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POST UTME CHRISTOPHER UNIVERSITY 2021 Mathematics | Objective

Prepare for your exams with POST UTME CHRISTOPHER UNIVERSITY questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1 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.

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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Question 2 View Details

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first 5 terms.

Correct A. -1102

B. -1020

C. -1000

D. -980

Correct Answer: A

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Question 3 View Details

A right circular cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone.

Correct A. 200\pi

B. 400\pi

C. 800\pi

D. 1600\pi

Correct Answer: A

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Question 4 View Details

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

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

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

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

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

Correct Answer: A

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Question 5 View Details

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

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

Let $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} -1 \ 4 end{pmatrix}$. Find the vector $\\(end{pmatrix}). Find the vector \mathbf{a} \times \mathbf{b}$ using the determinant method.

Correct A. \begin{pmatrix} 11 \ 2 \end{pmatrix}

B. \begin{pmatrix} -11 \ 2 \end{pmatrix}

C. \begin{pmatrix} 11 \ -2 \end{pmatrix}

D. \begin{pmatrix} -11 \ -2 \end{pmatrix}

Correct Answer: A

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Question 7 View Details

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

Correct A. $\frac{4}{5}$\)

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

C. $\frac{4}{15}$\)

D. $\frac{4}{9}$\)

Correct Answer: A

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Question 8 View Details

Find the area under the curve $y = e^x$ from $x = 0$ to $x = 1$.

Correct A. e - 1

B. e + 1

C. $e^2 - 1$

D. $e^2 + 1$

Correct Answer: A

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Question 9 View Details

Solve the equation $x^3 + 2x^2 - 7x + 12 = 0$ using the rational root theorem.

Correct A. $x = 1$

B. $x = -1$

C. $x = 3$

D. $x = -3$

Correct Answer: A

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Question 10 View Details

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

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

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

C. $\frac{8}{5}$\)

D. $\frac{4}{5}$\)

Correct Answer: A

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Question 11 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. $y = 2x - 1$

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

D. $y = 2x + 1$

Correct Answer: A

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Question 12 View Details

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

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

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

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

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

Correct Answer: A

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Question 13 View Details

Find the volume of the frustum of a cone with height (h = 10\) cm, and radii of the bases $r_1 = 4\\((h = 10) cm, and radii of the bases$ cm and $r_2 = 6$ cm.

Correct A. $\frac{1}{3} \pi 4^2 + 6^2 + 4 \cdot 6 \$ cdot 10 )

B. $\frac{1}{3} \pi 4^2 + 6^2 - 4 \cdot 6 \$ cdot 10 )

C. $\frac{1}{3} \pi 4^2 + 6^2 + 4 \cdot 6 \$ cdot 5 )

D. $\frac{1}{3} \pi 4^2 + 6^2 - 4 \cdot 6 \$ cdot 5 )

Correct Answer: A

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Question 14 View Details

Find the sum of the first ( n ) terms of the arithmetic progression ( 2, 5, 8, ldots ).

Correct A. $\frac{n}{2} [2 + n - 1 \$ cdot 3] )

B. $\frac{n}{2} [2 + n + 1 \$ cdot 3] )

C. $\frac{n}{2} [2 + n - 1 \$ cdot 2] )

D. $\frac{n}{2} [2 + n + 1 \$ cdot 2] )

Correct Answer: A

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Question 15 View Details

Solve the system of equations $x + y = 4$ and $x^2 + y^2 = 16$.

Correct A. $x = 2, y = 2$

B. $x = 2, y = 2$ or $x = -2, y = -2$

C. $x = 2, y = 2$ or $x = -2, y = -2$ or $x = 0, y = 4$

D. $x = 2, y = 2$ or $x = -2, y = -2$ or $x = 4, y = 0$

Correct Answer: A

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Question 16 View Details

Find the area of the triangle with vertices ( (0,0), (3,0), (0,4) ).

Correct A. $\frac{1}{2} \cdot 3 \cdot 4$

B. $\frac{1}{2} \cdot 3 \cdot 4 \cdot $160^circ$

C. $\frac{1}{2} \cdot 3 \cdot 4 \cdot $160^circ$

D. $\frac{1}{2} \cdot 3 \cdot 4 \cdot $160^circ$

Correct Answer: A

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Question 17 View Details

Find the equation of the circle with center ( (2,3) ) and radius $r = 4$.

Correct A. $x - 2 \$^2 + $y - 3$^$2 = 16$ )

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

C. $x - 2 \$^2 + $y - 3$^$2 = 9$ )

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

Correct Answer: A

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Question 18 View Details

Find the sum of the first ( n ) terms of the geometric progression ( 2, 6, 18, ldots ).

A. $2 \cdot \frac{6^n - 1}{5}$

B. $2 \cdot \frac{6^n + 1}{5}$

C. $2 \cdot \frac{6^n - 1}{6}$

D. $2 \cdot \frac{6^n + 1}{6}$

Correct Answer: VIEW ANSWER

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Question 19 View Details

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 20 View Details

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

Correct A. $\frac{-5 + \sqrt{37}$}{4}\)

B. $\frac{-5 - \sqrt{37}$}{4}\)

C. $\frac{-5 + \sqrt{37}$}{2}\)

D. $\frac{-5 - \sqrt{37}$}{2}\)

Correct Answer: A

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Question 21 View Details

Find the equation of the circle with center $-2, 3$ and radius $4$.

Correct A. \left$x + 2 \right$^2 + \left$y - 3 \right$^$2 = 16$

B. \left$x - 2 \right$^2 + \left$y + 3 \right$^$2 = 16$

C. \left$x + 2 \right$^2 + \left$y + 3 \right$^$2 = 16$

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

Correct Answer: A

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Question 22 View Details

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

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

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

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

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

Correct Answer: A

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Question 23 View Details

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

Correct A. $x =$$\frac{3}{2}$\),$y =$$\frac{1}{2}$\)

B. $x =$$\frac{1}{2}$\),$y =$$\frac{3}{2}$\)

C. $x = 2$, $y = 1$

D. $x = 1$, $y = 2$

Correct Answer: A

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Question 24 View Details

Find the area of the triangle with vertices ((0, 0), (3, 0), (0, 4)\) using the formula $\\(((0, 0), (3, 0), (0, 4)) using the formula \frac{1}{2} \times \text{base} \times \text{height}$.

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 25 View Details

Find the equation of the line passing through the points $(2, 3)$ and $(4, 5)$ using the slope-intercept form.

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

B. $y =$$\frac{2}{4}$\) x + 1

C. $y =$$\frac{4}{2}$\) x + 1

D. $y =$$\frac{4}{4}$\) x + 1

Correct Answer: A

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