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POST UTME CHRISTOPHER UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

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

A. $x = -2 \$

Correct B. $x = -3 \$

C. $x = 2 \$

D. $x = 3 \$

Correct Answer: B

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Question 2 View Details

Find the area under the curve $y = x^2 - 4x + 3$ from $x = 0$ to $x = 2$.

Correct A. $\frac{5}{3} \$

B. $\frac{7}{3} \$

C. $\frac{9}{3} \$

D. $\frac{11}{3} \$

Correct Answer: A

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Question 3 View Details

Solve the inequality $x^2 - 4x - 5 > 0$.

Correct A. $x < -1 \$ or $x > 5 \$

B. $x < 1 \$ or $x > 5 \$

C. $x < -1 \$ or $x < 5 \$

D. $x > 1 \$ or $x < 5 \$

Correct Answer: A

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Question 4 View Details

Find the value of $\log_{10} 1000 \$.

A. $3 \$

Correct B. $4 \$

C. $5 \$

D. $6 \$

Correct Answer: B

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Question 5 View Details

Solve the trigonometric equation $\sin^2 x + \cos^2 x = 1 \$.

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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Question 6 View Details

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

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

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

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

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

Correct Answer: A

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Question 7 View Details

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

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

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

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

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

Correct Answer: A

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Question 8 View Details

Find the sum of the first 5 terms of the geometric series $2x + 3x^2 + 4x^3 + ldots$.

Correct A. $2x + 3x^2 + 4x^3 + 5x^4 + 6x^5$

B. $2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6$

C. $2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7$

D. $2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8$

Correct Answer: A

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Question 9 View Details

Find the equation of the line passing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. $y = \frac{1}{2}x + \frac{1}{2}$

B. $y = \frac{1}{2}x - \frac{1}{2}$

C. $y = 2x - 1$

D. $y = 2x + 1$

Correct Answer: A

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Question 10 View Details

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

Correct A. ( 6 )

B. ( 7 )

C. ( 8 )

D. ( 9 )

Correct Answer: A

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Question 11 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 12 View Details

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

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

B. $x = \frac{3\pi}{4}$

Correct C. $x = \frac{\pi}{2}$

D. $x = \frac{5\pi}{4}$

Correct Answer: C

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Question 13 View Details

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find its volume.

A. ( 400 ) cm³

B. ( 500 ) cm³

Correct C. ( 600 ) cm³

D. ( 800 ) cm³

Correct Answer: C

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Question 14 View Details

Find the area of the triangle with vertices ( A(2, 3) ), ( B(4, 5) ), and ( C(6, 7) ).

A. ( 10 ) cm²

B. ( 15 ) cm²

Correct C. ( 20 ) cm²

D. ( 25 ) cm²

Correct Answer: C

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Question 15 View Details

Solve the system of equations $x + y = 3$ and $x - y = 1$.

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 16 View Details

Let ( f(x) = $\frac{x^2 - 4}{x - 2}$\)\) ). Find the derivative of ( f(x) ) using the quotient rule.

Correct A. ( f'$(x) =$$\frac{2x x - 2 - x^2 - 4$ }{ x - 2 ^2}\)\) \)

B. ( f'$(x) =$$\frac{2x x - 2 + x^2 - 4$ }{ x - 2 ^2}\)\) \)

C. ( f'$(x) =$$\frac{2x x - 2 - x^2 - 4$ }{ x - 2 ^2}\)\) \) + 2

D. ( f'$(x) =$$\frac{2x x - 2 + x^2 - 4$ }{ x - 2 ^2}\)\) \) - 2

Correct Answer: A

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Question 17 View Details

In a histogram with 5 classes, the frequency of the first class is 10, the second class is 15, the third class is 20, the fourth class is 25, and the fifth class is 30. What is the mean of the frequencies?

A. 20

Correct B. 22.5

C. 25

D. 27.5

Correct Answer: B

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Question 18 View Details

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

A. 2

Correct B. 4

C. -2

D. -4

Correct Answer: B

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Question 19 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.24

B. 50.27

C. 50.29

D. 50.31

Correct Answer: A

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Question 20 View Details

Find the value of ($12x \$ ) given that \$($12x $$1x \$ = $\frac{1}{2}$\) ).

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

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

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

D. $\frac{1}{3}$\)

Correct Answer: B

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Question 21 View Details

In a survey of 50 students, the mean height was 175 cm with a standard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

Correct A. 0.3085

B. 0.1915

C. 0.1359

D. 0.0228

Correct Answer: A

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Question 22 View Details

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

Correct A. 100

B. 10

C. 1000

D. 10000

Correct Answer: A

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Question 23 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side using the cosine rule.

Correct A. 8

B. 6

C. 10

D. 12

Correct Answer: A

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Question 24 View Details

A binary operation (*\) on the set of integers is defined as $a * b = a^2 + b^2\\((*) on the set of integers is defined as$. Find the value of $2 * 3$.

A. 13

B. 19

Correct C. 25

D. 37

Correct Answer: C

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Question 25 View Details

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment is terminated. What is the probability that the experiment will be terminated on the first roll?

A. $1/2$

Correct B. $1/3$

C. $2/3$

D. $1/6$

Correct Answer: B

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