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POST UTME NILE UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

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

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

B. ( 3 )

C. ( 4 )

Correct D. ( 6 )

Correct Answer: D

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Question 2 View Details

A set of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?

A. 0.68

B. 0.84

Correct C. 0.95

D. 0.99

Correct Answer: C

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Question 3 View Details

Find the derivative of the function $y = \sin^2 x \$ ) using the chain rule.

Correct A. $2$1x$\cos(x \) )

B. $\cos^2 x \$ )

C. $\sin^2 x \$ )

D. $\tan^2 x \$ )

Correct Answer: A

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Question 4 View Details

Solve the equation $$1x \$ = $\frac{1}{2}$\) ) for ( x ) in the interval ( [0, 2pi] ).

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

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

C. $\frac{5\pi}{6}$

D. $\frac{7\pi}{6}$

Correct Answer: B

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Question 5 View Details

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

A. ( 15 )

B. ( 25 )

C. ( 35 )

Correct D. ( 45 )

Correct Answer: D

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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. 24\pi $cm^3$

B. 36\pi $cm^3$

Correct C. 48\pi $cm^3$

D. 60\pi $cm^3$

Correct Answer: C

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Question 7 View Details

Solve for x in the equation $\begin{array}{rcl} 2x + 5 & = & 11 \ 3x - 2 & = & 7 \ \hline \end{array}$

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 8 View Details

Find the surface area of the sphere with radius 5 cm.

A. 100\pi $cm^2$

B. 150\pi $cm^2$

Correct C. 200\pi $cm^2$

D. 250\pi $cm^2$

Correct Answer: C

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Question 9 View Details

Solve the system of equations $\begin{array}{rcl} x + y + z & = & 6 \ x + 2y + 3z & = & 11 \ 2x + 3y + 4z & = & 14 \ \hline \end{array}$

Correct A. [1, 2, 3]

B. [2, 3, 1]

C. [3, 1, 2]

D. [4, 2, 0]

Correct Answer: A

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Question 10 View Details

Find the value of $\frac{1}{2} \int_{0}^{2} 2x + 1$ dx\)

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 11 View Details

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

A. 12

B. 16

Correct C. 20

D. 24

Correct Answer: C

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Question 12 View Details

Solve the system of equations $\begin{cases} x + y = 4 \ x - 2y = -3 \end{cases}$.

Correct A. (1, 3)

B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: A

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Question 13 View Details

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

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 14 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. $1/2$

B. $1/3$

Correct C. $2/3$

D. $1/6$

Correct Answer: C

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Question 15 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. $y = -2x + 1$

D. $y = -2x - 1$

Correct Answer: A

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Question 16 View Details

In the given diagram, what is the value of x?

A. 1

Correct B. $\frac{\sqrt{3}}{2}$

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

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

Correct Answer: B

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Question 17 View Details

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

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 18 View Details

A set of numbers has a mean of 10 and a standard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?

A. 0.25

B. 0.5

C. 0.75

Correct D. 0.9

Correct Answer: D

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Question 19 View Details

A right circular cylinder has a height of 10 cm and a radius of 5 cm. What is its volume?

A. 500\pi

Correct B. 1000\pi

C. 2000\pi

D. 5000\pi

Correct Answer: B

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Question 20 View Details

A sequence is defined as: 1, 2, 4, 8, 16, ... . What is the next term in the sequence?

A. 32

B. 64

C. 128

Correct D. 256

Correct Answer: D

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Question 21 View Details

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

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

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

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

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

Correct Answer: A

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Question 22 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$ using the quadratic formula.

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

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

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

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

Correct Answer: A

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Question 23 View Details

Find the area of the triangle with vertices ( A(0, 0), B(3, 0), C(0, 2) ) using the formula for the area of a triangle.

A. $A = 3$

Correct B. $A = 6$

C. $A = 9$

D. $A = 12$

Correct Answer: B

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Question 24 View Details

Solve the system of equations $x + y = 2, x - y = 1$ using the method of substitution.

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 25 View Details

Find the derivative of the function ( f(x) = $x^2$ \sin x ) using the product rule.

Correct A. f'$(x) = 2x$\sin x + $x^2$ \cos x

B. f'$(x) = 2x$\sin x - $x^2$ \cos x

C. f'$(x) =$$x^2$ \sin x - 2x \cos x

D. f'$(x) =$$x^2$ \sin x + 2x \cos x

Correct Answer: A

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