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POST UTME OAU 2020 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 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. \(x + 2\)^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 View Details

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

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 6 View Details

Find the equation of the circle passing 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 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the tangent line to the curve \(y = \(1x\) at the point \\(tangent line to the curve (y =\)1x\(\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 View Details

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 View Details

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

Correct Answer: A

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Question 14 View Details

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

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 View Details

Find the mean of the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} using 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 View Details

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 View Details

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 19 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 - 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 View Details

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 View Details

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 View Details

Solve the system of equations using 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 View Details

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 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. \(x - 2\)^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 View Details

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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