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POST UTME REDEEMERS UNIVERSITY 2020 Mathematics | Objective

Are you preparing for POST UTME REDEEMERS UNIVERSITY 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 volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 2

A random variable X has a probability distribution given by the following table:

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 3

If ( f(x) = \frac{1}{x^2 + 1} ), find ( f'(x) ).

A. \( -\frac{2x}{\( x^2 + 1 \ \)^2} )

Correct B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )

C. \( -\frac{2}{\( x^2 + 1 \ \)^2} )

D. \( \frac{2}{\( x^2 + 1 \ \)^2} )

Correct Answer: B

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Question 4

Solve the system of equations:

Correct A. \( x = 2, y = 3 \)

B. \( x = 3, y = 2 \)

C. \( x = 1, y = 4 \)

D. \( x = 4, y = 1 \)

Correct Answer: A

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Question 5

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 6

Find the area under the curve y = \sin(x) from x = 0 to x = π/2.

A. 1

Correct B. 1/2

C. π/2

D. π

Correct Answer: B

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Question 7

Solve the equation \frac{1}{x} + \frac{1}{y} = \frac{1}{2} for x in terms of y.

Correct A. x = 2y/\( y-2 \)

B. x = 2y/\( y+2 \)

C. x = 2y/\( y-1 \)

D. x = 2y/\( y+1 \)

Correct Answer: A

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Question 8

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. 1/2

B. 1/3

Correct C. 2/3

D. 1/6

Correct Answer: C

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Question 9

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

A. 10^4

Correct B. 10^8

C. 10^2

D. 10^6

Correct Answer: B

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Question 10

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

Correct A. 16π

B. 32π

C. 64π

D. 128π

Correct Answer: A

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Question 11

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 256\pi cm^3

B. 512\pi cm^3

Correct C. 768\pi cm^3

D. 1024\pi cm^3

Correct Answer: C

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Question 12

In the circle with equation \( x^2 + y^2 - 6x + 4y - 12 = 0 \), find the equation of the \tangent at the point ( (2, 3) ).

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 1

D. y = x + 2

Correct Answer: A

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Question 13

Find the sum of the first 10 terms of the geometric progression with first term 2 and common ratio 3.

A. 3210

B. 3220

Correct C. 3230

D. 3240

Correct Answer: C

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Question 14

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

A. 20

B. 30

Correct C. 40

D. 50

Correct Answer: C

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Question 15

In the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(5, 6) ), find the equation of the median from vertex ( A ) to side ( BC ).

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 1

D. y = x + 2

Correct Answer: A

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Question 16

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{array} ].

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 17

A rec\tangular solid has a length of 10cm, a width of 5cm, and a height of 8cm. Find its surface area.

A. 240cm^2

Correct B. 250cm^2

C. 260cm^2

D. 270cm^2

Correct Answer: B

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Question 18

Find the sum of the first 10 terms of the arithmetic sequence 2, 5, 8, ...

A. 50

B. 55

Correct C. 60

D. 65

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 = 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 20

Solve the inequality 2x^2 + 5x - 3 > 0.

Correct A. x < -1 or x > 3/2

B. x < 1 or x > 3/2

C. x < -1 or x < 3/2

D. x > 1 or x > 3/2

Correct Answer: A

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Question 21

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the determinant method.

Correct A. \( egin{pmatrix} 6 \ -2 \end{pmatrix} \)

B. \( egin{pmatrix} -6 \ 2 \end{pmatrix} \)

C. \( egin{pmatrix} 2 \ -6 \end{pmatrix} \)

D. \( egin{pmatrix} -2 \ 6 \end{pmatrix} \)

Correct Answer: A

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Question 22

A random experiment has two indep\endent events, A and B, with probabilities ( P(A) = 0.4 ) and ( P(B) = 0.6 ). Find the probability that both events occur.

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.76

Correct Answer: A

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Question 23

Find the determinant of the matrix \( egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} \).

Correct A. -1

B. 1

C. 2

D. 4

Correct Answer: A

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Question 24

The equation of a circle is \( x^2 + y^2 - 4x + 6y + 4 = 0 \). Find the center and radius of the circle.

Correct A. Center: \( 2, -3 \ \) ), Radius: 1

B. Center: \( 2, -3 \ \) ), Radius: 2

C. Center: \( 2, -3 \ \) ), Radius: 3

D. Center: \( 2, -3 \ \) ), Radius: 4

Correct Answer: A

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Question 25

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).

Correct A. \( x = -2 \)

B. \( x = -1 \)

C. \( x = 1 \)

D. \( x = 2 \)

Correct Answer: A

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