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Subject

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POST UTME UNILAG 2018 Mathematics | Objective

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Question 1 View Details

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

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

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

C. $\frac{1}{4}$

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

Correct Answer: A

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Question 2 View Details

A set ( A ) contains 5 elements, and a set ( B ) contains 3 elements. If ( A cap B ) contains 2 elements, find the number of elements in ( A cup B ).

A. 7

B. 8

Correct C. 9

D. 10

Correct Answer: C

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Question 3 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 - 3 \$^2 + $y - 2$^$2 = 16$ )

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

D. $x - 3 \$^2 + $y - 4$^$2 = 16$ )

Correct Answer: A

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Question 4 View Details

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

A. 35

B. 40

Correct C. 45

D. 50

Correct Answer: C

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Question 5 View Details

A random experiment has 3 possible outcomes, each with a probability of $\frac{1}{3}$. Find the probability that at least one of the outcomes occurs.

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

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

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

D. $\frac{2}{5}$

Correct Answer: B

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Question 6 View Details

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

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 7 View Details

A circle has a diameter of 10 cm. Find the area of the circle.

A. 50\pi

B. 75\pi

Correct C. 100\pi

D. 125\pi

Correct Answer: C

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Question 8 View Details

A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.

Correct A. $y = x + 1$

B. $y = x - 1$

C. $y = -x + 1$

D. $y = x + 2$

Correct Answer: A

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Question 9 View Details

Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, find P(A and B).

A. 0.2

Correct B. 0.24

C. 0.3

D. 0.36

Correct Answer: B

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Question 10 View Details

A vector \overrightarrow{a} has a magnitude of 5 units and makes an angle of 60 degrees with the positive x-axis. Find the x and y components of the vector.

Correct A. $a_x = 2.5$, $a_y = 4.33$

B. $a_x = 4.33$, $a_y = 2.5$

C. $a_x = 3.54$, $a_y = 3.54$

D. $a_x = 4.33$, $a_y = 3.54$

Correct Answer: A

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Question 11 View Details

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

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

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

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

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

Correct Answer: B

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Question 12 View Details

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

Correct A. x < -1 or $x > 3/2$\)

B. $x < 1$ or x > $-3/2$

C. $x <$$-3/2$ or $x > 1$

D. $x < 3/2$\) or x > -1

Correct Answer: A

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Question 13 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. $1/2$

B. $1/3$

Correct C. $2/5$

D. $3/8$

Correct Answer: C

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Question 14 View Details

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

Correct A. $\frac{16\pi}{3}$\)

B. $\frac{32\pi}{3}$\)

C. $\frac{64\pi}{3}$\)

D. $\frac{128\pi}{3}$\)

Correct Answer: A

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Question 15 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 16 View Details

Find the value of $\int_0^1 \frac{1}{x^2 + 2x + 2} dx$.

A. $1/2$

Correct B. $1/3$

C. $1/4$

D. $1/5$

Correct Answer: B

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Question 17 View Details

Solve the equation $\log_2 x + 1$ + \log_2 $x - 1$$= 2$\).

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 18 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 + $y + 3$^$2 = 16$

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

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

Correct Answer: A

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Question 19 View Details

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

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

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

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

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

Correct Answer: A

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Question 20 View Details

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

Correct A. $\frac{4}{3}$\)\pi

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

C. $\frac{1}{3}$\)\pi

D. $\frac{1}{2}$\)\pi

Correct Answer: A

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Question 21 View Details

Solve the equation $\tan^2 x + $1x - 6 = 0$.

A. \tan $x = 2$

B. \$tan x = -3$

Correct C. \tan $x = 3$

D. \$tan x = -2$

Correct Answer: C

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Question 22 View Details

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

Correct A. $y = x + 5$

B. $y = x - 1$

C. $y = x + 1$

D. $y = x - 5$

Correct Answer: A

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Question 23 View Details

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

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

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

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

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

Correct Answer: VIEW ANSWER

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Question 24 View Details

Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes a value greater than 0.5.

A. 0.25

B. 0.5

Correct C. 0.75

D. 1

Correct Answer: C

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Question 25 View Details

Solve the equation $\sin^2 x + \cos^2 x = 1$ for $x \\\() for (x$ in the interval $[0, \pi] \$.

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

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

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

D. $x =$\pi

Correct Answer: A

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