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POST UTME UNIPORT 2020 Mathematics | Objective

Are you preparing for POST UTME UNIPORT exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

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

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

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

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

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

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

Correct A. 1

B. \frac{1}{2}

C. \frac{2}{3}

D. \frac{3}{2}

Correct Answer: A

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Question 6

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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. \pi\int_0^1 $ x^2 - x^{4/3} $ dx

B. \pi\int_0^1 $ x^{4/3} - x^2 $ dx

C. \pi\int_0^1 $ x^{2/3} - x^2 $ dx

D. \pi\int_0^1 $ x^2 - x^{2/3} $ dx

Correct Answer: A

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Question 22

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

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

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. \pi\int_0^2 $ 2x - x^2 $ dx

B. \pi\int_0^2 $ x^2 - 2x $ dx

C. \pi\int_0^2 $ 2x^2 - x $ dx

D. \pi\int_0^2 $ x^2 - 2x^2 $ dx

Correct Answer: A

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Question 25

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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