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POST UTME OAU 2020 Mathematics | Objective

Are you preparing for POST UTME OAU 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

Find the value of ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2

In the diagram below, the graph of \( y = x^2 + 2x + 1 \) intersects the x-axis at two points. Find the sum of the x-coordinates of these points.

A. -1

Correct B. -2

C. -3

D. -4

Correct Answer: B

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Question 3

A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 6m, find the volume of water in the \tank.

A. 1200

B. 2400

Correct C. 3600

D. 4800

Correct Answer: C

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Question 4

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

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

B. \( x + 2 \)^2 + \( y - 3 \)^2 = 16

C. \( x - 2 \)^2 + \( y + 3 \)^2 = 16

D. \( x + 2 \)^2 + \( y + 3 \)^2 = 16

Correct Answer: A

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Question 5

A curve is defined by the equation \( y = \frac{1}{x} \). Find the area under the curve between x = 1 and x = 2.

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 6

Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).

Correct A. \( x^2 + y^2 + 4x - 8y + 12 = 0 \)

B. \( x^2 + y^2 - 4x + 8y + 12 = 0 \)

C. \( x^2 + y^2 + 8x - 4y + 12 = 0 \)

D. \( x^2 + y^2 - 8x + 4y + 12 = 0 \)

Correct Answer: A

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Question 7

A particle moves along the curve \( y = x^2 + 2x \) from \( x = 0 \) to \( x = 4 \). Find the work done by the force of gravity.

A. \( \frac{128}{3} \) Joules

Correct B. \( \frac{256}{3} \) Joules

C. \( \frac{512}{3} \) Joules

D. \( \frac{1024}{3} \) Joules

Correct Answer: B

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Question 8

Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.

A. \( \frac{8}{3} pi \) cubic units

B. \( \frac{16}{3} pi \) cubic units

Correct C. \( \frac{32}{3} pi \) cubic units

D. \( \frac{64}{3} pi \) cubic units

Correct Answer: C

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Question 9

A circle of radius 4 cm is inscribed in a square. Find the area of the region outside the circle but inside the square.

A. ( 48 pi ) square cm

B. ( 64 pi ) square cm

Correct C. ( 96 pi ) square cm

D. ( 128 pi ) square cm

Correct Answer: C

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Question 10

Find the equation of the \tangent line to the curve \( y = \sin x \) at the point \( \frac{pi}{4}, \frac{1}{\sqrt{2}} \ \) ).

Correct A. \( y = x - \frac{pi}{4} + \frac{1}{\sqrt{2}} \)

B. \( y = x - \frac{pi}{4} - \frac{1}{\sqrt{2}} \)

C. \( y = x + \frac{pi}{4} + \frac{1}{\sqrt{2}} \)

D. \( y = x + \frac{pi}{4} - \frac{1}{\sqrt{2}} \)

Correct Answer: A

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Question 11

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. ( 20 )

B. ( 30 )

Correct C. ( 40 )

D. ( 50 )

Correct Answer: C

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Question 12

Solve the equation \( \log_{10} \( x^2 \ \) = 4 ).

Correct A. \( x = 10^4 \)

B. \( x = 10^2 \)

C. \( x = 10^{-2} \)

D. \( x = 10^{-4} \)

Correct Answer: A

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Question 13

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. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )

Correct Answer: A

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Question 14

A particle moves in a straight line with an initial velocity of \( 5 , \text{m/s} \) and an acceleration of \( 2 , \text{m/s}^2 \). Find its velocity after ( 3 ) seconds.

A. \( 13 , \text{m/s} \)

B. \( 15 , \text{m/s} \)

Correct C. \( 17 , \text{m/s} \)

D. \( 19 , \text{m/s} \)

Correct Answer: C

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Question 15

Solve the inequality \( x^2 - 4x + 3 > 0 \).

Correct A. \( x < -1 \) or \( x > 3 \)

B. \( x < 1 \) or \( x > 3 \)

C. \( x < -1 \) or \( x < 3 \)

D. \( x < 1 \) or \( x < 3 \)

Correct Answer: A

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Question 16

Find the mean of the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} u\sing the formula \( ar{x} = \frac{1}{n} sum_{i=1}^{n} x_i \).

Correct A. 5

B. 6

C. 7

D. 8

Correct Answer: A

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Question 17

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the value of \( a_6 \).

A. 33

B. 35

Correct C. 37

D. 39

Correct Answer: C

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Question 18

The area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) can be found u\sing the definite integral \( int_{0}^{2} x^2 dx \). Evaluate this integral.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 19

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

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

B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 20 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 24 )

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 28 )

Correct Answer: A

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Question 20

A histogram is constructed from the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} with class width ( 2 ). Find the area of the histogram.

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 21

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

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 22

Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \end{bmatrix}.

Correct A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}

Correct Answer: A

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Question 23

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 2047

Correct B. 2048

C. 2049

D. 2050

Correct Answer: B

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Question 24

Find the equation of the circle with center \( -2, 3 \) and radius 4.

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

B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16

C. \( x + 3 \)^2 + \( y - 2 \)^2 = 16

D. \( x - 3 \)^2 + \( y + 2 \)^2 = 16

Correct Answer: A

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Question 25

Find the mean deviation of the data 2, 4, 6, 8, 10.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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