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POST UTME CHRISTOPHER UNIVERSITY 2025 Mathematics | Objective

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Question 1 View Details

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

A. 2x

B. -2x

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

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

Correct Answer: C

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Question 2 View Details

Evaluate the definite integral $\int_0^1 x^2 dx$.

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

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

C. $\frac{2}{3}$\)

D. $\frac{1}{6}$\)

Correct Answer: A

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Question 3 View Details

Solve the inequality $x^2 - 4x + 4 \geq 0$.

Correct A. x \leq 2

B. x \geq 2

C. $x < 2$

D. $x > 2$

Correct Answer: A

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Question 4 View Details

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

Correct A. $\frac{8}{3}$\)

B. $\frac{16}{3}$\)

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

D. $\frac{2}{3}$\)

Correct Answer: A

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Question 5 View Details

Determine the value of ( x ) in the equation $2^x = 16$.

A. 4

B. 2

Correct C. 3

D. 1

Correct Answer: C

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Question 6 View Details

Find the volume of the solid formed by revolving the region bounded by the parabola (y = $x^2$\), the line $x = 2\\((y = x^2), the line$, and the x-axis about the x-axis.

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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Question 7 View Details

Solve the inequality $\frac{x^2 - 4}{x^2 - 9} > 0$.

A. $-∞, -3$ ∪ (2, ∞)

Correct B. $-∞, -3$ ∪ (0, 2) ∪ (3, ∞)

C. $-∞, -3$ ∪ (0, 3)

D. $-∞, -3$ ∪ (2, 3)

Correct Answer: B

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Question 8 View Details

Find the equation of the circle passing through the points (2, 3), (4, 1), and $6, -1$.

Correct A. $x^2 + y^2 - 12x - 4y + 20 = 0$

B. $x^2 + y^2 - 8x - 6y + 15 = 0$

C. $x^2 + y^2 - 10x - 2y + 25 = 0$

D. $x^2 + y^2 - 12x - 8y + 32 = 0$

Correct Answer: A

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Question 9 View Details

A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 3$ with initial term $a_1 = 2$. Find the sum of the first five terms of the sequence.

A. 35

B. 40

Correct C. 45

D. 50

Correct Answer: C

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Question 10 View Details

A right-angled triangle has sides of length 3, 4, and 5. Find the area of the triangle.

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 11 View Details

Determine the mean of the following data set: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Correct A. 6

B. 5

C. 7

D. 8

Correct Answer: A

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Question 12 View Details

A random variable X has a probability distribution given by P$X = 1 = 0.2$, P$X = 2 = 0.3$, P$X = 3 = 0.5$. What is the expected value of X?

A. 1.5

Correct B. 2.0

C. 2.5

D. 3.0

Correct Answer: B

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Question 13 View Details

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

A. 10

B. 100

Correct C. 1000

D. 10000

Correct Answer: C

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Question 14 View Details

In a circle with center O and radius 5, what is the length of the arc intercepted by a central angle of 60 degrees?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 15 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 2197

Correct B. 2401

C. 2605

D. 2809

Correct Answer: B

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Question 16 View Details

Let $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} 1 \ -2 end{pmatrix}$. Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula $\\(end{pmatrix}). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula \mathrm{proj}_{\mathbf{a}} \mathbf{b} = \frac{\mathbf{a} \cdot \mathbf{b}}{| \mathbf{a} |^2} \mathbf{a}$.

A. 0

Correct B. \begin{pmatrix} $\frac{4}{13}$\) \\ $\frac{6}{13}$\) \end{pmatrix}

C. \begin{pmatrix} $\frac{2}{13}$\) \\ $\frac{3}{13}$\) \end{pmatrix}

D. \begin{pmatrix} $\frac{1}{13}$\) \\ $\frac{-2}{13}$\) \end{pmatrix}

Correct Answer: B

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Question 17 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to (x = 4\) using the definite integral $\\((x = 4) using the definite integral \int_{a}^{b} f x \$ \, dx ).

A. 64

B. 80

Correct C. 96

D. 128

Correct Answer: C

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Question 18 View Details

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

A. 0

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

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

D. \pi

Correct Answer: B

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Question 19 View Details

Find the equation of the circle with center ( (3, 4) ) and radius 5.

Correct A. $x - 3$^2 + $y - 4$^$2 = 25$

B. $x - 4$^2 + $y - 3$^$2 = 25$

C. $x - 5$^2 + $y - 3$^$2 = 25$

D. $x - 3$^2 + $y - 5$^$2 = 25$

Correct Answer: A

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Question 20 View Details

Find the sum of the first 10 terms of the geometric series $2 + 6 + 18 + \cdots$.

A. 4095

Correct B. 4096

C. 4097

D. 4098

Correct Answer: B

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Question 21 View Details

Evaluate the definite integral $int_{0}^{1} x^2 $1x \$ , dx ) using integration by parts.

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

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

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

D. $\frac{1}{6}$\)

Correct Answer: C

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Question 22 View Details

Determine the value of ( x ) in the equation $2^x + 3^x = 5^x$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 23 View Details

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

Correct A. $-\infty, -1$ \cup $3, \infty$

B. $-\infty, -3$ \cup $1, \infty$

C. $-\infty, 1$ \cup $3, \infty$

D. $-\infty, -3$ \cup $1, \infty$

Correct Answer: A

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Question 24 View Details

Find the area under the curve $y = x^3 - 6x^2 + 9x + 2$ from $x = 0$ to $x = 2$.

A. 14

Correct B. 16

C. 18

D. 20

Correct Answer: B

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Question 25 View Details

Determine the value of ( x ) in the equation $x^2 + 4x + 4 = 0$.

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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