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POST UTME IMS U 2017 Mathematics | Objective

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Question 1 View Details

Find the value of $\frac{d}{dx} \left \frac{1}{x^2 + 1} \right$\) using the quotient 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 2 View Details

Solve the inequality $|2x - 1| \geq 3$.

Correct A. $x \leq -1$ or $x \geq 2$

B. $x \leq -2$ or $x \geq 1$

C. $x \leq 1$ or $x \geq 2$

D. $x \leq -1$ or $x \geq 3$

Correct Answer: A

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Question 3 View Details

Find the area of the triangle with vertices $(0, 0), (3, 0),$ and $(0, 2)$.

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 4 View Details

Solve the system of equations $x + y = 2$ and $x - y = 1$.

Correct A. $x = 1.5, y = 0.5$

B. $x = 0.5, y = 1.5$

C. $x = 1, y = 1$

D. $x = 2, y = 0$

Correct Answer: A

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Question 5 View Details

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$ using the quotient 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 6 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 7 View Details

Evaluate the integral $int_{0}^{1} x^2 $1x , dx$.

Correct A. $-\(1x^2 + 2x$1x + 2 $1x\)

B. $-\(1x^2 - 2x$1x - 2 $1x\)

C. $\(1x^2 - 2x$1x + 2 $1x\)

D. $\(1x^2 + 2x$1x - 2 $1x\)

Correct Answer: A

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Question 8 View Details

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

Correct A. $x < -1$ or $x > 1$

B. $x < 0$ or $x > 1$

C. $x < 0$ or $x > 2$

D. $x < -1$ or $x > 2$

Correct Answer: A

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Question 9 View Details

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

Correct A. ₦1250

B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: A

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Question 10 View Details

Find the mean of the numbers 2, 4, 6, 8, 10.

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 11 View Details

Let X be a random variable with probability density function f(x) = \begin{cases} 2x & $0 < x$$< 1$\\ 0 & \text{otherwise} \end{cases}. Find the probability that X is greater than 0.5.

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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Question 12 View Details

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 13 View Details

Solve the equation \tan x + \cot $x = 3$.

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

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

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

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

Correct Answer: B

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Question 14 View Details

Let a, b, and c be positive real numbers such that $a^2 + b^2$ + \$(c^2) = 1.$ Find the maximum value of $a^2b\\() = 1.) Find the maximum value of$^2.

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

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

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

D. 1

Correct Answer: C

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Question 15 View Details

Find the value of x in the equation \$\frac{1}{x}$\) + \$\frac{1}{x+1}$\) = \$\frac{1}{2}$\).

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 16 View Details

A solid right circular cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.

A. 256\pi

B. 512\pi

Correct C. 768\pi

D. 1024\pi

Correct Answer: C

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Question 17 View Details

A die is rolled twice. What is the probability that the sum of the two numbers shown on the dice is 7?

Correct A. $\frac{1}{6}$\)

B. $\frac{1}{12}$\)

C. $\frac{1}{36}$\)

D. $\frac{1}{24}$\)

Correct Answer: A

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Question 18 View Details

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

Correct A. \left$-2, \ 0 \right$

B. \left$0, \ -2 \right$

C. \left$-2, \ -2 \right$

D. \left$2, \ 0 \right$

Correct Answer: A

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Question 19 View Details

Find the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, ...

A. 55

B. 65

Correct C. 75

D. 85

Correct Answer: C

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Question 20 View Details

A circle has a diameter of 14 cm. Find the area of the circle in square centimeters.

A. 154\pi

Correct B. 196\pi

C. 245\pi

D. 308\pi

Correct Answer: B

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Question 21 View Details

Determine the value of (x\) in the equation $\\((x) in the equation \left| 2x - 3 \right| + 2 = 7$.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 22 View Details

A histogram of exam scores is shown below. If the mean score is 75, what is the median score?

A. 70

Correct B. 75

C. 80

D. 85

Correct Answer: B

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Question 23 View Details

Solve the equation $\frac{1}{2} \log_{10} x^2$$= 4$\) for $x$.

A. 10

B. 20

C. 40

Correct D. 80

Correct Answer: D

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Question 24 View Details

In the diagram below, what is the value of $x$?

A. 30

B. 45

Correct C. 60

D. 90

Correct Answer: C

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Question 25 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?

A. 30

B. 50

Correct C. 60

D. 70

Correct Answer: C

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