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POST UTME OSUSTECH 2023 Mathematics | Objective

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Question 1 View Details

Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 6cm.

A. 100\pi \(cm^3\)

B. 200\pi \(cm^3\)

Correct C. 300\pi \(cm^3\)

D. 400\pi \(cm^3\)

Correct Answer: C

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Question 2 View Details

Solve for x in the equation \\(tan x =\)\(\frac{1}\){\(\sqrt{3}\)}\).

Correct A. \(\frac{\pi}{6}\)\)

B. \(\frac{\pi}{3}\)\)

C. \(\frac{\pi}{2}\)\)

D. \(\frac{2\pi}{3}\)\)

Correct Answer: A

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Question 3 View Details

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. \(\frac{1}{6}\)\)

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

C. \(\frac{1}{2}\)\)

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

Correct Answer: B

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Question 4 View Details

Find the mean of the numbers 2, 4, 6, 8, 10.

A. 6

B. 7

Correct C. 8

D. 9

Correct Answer: C

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Question 5 View Details

A circle has a radius of 4cm. Find the area of the circle.

A. 16\pi \(cm^2\)

B. 32\pi \(cm^2\)

Correct C. 64\pi \(cm^2\)

D. 128\pi \(cm^2\)

Correct Answer: C

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Question 6 View Details

In the diagram below, a circle is inscribed in a square. If the radius of the circle is 4 cm, what is the area of the shaded region?

Correct A. 16π

B. 64

C. 32

D. 128

Correct Answer: A

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Question 7 View Details

A polynomial function f(x) is defined as f(x) = \((x^3 + 2x^2 - 7x - 12\)\). Find the value of f\(-2\\((x^3 + 2x^2 - 7x - 12). Find the value of f\).

Correct A. -2

B. 4

C. -4

D. 12

Correct Answer: A

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Question 8 View Details

In a histogram, the class width is 5 and the number of classes is 6. If the total frequency is 30, what is the class frequency?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 9 View Details

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the prism.

A. 400

B. 500

Correct C. 600

D. 800

Correct Answer: C

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Question 10 View Details

In a circle, the length of the major axis is 10 cm and the length of the minor axis is 8 cm. Find the area of the circle.

A. 50π

B. 75π

Correct C. 100π

D. 125π

Correct Answer: C

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Question 11 View Details

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

Correct A. text{Equation: } \(x - 2\)^2 + \\(text{Equation:} (x - 2\(y - 3\)^\(2 = 16\)

B. text{Equation: } \(x + 2\)^2 + \\(text{Equation:} (x + 2\(y - 3\)^\(2 = 16\)

C. text{Equation: } \(x - 2\)^2 + \\(text{Equation:} (x - 2\(y + 3\)^\(2 = 16\)

D. text{Equation: } \(x + 2\)^2 + \\(text{Equation:} (x + 2\(y + 3\)^\(2 = 16\)

Correct Answer: A

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Question 12 View Details

Solve the system of equations using matrices: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}

Correct A. \text{Solution: } \(x = 3\), \(y = 1\)

B. \text{Solution: } \(x = 1\), \(y = 3\)

C. \text{Solution: } \(x = 2\), \(y = 2\)

D. \text{Solution: } \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 13 View Details

Find the mean and standard deviation of the data set: \{2, 4, 6, 8, 10\}

Correct A. \text{Mean: } 6, \text{Standard Deviation: } 2

B. \text{Mean: } 4, \text{Standard Deviation: } 2

C. \text{Mean: } 6, \text{Standard Deviation: } 4

D. \text{Mean: } 4, \text{Standard Deviation: } 4

Correct Answer: A

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Question 14 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

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

B. \(\frac{3}{5}\)\)

Correct C. \(\frac{3}{8}\)\)

D. \(\frac{5}{8}\)\)

Correct Answer: C

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Question 15 View Details

Find the sum of the first 5 terms of the geometric progression: \{2, 6, 18, 54, 162\}

Correct A. 242

B. 242.5

C. 243

D. 243.5

Correct Answer: A

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Question 16 View Details

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 17 View Details

A particle moves in a straight line with its position given by ( s(t) = \((2t^3 - 5t^2 + 3t + 1\)\) ). Find the velocity of the particle at time \(t = 2\\((2t^3 - 5t^2 + 3t + 1) ). Find the velocity of the particle at time\) seconds.

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 18 View Details

Solve the system of linear equations: \(egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}\).

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 19 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 1 & 4 \ 3 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix}\).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 20 View Details

A binary operation ( ast ) on the set ( {1, 2, 3, 4} ) is defined by \(a ast b = a + b\). Find the result of ( 2 ast 3 ).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 21 View Details

Determine the mean of the following dataset: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 22 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 23 View Details

Solve the system of linear equations using matrices: \(2x + 3y = 7\) 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 24 View Details

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

Correct A. \(y = x + 1\)

B. \(y = x - 1\)

C. \(y = x + 2\)

D. \(y = x - 2\)

Correct Answer: A

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Question 25 View Details

Determine the standard deviation of the dataset: 1, 3, 5, 7, 9.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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