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POST UTME MADONNA UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

Let X and Y be independent random variables with probability density functions f_$X(x) = 2x$, $0 < x$$< 1$, and f_$Y(y) =$$3y^2$,$(0 < y$\) < 1. Find the probability that $X + Y < 1\\((0 < y) < 1. Find the probability that$.

Correct A. $1/4$

B. $1/2$

C. $3/4$

D. 1

Correct Answer: A

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Question 2 View Details

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

Correct A. $x \leq -3$ or $x \geq 1$

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

C. $x \leq 1$ or $x \geq 3$

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

Correct Answer: A

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Question 3 View Details

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

Correct A. $8/3$

B. $16/3$

C. $32/3$

D. $64/3$

Correct Answer: A

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Question 4 View Details

Let $a$ and $b$ be the roots of the quadratic equation $(x^2 + 2x + 3$ = 0\). Find the value of $a^2 + b^2\\((x^2 + 2x + 3 = 0). Find the value of$.

Correct A. $4$

B. $5$

C. $6$

D. $7$

Correct Answer: A

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Question 5 View Details

Solve the system of linear equations $2x + 3y = 7$ and $x - 2y = -3$.

Correct A. $x = 1, y = 2$

B. $x = 2, y = 1$

C. $x = 3, y = 4$

D. $x = 4, y = 3$

Correct Answer: A

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Question 6 View Details

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 7 View Details

Find the value of $\frac{1}{2} \(12x + \frac{1}{4}$12x\) when $x = \frac{\pi}{6}$.

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

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

C. $\frac{1}{8}$\)

D. $\frac{1}{16}$\)

Correct Answer: A

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Question 8 View Details

In the diagram below, the line (y = 2x - 3\) intersects the circle $x^2 + y^2 = 16\\((y = 2x - 3) intersects the circle$. Find the coordinates of the point of intersection.

A. (3, 3)

Correct B. (4, 5)

C. (5, 7)

D. (6, 9)

Correct Answer: B

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Question 9 View Details

Differentiate the function ( f(x) = $\frac{x^2}{x$^2 + 1}\)\) ) with respect to x.

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

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

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

D. $\frac{2x^4}{$ $x^2 + 1$ ^2}\)\)

Correct Answer: A

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Question 10 View Details

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

Correct A. $-\infty, -1$ \cup $5, \infty$

B. $-\infty, -5$ \cup $1, \infty$

C. $-\infty, 1$ \cup $5, \infty$

D. $-\infty, -5$ \cup $1, \infty$

Correct Answer: A

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Question 11 View Details

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

Correct A. 59048

B. 59049

C. 59050

D. 59051

Correct Answer: A

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Question 12 View Details

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

A. $-3, -1$ \cup (1, 3)

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

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

D. $-3, -1$ \cup (1, 3)

Correct Answer: B

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Question 13 View Details

Find the equation of the tangent line to the curve $y = x\^2 + 2x - 3\\(tangent line to the curve (y = x$ at the point (1, 2).

Correct A. $y = 2x + 1$

B. $y = 2x - 1$

C. $y = 2x + 3$

D. $y = 2x - 3$

Correct Answer: A

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Question 14 View Details

Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= 3 \end{align*}.

Correct A. $x = 1$, $y = 3$

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

C. $x = 3$, $y = 1$

D. $x = 4$, $y = 0$

Correct Answer: A

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Question 15 View Details

Find the derivative of the function f(x) = $x^3 - 2x^2 + x - 1$.

Correct A. $3x^2 - 4x + 1$

B. $3x^2 - 4x - 1$

C. $3x^2 + 4x + 1$

D. $3x^2 + 4x - 1$

Correct Answer: A

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Question 16 View Details

Find the equation of the plane passing through the points (1, 2, 3), (2, 3, 4), and (3, 4, 5).

Correct A. $x - y + z - 6 = 0$

B. $x + y - z + 6 = 0$

C. $x - y + z + 6 = 0$

D. $x + y + z + 6 = 0$

Correct Answer: A

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Question 17 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 18 View Details

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

Correct A. $\frac{32}{3} \pi$

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

C. $\frac{64}{3} \pi$

D. $\frac{128}{3} \pi$

Correct Answer: A

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Question 19 View Details

Find the area under the curve $y = $1x$ from $x = 0$ to $x = \frac{\pi}{2}$.

Correct A. ( 1 )

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

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

D. ( pi )

Correct Answer: A

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Question 20 View Details

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

Correct A. $x^2 + y^2 - 4x - 6y + 9 = 0$

B. $x^2 + y^2 + 4x - 6y + 9 = 0$

C. $x^2 + y^2 - 4x + 6y + 9 = 0$

D. $x^2 + y^2 + 4x + 6y + 9 = 0$

Correct Answer: A

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Question 21 View Details

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

A. 2

Correct B. 61

C. 62

D. 63

Correct Answer: B

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Question 22 View Details

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

Correct A. $-2, -1$ \cup $1, \infty$

B. $-2, 1$ \cup $2, \infty$

C. $-2, 1$ \cup $2, \infty$

D. $-2, \infty$ \cup $1, \infty$

Correct Answer: A

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Question 23 View Details

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

Correct A. $y = 2x - 1$

B. $y = 2x + 1$

C. $y = x - 1$

D. $y = x + 1$

Correct Answer: A

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Question 24 View Details

Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}.

Correct A. $x = 1$, $y = 2$

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

C. $x = 1$, $y = 3$

D. $x = 2$, $y = 4$

Correct Answer: A

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Question 25 View Details

Find the area of the circle with radius 4.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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