Exam Body

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POST UTME FUTO 2018 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 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

D. \( \frac{1}{2} \times 4^2 + 3 \times \frac{4^2}{2} - 2 \)

Correct Answer: A

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Question 2

A circle with center ( C(2, 3) ) and radius ( 4 ) has a chord ( AB ) of length ( 6 ). Find the dis\tance from the center ( C ) to the chord ( AB ).

Correct A. \( 2 \sqrt{5} \)

B. \( \sqrt{5} \)

C. \( 2 \sqrt{3} \)

D. \( \sqrt{3} \)

Correct Answer: A

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Question 3

Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \), the ( x )-axis, and the line \( x = 2 \) about the ( x )-axis.

Correct A. \( \frac{16}{3} pi \)

B. \( \frac{32}{3} pi \)

C. \( \frac{64}{3} pi \)

D. \( \frac{128}{3} pi \)

Correct Answer: A

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Question 4

A histogram with class boundaries ( 0, 2, 4, 6, 8 ) and corresponding frequencies ( 3, 5, 7, 2, 1 ) has a mean of ( 4 ). Find the median of the data.

Correct A. ( 4 )

B. ( 5 )

C. ( 6 )

D. ( 7 )

Correct Answer: A

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Question 5

Solve the inequality \( \log_{10} \( x^2 \ \) > 4 ).

Correct A. \( x > 10 \)

B. \( x < 10 \)

C. \( x > 100 \)

D. \( x < 100 \)

Correct Answer: A

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Question 6

A cylindrical \tank with a radius of 5m and a height of 10m is filled with water. If the water level rises by 2m, calculate the volume of water added in cubic meters.

A. 100π

Correct B. 200π

C. 50π

D. π

Correct Answer: B

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Question 7

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, calculate 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 8

A polynomial function f(x) = ax^3 + bx^2 + cx + d has roots at x = -2, x = 1, and x = 3. If f(0) = 10, calculate the value of a.

A. -2

B. 2

Correct C. 4

D. 6

Correct Answer: C

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Question 9

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, calculate the probability that a randomly selected score is between 50 and 70.

A. 0.34

Correct B. 0.68

C. 0.84

D. 0.98

Correct Answer: B

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Question 10

A circle with a radius of 4cm has a chord that is 6cm long. Calculate the dis\tance from the center of the circle to the midpoint of the chord.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 11

Determine the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm. The slant height of the frustum is 8 cm.

A. 48\pi

B. 64\pi

Correct C. 80\pi

D. 96\pi

Correct Answer: C

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Question 12

A binary operation \(*\) on the set \{0, 1, 2\} is defined as follows: \begin{align*}\n0\*0&=0,\quad 0\*1=1,\quad 0\*2=2,\\n1\*0&=1,\quad 1\*1=0,\quad 1\*2=2,\\n2\*0&=2,\quad 2\*1=2,\quad 2\*2=0.\n\end{align*}Find the value of \(\( 1\*2)\*0\ \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 13

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even, the coin is flipped twice. If the number on the die is odd, the coin is flipped only once. Find the probability that the number of heads observed is 2.

A. \frac{1}{6}

B. \frac{1}{12}

Correct C. \frac{1}{4}

D. \frac{1}{3}

Correct Answer: C

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Question 14

The surface area of a sphere of radius 5 cm is 250\pi cm^2. Find the volume of the sphere.

A. 125\pi

Correct B. 250\pi

C. 500\pi

D. 1000\pi

Correct Answer: B

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Question 15

Solve for x in the equation \(\log_2\( x^2 \) - \log_2(x) = 2\).

A. 4

B. 8

Correct C. 16

D. 32

Correct Answer: C

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Question 16

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

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)

D. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \times 4 \)

Correct Answer: A

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Question 17

Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = -1 \end{cases} \) u\sing matrices.

Correct A. \( egin{pmatrix} 1 & 1 \ 2 & -3 \end{pmatrix} \)

B. \( egin{pmatrix} 1 & 2 \ 1 & -3 \end{pmatrix} \)

C. \( egin{pmatrix} 1 & 1 \ 2 & -1 \end{pmatrix} \)

D. \( egin{pmatrix} 1 & 1 \ 2 & 3 \end{pmatrix} \)

Correct Answer: A

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Question 18

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

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

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

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

Correct D. \( \frac{5}{6} \)

Correct Answer: D

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Question 19

Find the derivative of the function \( y = \sin^2 x \) u\sing the chain rule.

Correct A. \( 2 \sin x \cos x \)

B. \( \cos^2 x \)

C. \( \sin x \cos x \)

D. \( \sin^2 x \)

Correct Answer: A

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Question 20

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

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

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

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

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

Correct Answer: A

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Question 21

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

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 22

Solve the equation [ x^2 + 4x + 4 = 0 ].

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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Question 23

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

A. \frac{1}{2}

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

C. \frac{1}{\sqrt{2}}

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

Correct Answer: B

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Question 24

If [ \overrightarrow{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} \] and [ \overrightarrow{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \], find the value of [ \overrightarrow{a} \cdot \overrightarrow{b} \].

Correct A. 25

B. 26

C. 27

D. 28

Correct Answer: A

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Question 25

Solve the equation [ x^2 + 2x + 1 = 0 \] u\sing the quadratic formula.

Correct A. x = -1

B. x = 1

C. x = -2

D. x = 2

Correct Answer: A

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