \end{cases} ). Find the probability that $X + Y \\(text{otherwise} end{cases} ). Find the probability that \leq 1$.

Correct A. $\frac{1}{2}$

B. $\frac{1}{3}$

C. $\frac{2}{3}$

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

Correct Answer: A

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Question 12 View Details

Solve the inequality $\log_{10} x^2 \$$> 2 ).$

Correct A. $x > 10$

B. $x < 10$

C. $x > 100$

D. $x < 100$

Correct Answer: A

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Question 13 View Details

Find the area under the curve $y = $1x$ from $x = 0$ to $x = \frac{\pi}{2}$.

Correct A. ( 1 )

B. $\frac{1}{2}$

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

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

Correct Answer: A

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Question 14 View Details

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

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

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

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

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

Correct Answer: A

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Question 15 View Details

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

Correct A. $x = -2$

B. $x = 2$

C. $x = -1$

D. $x = 1$

Correct Answer: A

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Question 16 View Details

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

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 17 View Details

Solve the system of equations: $2x + 3y = 7$ and $x - 2y = -3$.

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

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

C. $x = 3$, $y = 4$

D. $x = 4$, $y = 3$

Correct Answer: A

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Question 18 View Details

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

A. 0

Correct B. 2

C. 4

D. 6

Correct Answer: B

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Question 19 View Details

Find the sum of the infinite geometric series $1 + \frac{1}{2} + \frac{1}{4} + \cdots$.

Correct A. 2

B. 4

C. 6

D. 8

Correct Answer: A

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Question 20 View Details

Find the equation of the line passing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. $y = 2x - 1$

B. $y = 2x + 1$

C. $y = x - 1$

D. $y = x + 1$

Correct Answer: A

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Question 21 View Details

Solve the inequality ($\frac{x}{x-1}\(> 1$\) for \$(frac{x}{x-1} > 1\(x > 1$\).

Correct A. $x > 2$

B. $x > 3$

C. $x > 4$

D. $x > 5$

Correct Answer: A

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Question 22 View Details

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 + $y - 3$^$2 = 25$

C. $x - 2$^2 + $y - 3$^$2 = 36$

D. $x - 2$^2 + $y - 3$^$2 = 49$

Correct Answer: A

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Question 23 View Details

A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 1$, with initial term $a_1 = 3$. Find the sum of the first five terms of the sequence.

Correct A. 3 + 7 + 15 + 31 + 63

B. 3 + 5 + 11 + 23 + 47

C. 3 + 7 + 15 + 31 + 63

D. 3 + 5 + 11 + 23 + 47

Correct Answer: A

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Question 24 View Details

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

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

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

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

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

Correct Answer: A

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Question 25 View Details

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

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

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

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

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

Correct Answer: B

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