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POST UTME UI 2019 Mathematics | Objective

Are you preparing for POST UTME UI exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the value of x in the equation $ \log_{10} \( x^2 \ $ = 4 ).

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2

Solve the quadratic equation $ x^2 + 5x + 6 = 0 $.

A. -2

Correct B. -3

C. 1

D. 2

Correct Answer: B

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Question 3

A histogram is shown below. What is the mean of the data?

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 4

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 4 $.

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 5

A circle with center ( C(0, 0) ) and radius $ r = 4 $ is shown below. What is the equation of the circle?

Correct A. x^2 + y^2 = 16

B. x^2 + y^2 = 32

C. x^2 + y^2 = 64

D. x^2 + y^2 = 128

Correct Answer: A

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Question 6

Find the volume of the solid formed by revolving the region bounded by $y = \sqrt{x}$, $y = 0$, and $x = 4$ about the $x$-axis.

Correct A. 128\pi

B. 256\pi

C. 512\pi

D. 1024\pi

Correct Answer: A

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Question 7

Solve the inequality $\frac{1}{x^2-4x+3}\geq 0$.

Correct A. $x\in $ -\infty, 1)\cup \( 3, \infty \ $$

B. $x\in $ -\infty, 1)\cup \( 1, 3)\cup (3, \infty \ $$

C. $x\in $ -\infty, 1)\cup \( 3, \infty \ $$

D. $x\in $ -\infty, 3)\cup \( 3, \infty \ $$

Correct Answer: A

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Question 8

Find the derivative of $f(x) = \frac{x^2}{x^2+1}$ u\sing the quotient rule.

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

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

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

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

Correct Answer: C

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Question 9

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

A. $x = \pm 10$

Correct B. $x = \pm 100$

C. $x = \pm 1000$

D. $x = \pm 10000$

Correct Answer: B

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Question 10

Find the surface area of the solid formed by revolving the region bounded by $y = x^2$ and $y = 0$ about the $x$-axis.

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

B. $\frac{8\pi}{3}$

Correct C. $\frac{16\pi}{3}$

D. $\frac{32\pi}{3}$

Correct Answer: C

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Question 11

Find the sum of the infinite geometric series $ sum_{n=1}^{infty} \frac{1}{2^n} $.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 12

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

A. x = -2

Correct B. x = 2

C. x = -1

D. x = 1

Correct Answer: B

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Question 13

A set of 5 numbers has an average of 10. If one number is removed, the average becomes 12. What is the sum of the remaining 4 numbers?

A. 48

B. 50

Correct C. 52

D. 54

Correct Answer: C

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Question 14

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

Correct A. 18

B. 20

C. 22

D. 24

Correct Answer: A

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Question 15

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. ₦1255

C. ₦1260

D. ₦1265

Correct Answer: A

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Question 16

Determine the value of $\frac{d}{dx} \left$ \frac{1}{x^2 + 1} \right $$ u\sing 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 17

A histogram is constructed with 5 classes of equal width. The first class has a frequency of 10, the second class has a frequency of 15, the third class has a frequency of 20, the fourth class has a frequency of 12, and the fifth class has a frequency of 8. What is the mean of the data?

A. 12.4

Correct B. 13.2

C. 14.1

D. 15.0

Correct Answer: B

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Question 18

Solve the inequality $x^2 - 6x + 8 \geq 0$.

Correct A. $x \in $ -\infty, 2 $ \cup $ 4, \infty $$

B. $x \in $ -\infty, 4 $ \cup $ 2, \infty $$

C. $x \in $ -\infty, 2 $ \cup $ 4, \infty $$

D. $x \in $ -\infty, 4 $ \cup $ 2, \infty $$

Correct Answer: A

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Question 19

A binary operation $\star$ is defined as $a \star b = ab + 2$. Find the value of $3 \star 4$.

A. 14

B. 16

Correct C. 18

D. 20

Correct Answer: C

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Question 20

A quadratic equation is given by $x^2 + 4x + 4 = 0$. Solve for $x$.

Correct A. $x = -2$

B. $x = -1$

C. $x = 1$

D. $x = 2$

Correct Answer: A

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Question 21

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

A. 2.5 cm

Correct B. 3.0 cm

C. 3.5 cm

D. 4.0 cm

Correct Answer: B

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Question 22

A rec\tangular solid has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Calculate the surface area of the solid.

A. 104 cm^2

Correct B. 120 cm^2

C. 140 cm^2

D. 160 cm^2

Correct Answer: B

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Question 23

If f(x) = 3x^2 + 2x - 5, find the derivative of the function.

Correct A. 6x + 2

B. 6x - 2

C. 3x^2 + 2

D. 3x^2 - 2

Correct Answer: A

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Question 24

Solve the equation: 2\sin^2(x) + \cos(x) = 1.

A. \frac{\pi}{6}

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

C. \frac{\pi}{3}

D. \frac{\pi}{2}

Correct Answer: B

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Question 25

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 = 25

C. $ x - 2 $^2 + $ y - 3 $^2 = 36

D. $ x - 2 $^2 + $ y - 3 $^2 = 49

Correct Answer: A

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