Exam Body

Year

Subject

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POST UTME UNILAG 2021 Mathematics | Objective

Are you preparing for POST UTME UNILAG exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Let X be a random variable with probability density function f(x) = \\begin{cases} 2x & 0 < x < 1 \\ 0 & \text{otherwise} \\end{cases}. Find the probability that X is greater than 1/2.

A. 1/4

B. 1/2

Correct C. 3/4

D. 1

Correct Answer: C

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Question 2

Solve the differential equation \\frac{dy}{dx} = \\frac{y}{x} u\sing the chain rule.

Correct A. y = x^2

B. y = x^3

C. y = x^2 + 1

D. y = x^3 + 1

Correct Answer: A

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Question 3

Find the area under the curve y = x^2 from x = 0 to x = 2.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 4

Let A and B be two events such that P(A) = 1/4 and P(B) = 1/2. Find P\( A \cap B \) if A and B are indep\endent.

Correct A. 1/8

B. 1/4

C. 1/2

D. 3/4

Correct Answer: A

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Question 5

Solve the equation x^3 + 2x^2 - 7x + 12 = 0.

A. x = -3

B. x = -1

Correct C. x = 3

D. x = 4

Correct Answer: C

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Question 6

In the diagram below, the graph of \( y = \frac{1}{2} \sin 2x \) is shown. What is the amplitude of the graph?

A. 1

Correct B. 0.5

C. 2

D. 0.25

Correct Answer: B

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Question 7

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

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

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

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

D. \( f\( -x \ \) = \frac{1}{x^2 - 1} )

Correct Answer: B

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Question 8

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

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x < -1 \) or \( x < \frac{3}{2} \)

C. \( x > -1 \) or \( x > \frac{3}{2} \)

D. \( x > -1 \) or \( x < \frac{3}{2} \)

Correct Answer: A

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Question 9

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 10

If \( x^2 + 2x - 3 = 0 \), find the value of ( x ).

A. \( x = -3 \)

Correct B. \( x = 1 \)

C. \( x = -1 \)

D. \( x = 3 \)

Correct Answer: B

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Question 11

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

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

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

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

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

Correct Answer: A

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Question 12

Solve the matrix equation \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 7 \\ 10 \end{bmatrix}.

Correct A. \text{Solution: } x = 1, y = 2

B. \text{Solution: } x = 2, y = 1

C. \text{Solution: } x = 3, y = 4

D. \text{Solution: } x = 4, y = 3

Correct Answer: A

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Question 13

Find the value of \sin 2x if \sin x = \frac{3}{5}.

Correct A. \frac{12}{25}

B. \frac{24}{25}

C. \frac{36}{25}

D. \frac{48}{25}

Correct Answer: A

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Question 14

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

Correct A. \text{Solution: } x = -2

B. \text{Solution: } x = -1

C. \text{Solution: } x = 0

D. \text{Solution: } x = 1

Correct Answer: A

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Question 15

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

Correct A. 124

B. 126

C. 128

D. 130

Correct Answer: A

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Question 16

Determine 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 17

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.

A. \frac{16}{15}\pi

B. \frac{32}{15}\pi

Correct C. \frac{64}{15}\pi

D. \frac{128}{15}\pi

Correct Answer: C

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Question 18

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

A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, -3 \) \cup \( 1, \infty \)

Correct C. \( -\infty, -1 \) \cup \( 1, \infty \)

D. \( -\infty, -3 \) \cup \( 3, \infty \)

Correct Answer: C

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Question 19

Find the equation of the \tangent line to the curve \( y = x^3 - 6x^2 + 9x + 2 \) at the point \( 1, -4 \ \) ).

Correct A. y = -3x + 1

B. y = -3x - 1

C. y = 3x - 1

D. y = 3x + 1

Correct Answer: A

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Question 20

A right circular cone has a height of 12 cm and a base radius of 4 cm. Find the volume of the cone.

A. 192\pi

B. 384\pi

Correct C. 576\pi

D. 768\pi

Correct Answer: C

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Question 21

In the circle with equation \( x - 1 \ \)^2 + \( y - 2 \)^2 = 4 ), find the equation of the \tangent line at the point where it intersects the line \( y = x + 1 \).

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

B. \( y = x - 3 \)

C. \( y = -x + 1 \)

D. \( y = x + 1 \)

Correct Answer: A

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Question 22

A right circular cone has a height of 12 cm and a base radius of 6 cm. Find the volume of the cone.

Correct A. ( 288pi ) cm^3

B. ( 288pi ) m^3

C. ( 288pi ) in^3

D. ( 288pi ) ft^3

Correct Answer: A

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Question 23

Find the sum of the first 10 terms of the geometric series ( 2, 6, 18, ldots ).

Correct A. ( 10494 )

B. ( 10494.5 )

C. ( 10494.9 )

D. ( 10495 )

Correct Answer: A

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Question 24

A set of 5 numbers has a mean of 10. If 2 more numbers are added to the set, the mean becomes 12. Find the sum of the original 5 numbers.

Correct A. ( 40 )

B. ( 45 )

C. ( 50 )

D. ( 55 )

Correct Answer: A

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Question 25

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

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x < -1 \) or \( x < \frac{3}{2} \)

C. \( x > -1 \) or \( x > \frac{3}{2} \)

D. \( x > -1 \) or \( x < \frac{3}{2} \)

Correct Answer: A

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