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POST UTME UNIPORT 2020 Mathematics | Objective

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Question 1 View Details

In a triangle (ABC\), if $\(1A = \\((ABC), if \frac{1}{2}$ and 1B = $\frac{1}{3}$\), find $$1C$.

Correct A. $\frac{11}{7}$\)

B. $\frac{7}{11}$\)

C. $\frac{5}{3}$\)

D. $\frac{3}{5}$\)

Correct Answer: A

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Question 2 View Details

Find the area under the curve $y = x^2 + 2x + 1$ from $x = 0$ to $x = 2$.

A. $\frac{14}{3}$\)

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

C. $\frac{18}{3}$\)

D. $\frac{20}{3}$\)

Correct Answer: B

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Question 3 View Details

Solve the system of equations $\begin{cases} x + y = 2 \ x - 2y = -3 \end{cases}$.

Correct A. \begin{cases} $x = 1$ \ $y = 1$ \end{cases}

B. \begin{cases}$x = -1$\ $y = 3$ \end{cases}

C. \begin{cases} $x = 2$ \ $y = 0$ \end{cases}

D. \begin{cases} $x = 0$ \ $y = 2$ \end{cases}

Correct Answer: A

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Question 4 View Details

Find the value of ($12\theta$ if \$($12theta$$1\theta = \frac{1}{2}$.

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

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

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

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

Correct Answer: B

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Question 5 View Details

Find the value of $$1\frac{\pi}{4}$.

Correct A. 1

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

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

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

Correct Answer: A

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Question 6 View Details

Determine the value of x in the equation $\frac{1}{2}x + 5 = 11$ in base 8.

Correct A. 6

B. 7

C. 8

D. 9

Correct Answer: A

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Question 7 View Details

A histogram of exam scores is shown below. What is the mean score of the exam?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 8 View Details

Find the sum of the first 10 terms of the geometric series $2x^2, 4x^3, 8x^4, ldots$.

A. $1023x^{10}$

Correct B. $1024x^{10}$

C. $1025x^{10}$

D. $1026x^{10}$

Correct Answer: B

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Question 9 View Details

Solve for x in the matrix equation $egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}$.

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 10 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. $x - 3$^2 + $y - 2$^$2 = 16$

C. $x - 4$^2 + $y - 3$^$2 = 16$

D. $x - 3$^2 + $y - 4$^$2 = 16$

Correct Answer: A

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Question 11 View Details

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

Correct A. 10

B. 12

C. 14

D. 16

Correct Answer: A

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Question 12 View Details

Solve the equation $2x + 5y = 11$, where x and y are vectors.

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

B. $x = 3$, $y = 2$

C. $x = 4$, $y = 3$

D. $x = 5$, $y = 4$

Correct Answer: A

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Question 13 View Details

Express the number 456 in base 8.

Correct A. 720

B. 721

C. 722

D. 723

Correct Answer: A

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Question 14 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. $x - 3$^2 + $y - 2$^$2 = 16$

C. $x - 4$^2 + $y - 3$^$2 = 16$

D. $x - 3$^2 + $y - 4$^$2 = 16$

Correct Answer: A

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Question 15 View Details

Solve the inequality $2x - 5 > 3$.

Correct A. $x > 4$

B. $x > 3$

C. $x > 2$

D. $x > 1$

Correct Answer: A

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Question 16 View Details

Find the area under the curve $y = 2x\^2 + 3x - 1$ from $x = 0$ to $x = 2$.

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

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

Correct C. $\frac{20}{3}$\)

D. $\frac{22}{3}$\)

Correct Answer: C

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Question 17 View Details

Solve for x in the equation $2^x$ + \$(3^x$$= 5$\$)^x$.

A. $x = 2$

Correct B. $x = 3$

C. $x = 4$

D. $x = 5$

Correct Answer: B

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Question 18 View Details

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

A. $\frac{16\pi}{3}$\)

B. $\frac{32\pi}{3}$\)

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

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

Correct Answer: C

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Question 19 View Details

A circle passes through the points (0, 2), (2, 0), and $0, -2$. Find the equation of the circle.

A. $x^2$ + \$(y^2$$= 4$\)

Correct B. $x^2$ + \$(y^2$$= 8$\)

C. $x^2$ + \$(y^2$$= 16$\)

D. $x^2$ + \$(y^2$$= 32$\)

Correct Answer: B

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Question 20 View Details

Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...

A. 1023

B. 1024

Correct C. 1025

D. 1026

Correct Answer: C

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Question 21 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = \sqrt{x}$ and $y = x^2$ about the x-axis.

Correct A. \piint_$0^1$ $x^2 - x^{4/3}$ dx

B. \piint_$0^1$ $x^{4/3} - x^2$ dx

C. \piint_$0^1$ $x^{2/3} - x^2$ dx

D. \piint_$0^1$ $x^2 - x^{2/3}$ dx

Correct Answer: A

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Question 22 View Details

Solve the system of equations: \begin{align*} x + y + z &= 3 \ 2x + 2y + 2z &= 6 \ x + 2y + 4z &= 7 \end{align*}

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

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

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

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

Correct Answer: A

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Question 23 View Details

Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.

Correct A. $\frac{4}{3}$\)

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

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

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

Correct Answer: A

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Question 24 View Details

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

Correct A. \piint_$0^2$ $2x - x^2$ dx

B. \piint_$0^2$ $x^2 - 2x$ dx

C. \piint_$0^2$ $2x^2 - x$ dx

D. \piint_$0^2$ $x^2 - 2x^2$ dx

Correct Answer: A

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Question 25 View Details

Solve the equation $x^3 + 2x^2 - 5x - 6 = 0$.

Correct A. $x = -1$

B. $x = 2$

C. $x = -2$

D. $x = 3$

Correct Answer: A

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