Exam Body

Year

Subject

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POST UTME FUTO 2023 Mathematics | Objective

Are you preparing for POST UTME FUTO exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

Solve the matrix equation $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} $.

Correct A. x = 1, y = 2

B. x = 2, y = 3

C. x = 3, y = 4

D. x = 4, y = 5

Correct Answer: A

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Question 3

Find the area of the triangle with vertices (1, 2), (3, 4), and (5, 6).

Correct A. 10

B. 20

C. 30

D. 40

Correct Answer: A

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Question 4

Solve the trigonometric equation $ \sin^2 x + \cos^2 x = 1 $.

Correct A. x = 0

B. x = 90

C. x = 180

D. x = 270

Correct Answer: A

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Question 5

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

Correct A. 1200

B. 1300

C. 1400

D. 1500

Correct Answer: A

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Question 6

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. 32\pi cm^3

Correct B. 64\pi cm^3

C. 128\pi cm^3

D. 256\pi cm^3

Correct Answer: B

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Question 7

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

A. x < 2

B. x > 2

Correct C. x < 0 or x > 2

D. x > 0 or x < 2

Correct Answer: C

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Question 8

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

A. 36

B. 48

Correct C. 60

D. 72

Correct Answer: C

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Question 9

Solve the equation x^2 + 4x - 5 = 0.

Correct A. x = -5 or x = 1

B. x = -1 or x = 5

C. x = -2 or x = 3

D. x = -3 or x = 2

Correct Answer: A

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Question 10

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

Correct A. 242

B. 242.5

C. 243

D. 243.5

Correct Answer: A

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Question 11

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

A. 24

B. 28

Correct C. 32

D. 36

Correct Answer: C

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Question 12

Solve for ( x ) in the equation $ \sin^2 x + \cos^2 x = 1 \ $.

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

B. x = \frac{\pi}{2}

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

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

Correct Answer: A

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Question 13

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} \).

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

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

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

D. \frac{x}{$ x^2 + 1 $^2}

Correct Answer: B

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Question 14

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

A. x < -1

Correct B. x > -1

C. x < 3

D. x > 3

Correct Answer: B

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Question 15

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 16

Find the volume of the solid formed by rotating the region bounded by the curves $y=x^2$ and $y=4x$ about the x-axis.

Correct A. \frac{32}{15}\pi

B. \frac{16}{3}\pi

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

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

Correct Answer: A

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Question 17

Solve the inequality $\log_2$ x^2+1 $ > 2$.

Correct A. x<-1\lor x>1

B. x>-1\lor x>1

C. x<-1\lor x<1

D. x>-1\lor x<1

Correct Answer: A

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Question 18

Find the area of the region bounded by the curves $y=x^2+1$ and $y=2x+1$.

A. \frac{3}{2}

Correct B. \frac{5}{2}

C. \frac{7}{2}

D. \frac{9}{2}

Correct Answer: B

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Question 19

Solve the equation $\frac{1}{x+1}+\frac{1}{x-1}=\frac{3}{2}$.

A. x=-2

B. x=-1

Correct C. x=1

D. x=2

Correct Answer: C

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Question 20

Find the equation of the line pas\sing through the points $$ -2,3 $$ and $(1,2)$.

Correct A. y=-x+5

B. y=x-1

C. y=-x-1

D. y=x+1

Correct Answer: A

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Question 21

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

A. 5

Correct B. -2

C. 10

D. 0

Correct Answer: B

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Question 22

A histogram is constructed with the following data: [ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ]. If the width of each bar is 2, what is the area of the histogram?

Correct A. 100

B. 200

C. 50

D. 150

Correct Answer: A

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Question 23

Solve the equation [ x^2 + 5x + 6 = 0 ].

Correct A. -2

B. -3

C. 2

D. 3

Correct Answer: A

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Question 24

Find the value of [ \sin(2x) \] when [ \sin(x) = \frac{1}{2} \].

Correct A. \frac{\sqrt{3}}{2}

B. \frac{1}{2}

C. \frac{\sqrt{3}}{2}

D. \frac{1}{2}

Correct Answer: A

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Question 25

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?

A. \frac{1}{3}

Correct B. \frac{2}{5}

C. \frac{4}{12}

D. \frac{1}{2}

Correct Answer: B

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