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POST UTME AFE BABALOLA UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

In a circle with center at point O and radius 6 units, what is the length of the arc intercepted by a central angle of 60 degrees?

Correct A. 6\pi

B. 3\pi

C. 2\pi

D. \pi

Correct Answer: A

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Question 2 View Details

Find the sum of the first 10 terms of the arithmetic sequence 3, 6, 9, ...

A. 60

B. 90

Correct C. 120

D. 150

Correct Answer: C

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Question 3 View Details

Solve the system of linear equations:\begin{align*} x + y &= 4 \ 2x - 3y &= -1 \end{align*}

Correct A. (1, 3)

B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: A

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Question 4 View Details

A histogram is constructed with a bin width of 5 units. If the mean of the data is 15 and the median is 10, what is the mode?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 5 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 6 View Details

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7 View Details

Solve the matrix equation $egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix}$.

Correct A. $x = 3$, $y = 2$

B. $x = 2$, $y = 3$

C. $x = 1$, $y = 4$

D. $x = 4$, $y = 1$

Correct Answer: A

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Question 8 View Details

Find the value of ( x ) in the equation $\sin^2 x + \cos^2 x = 1$.

A. 0

B. 30

Correct C. 45

D. 60

Correct Answer: C

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Question 9 View Details

Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, ... ).

A. 100

B. 120

Correct C. 140

D. 160

Correct Answer: C

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Question 10 View Details

Find the area of the triangle with vertices ( (0, 0), (3, 0), (0, 4) ).

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 11 View Details

A histogram is a graphical representation of the distribution of a set of data. What is the primary advantage of using a histogram over a bar chart?

Correct A. It provides a more detailed view of the data distribution

B. It is easier to read and understand

C. It is more suitable for large datasets

D. It is more visually appealing

Correct Answer: A

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Question 12 View Details

Given the equation $y = \frac{1}{2} $12x \$ ), find the value of ( y ) when $x = \frac{\pi}{4}$.

Correct A. 0.7071

B. 0.7072

C. 0.7073

D. 0.7074

Correct Answer: A

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Question 13 View Details

A curve has an equation of the form $y = ax^2 + bx + c$. If the curve passes through the points ( (1, 4) ), ( (2, 9) ), and ( (3, 16) ), find the value of ( a ).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 14 View Details

A right circular cone has a radius of 6 cm and a height of 8 cm. Find the volume of the cone.

Correct A. 452.389

B. 452.390

C. 452.391

D. 452.392

Correct Answer: A

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Question 15 View Details

A curve has an equation of the form $y = \frac{1}{x}$. Find the derivative of the curve.

Correct A. $-1/x\^2$

B. $1/x\^2$

C. $-1/x$

D. $1/x$

Correct Answer: A

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Question 16 View Details

Let X and Y be independent random variables with probability density functions f_$X(x) = 2x$, $0 < x$ < 1 and f_$Y(y) =$$3y^2$,$(0 < y$\) < 1. Find the probability that $X + Y < 1\\((0 < y) < 1. Find the probability that$.

Correct A. $\frac{1}{4}$\)

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

C. $\frac{3}{4}$\)

D. $\frac{5}{8}$\)

Correct Answer: A

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Question 17 View Details

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 18 View Details

Find the mean and standard deviation of the random variable X with probability density function f_$X(x) =$$\frac{1}{2}$\) x, $0 < x$$< 2.$

Correct A. \$\mu = 1$, \$sigma =$$\frac{1}${$\sqrt{3}$}\)

B. \$\mu = 1$, \$sigma =$$\frac{1}${$\sqrt{2}$}\)

C. \$\mu = 1$, \$sigma =$$\frac{1}${$\sqrt{5}$}\)

D. \$\mu = 1$, \$sigma =$$\frac{1}${$\sqrt{6}$}\)

Correct Answer: A

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Question 19 View Details

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

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

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

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

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

Correct Answer: A

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Question 20 View Details

Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}.

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 21 View Details

Solve the inequality $\frac{x^2 - 4}{x + 2} > 0$ for x in mathbb{R} setminus { -2 }.

Correct A. $-∞, -2$ ∪ (2, ∞)

B. $-∞, -2$ \cup $-2, 2$\)

C. $-∞, 2$

D. (2, ∞)

Correct Answer: A

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Question 22 View Details

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) in the form $x - h \$^2 + $y - k$^$2 = r\^2$ ).

Correct A. $x - 2$^2 + $y - 3$^$2 = 16$

B. $x - 3$^2 + $y - 2$^$2 = 16$

C. $x - 4$^2 + $y - 3$^$2 = 16$

D. $x - 2$^2 + $y - 4$^$2 = 16$

Correct Answer: A

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Question 23 View Details

If ( f(x) = $\frac{1}{x^2 + 1}$\)\) ), find ( f'(x) ) 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 24 View Details

Solve the system of linear equations $egin{cases} x + 2y = 4 \ 3x - 2y = 5 \end{cases}$.

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

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

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

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

Correct Answer: A

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Question 25 View Details

Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).

Correct A. 6

B. 8

C. 12

D. 16

Correct Answer: A

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