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POST UTME ESUT 2020 Mathematics | Objective

Are you preparing for POST UTME ESUT 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.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \)

Correct A. 2

B. -3

C. 4

D. -2

Correct Answer: A

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Question 2

Solve for y in the equation \( y = \log_{10} \( x^2 \ \) = 4 )

Correct A. 10^4

B. 10^2

C. 10^8

D. 10^6

Correct Answer: A

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Question 3

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 4

A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 5

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

Correct A. 50.24

B. 100.48

C. 200.96

D. 50.72

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 - 6x - 4y + 11 = 0

B. x^2 + y^2 - 8x - 6y + 15 = 0

C. x^2 + y^2 - 10x - 8y + 19 = 0

D. x^2 + y^2 - 12x - 10y + 23 = 0

Correct Answer: A

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Question 7

Solve the differential equation \( \frac{dy}{dx} = \frac{2x}{y} \) with the initial condition y(1) = 2.

Correct A. y = x^2 + 1

B. y = x^2 - 1

C. y = x^2 + 2x + 1

D. y = x^2 - 2x + 1

Correct Answer: A

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Question 8

Find the area under the curve y = x^2 from x = 0 to x = 4.

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 9

A sequence is defined by the recurrence relation a_n = 2a_\( n-1 \) + 1, with a_1 = 3. Find the value of a_5.

A. 33

B. 35

Correct C. 37

D. 39

Correct Answer: C

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Question 10

A circle has a radius of 4 cm and passes through the point (0, 3). Find the equation of the circle.

Correct A. x^2 + y^2 - 8x - 12y + 16 = 0

B. x^2 + y^2 - 12x - 8y + 16 = 0

C. x^2 + y^2 - 16x - 12y + 16 = 0

D. x^2 + y^2 - 20x - 15y + 16 = 0

Correct Answer: A

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Question 11

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

Correct A. \boxed{\( x + 2 \)^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 12

Solve the inequality \frac{x - 2}{x + 1} > 0.

Correct A. \boxed{x < -1 \text{ or } x > 2}

B. x < -1 \text{ or } x < 2

C. x > -1 \text{ or } x > 2

D. x < -1 \text{ or } x < 2

Correct Answer: A

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Question 13

Find the value of \sum_{n=1}^{5} n^2.

Correct A. \boxed{55}

B. 50

C. 60

D. 70

Correct Answer: A

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Question 14

A set of 5 numbers has a mean of 10. Find the sum of the numbers.

Correct A. \boxed{50}

B. 40

C. 60

D. 70

Correct Answer: A

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Question 15

Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P\( A \cap B \).

Correct A. \boxed{0.24}

B. 0.3

C. 0.4

D. 0.5

Correct Answer: A

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Question 16

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

Correct A. \boxed{50.24}

B. 40.96

C. 60.48

D. 70.72

Correct Answer: A

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Question 17

Solve the equation \frac{1}{x + 1} + \frac{1}{x - 1} = \frac{2}{x^2 - 1}.

Correct A. \boxed{x = 2}

B. x = -2

C. x = 1

D. x = -1

Correct Answer: A

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Question 18

A set of 4 numbers has a median of 10. Find the sum of the numbers.

Correct A. \boxed{40}

B. 30

C. 50

D. 60

Correct Answer: A

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Question 19

Two events A and B are mutually exclusive. If P(A) = 0.4 and P(B) = 0.6, find P\( A \cup B \).

Correct A. \boxed{1}

B. 0.8

C. 0.9

D. 0.95

Correct Answer: A

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Question 20

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

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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Question 21

Solve the equation 2x^2 + 5x - 3 = 0 u\sing the quadratic formula.

A. 1

Correct B. -1

C. -2

D. 2

Correct Answer: B

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Question 22

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

Solve the trigonometric equation \sin(x) = \cos(x).

Correct A. x = \frac{\pi}{4}

B. x = \\frac{3\\pi}{4}

C. x = \\frac{5\\pi}{4}

D. x = \\frac{7\\pi}{4}

Correct Answer: A

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Question 24

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 25

Solve the system of equations x + y = 4 and x - y = 2.

Correct A. x = 3, y = 1

B. x = 1, y = 3

C. x = 2, y = 2

D. x = 4, y = 0

Correct Answer: A

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