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POST UTME UNILORIN 2024 Mathematics | Objective

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Question 1 View Details

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

Correct A. ( f'$(x) =$$\frac{-x}${ $x^2 + 1$ \)^{$3/2$}}\) )

B. ( f'$(x) =$$\frac{x}${ $x^2 + 1$ \)^{$3/2$}}\) )

C. ( f'$(x) =$$\frac{1}${ $x^2 + 1$ \)^{$3/2$}}\) )

D. ( f'$(x) =$$\frac{x^2}$\){ $x^2 + 1$ \)^{$3/2$}}\) )

Correct Answer: A

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Question 2 View Details

Solve the system of equations using matrices: $egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix}$.

A. $egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix}$

Correct B. $egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix}$

C. $egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} -1 \ 3 \end{bmatrix}$

D. $egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ -2 \end{bmatrix}$

Correct Answer: B

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Question 3 View Details

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

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

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

C. $\frac{\pi}{6}$

D. $\frac{\pi}{8}$

Correct Answer: A

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Question 4 View Details

A particle moves along the x-axis with its position given by ( x(t) = $(2t^2 + 3t - 1$\) ). Find the velocity of the particle at time $t = 1\\((2t^2 + 3t - 1) ). Find the velocity of the particle at time$.

Correct A. $( v(1) = 5 )$

B. $( v(1) = 7 )$

C. $( v(1) = 9 )$

D. $( v(1) = 11 )$

Correct Answer: A

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Question 5 View Details

A company produces two products, A and B. The profit from producing x units of A and y units of B is given by ( P(x, y) = 2x + 3y - xy ). Find the maximum profit when $x = 10$ and $y = 20$.

A. ( P(10,$20) = 100 )$

Correct B. ( P(10,$20) = 120 )$

C. ( P(10,$20) = 140 )$

D. ( P(10,$20) = 160 )$

Correct Answer: B

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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. 48\pi $cm^3$

B. 64\pi $cm^3$

Correct C. 80\pi $cm^3$

D. 96\pi $cm^3$

Correct Answer: C

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Question 7 View Details

A particle moves in a straight line with a velocity of 5 $(m/s$\). Find its acceleration after 2 seconds, given that its initial velocity is 2 $m/s\\((m/s). Find its acceleration after 2 seconds, given that its initial velocity is 2$.

A. 1.5 $m/s\^2$

B. 2 $m/s\^2$

Correct C. 2.5 $m/s\^2$

D. 3 $m/s\^2$

Correct Answer: C

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Question 8 View Details

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

Correct A. $y - 2 = 4$$x - 1$

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

C. $y - 2 = 3$$x - 1$

D. $y - 2 = 5$$x - 1$

Correct Answer: A

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Question 9 View Details

A histogram has a mean of 25 and a standard deviation of 5. Find the probability that a randomly selected value lies between 20 and 30.

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 10 View Details

Solve the inequality \$(x^2 - 4x - 5$$> 0.$\)

Correct A. $x < -1$, $x > 5$

B. $x < -1$, $x < 5$

C. $x > -1$, $x > 5$

D. $x < -1$, $x < 0$

Correct Answer: A

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Question 11 View Details

In the vector equation $\mathbf{r} = \mathbf{a} + t \mathbf{b}), where ( mathbf{a} ) and ( mathbf{b} ) are vectors, and ( t ) is a scalar, find the vector ( mathbf{r} ) when \(\mathbf{a} = 2 \\(), where ( mathbf{a} ) and ( mathbf{b} ) are vectors, and ( t ) is a scalar, find the vector ( mathbf{r} ) when (\mathbf{i} + 3 \mathbf{j}$, mathbf{b}$= mathbf${i} - 2 mathbf{j}\), and $t = 3$.

Correct A. 9\mathbf{i} + 5\mathbf{j}

B. 6\mathbf{i} + 7\mathbf{j}

C. 8\mathbf{i} + 9\mathbf{j}

D. 10\mathbf{i} + 11\mathbf{j}

Correct Answer: A

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Question 12 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 13 View Details

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. $x - 3$^2 + $y - 4$^$2 = 25$

B. $x - 4$^2 + $y - 3$^$2 = 25$

C. $x - 5$^2 + $y - 3$^$2 = 25$

D. $x - 3$^2 + $y - 5$^$2 = 25$

Correct Answer: A

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Question 14 View Details

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

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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Question 15 View Details

Find the volume of the cylinder with radius ( 4 ) and height ( 6 ).

Correct A. 48\pi

B. 64\pi

C. 72\pi

D. 80\pi

Correct Answer: A

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Question 16 View Details

A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. If the population standard deviation is 6 cm, calculate the standard error of the mean.

A. 2.5 cm

Correct B. 3.5 cm

C. 4.5 cm

D. 5.5 cm

Correct Answer: B

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Question 17 View Details

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 18 View Details

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Calculate its volume.

A. 400 $cm^3$

B. 500 $cm^3$

Correct C. 600 $cm^3$

D. 800 $cm^3$

Correct Answer: C

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Question 19 View Details

A sequence is defined as $a_n = 2n + 1$. Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 20 View Details

Find the derivative of the function $f(x) = 3x^2 + 2x - 5$ using the power rule.

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 21 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x\^2$, $y = 0$, and $x = 2$ about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 22 View Details

A fair six-sided die is rolled. What is the probability that the product of the numbers on the two dice is a multiple of 3?

A. $\frac{1}{3}$\)

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

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

D. $\frac{5}{6}$\)

Correct Answer: C

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Question 23 View Details

Find the area under the curve $y = x\^3 - 6x^2 + 9x + 2$ from $x = 0$ to $x = 1$.

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

B. $\frac{3}{2}$\)

Correct C. $\frac{5}{2}$\)

D. $\frac{7}{2}$\)

Correct Answer: C

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Question 24 View Details

A vector $\vec{a} = 2\hat{i} + 3\hat{j} + 4\hat{k} and a vector \vec{b} = -1\hat{i} + 2\hat{j} - 3hat{k}$. Find the cross product of $\\(hat{k}). Find the cross product of \vec{a}$ and $\vec{b}$.

Correct A. \hat{i} - \hat{j} + \hat{k}

B. \hat{i} + \hat{j} + \hat{k}

C. \hat{i} - \hat{j} - \hat{k}

D. \hat{i} + \hat{j} - \hat{k}

Correct Answer: A

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Question 25 View Details

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

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

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

C. $x = 3$,$y = -1$

D. $x = -1$, $y = 3$

Correct Answer: A

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