Exam Body

Year

Subject

Paper Type

POST UTME LAUTECH 2018 Mathematics | Objective

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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

B. 48π cm³

Correct C. 60π cm³

D. 72π cm³

Correct Answer: C

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Question 2

In the circle shown, find the length of the arc intercepted by the central angle of 60°.

A. 3π cm

B. 6π cm

Correct C. 9π cm

D. 12π cm

Correct Answer: C

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Question 3

Solve the system of equations u\sing matrices:\n\( egin{cases} x + 2y = 6 \ 3x - 2y = -3 \end{cases} \)

Correct A. \( x = 3, y = 1.5 \)

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

C. \( x = 1, y = 2.5 \)

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

Correct Answer: A

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Question 4

Find the mean deviation of the data set: { 2, 4, 6, 8, 10 }.

A. 2

B. 4

Correct C. 6

D. 8

Correct Answer: C

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Question 5

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. \( y = 2x - 1 \)

B. \( y = 2x + 1 \)

C. \( y = -2x + 3 \)

D. \( y = 2x - 3 \)

Correct Answer: A

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Question 6

Solve for x in the equation \( \frac{1}{2} \log_{10} \( x^2 \ \) = 4 )

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7

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. 2

D. 3

Correct Answer: A

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Question 8

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. What is the probability that a randomly selected score will be between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 9

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 10

Find the value of \( \sin\( 2x \ \) ) given that \( \cos\( x \ \) = \frac{3}{5} ) and \( \sin\( x \ \) = \frac{4}{5} )

Correct A. \frac{24}{25}

B. \frac{16}{25}

C. \frac{12}{25}

D. \frac{8}{25}

Correct Answer: A

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Question 11

A survey of 100 students revealed that 60% of them preferred Mathematics, 20% preferred English, and 20% preferred neither. If 5 students who preferred Mathematics were randomly selected, what is the probability that at least 3 of them preferred English?

A. 0.25

B. 0.30

Correct C. 0.35

D. 0.40

Correct Answer: C

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Question 12

A rec\tangular box has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the volume of the box in cubic centimeters?

Correct A. 400

B. 500

C. 600

D. 800

Correct Answer: A

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Question 13

A quadratic equation has a discriminant of 12 and a leading coefficient of 2. What is the sum of the roots of the equation?

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 14

A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has 10 bars, what is the probability that the value of the 6th bar is greater than 30?

A. 0.20

B. 0.25

Correct C. 0.30

D. 0.35

Correct Answer: C

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Question 15

A linear equation has a slope of 2 and a y-intercept of 3. What is the equation of the line in slope-intercept form?

Correct A. y = 2x + 3

B. y = 2x - 3

C. y = -2x + 3

D. y = -2x - 3

Correct Answer: A

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Question 16

Let ( f(x) = x^3 - 6x^2 + 11x + 4 ) and ( g(x) = x^2 - 5x + 6 ). Find the value of ( f(g(2)) ).

Correct A. 4

B. -4

C. 0

D. 6

Correct Answer: A

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Question 17

A binary operation ( odot ) is defined as \( a odot b = ab + 2a + 3b \). Find the value of ( 2 odot 3 ).

Correct A. 19

B. 21

C. 23

D. 25

Correct Answer: A

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Question 18

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first 5 terms.

A. 305

Correct B. 315

C. 325

D. 335

Correct Answer: B

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Question 19

A circle with center ( C ) and radius 4 passes through the point ( P(3, 4) ). Find the equation of the circle.

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 16

B. \( x + 3 \)^2 + \( y - 4 \)^2 = 16

C. \( x - 3 \)^2 + \( y + 4 \)^2 = 16

D. \( x + 3 \)^2 + \( y + 4 \)^2 = 16

Correct Answer: A

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Question 20

A line passes through the points ( A(2, 3) ) and ( B(4, 5) ). Find the equation of the line.

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 5

D. y = x - 5

Correct Answer: A

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Question 21

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.

A. 12.5%

Correct B. 15%

C. 17.5%

D. 20%

Correct Answer: B

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Question 22

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

Correct A. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16

B. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16

C. \left\( x + 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16

D. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16

Correct Answer: A

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Question 23

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find its volume.

Correct A. 400 \text{ cm}^3

B. 500 \text{ cm}^3

C. 600 \text{ cm}^3

D. 800 \text{ cm}^3

Correct Answer: A

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Question 24

Solve the system of equations u\sing matrices: \begin{align*} x + y &= 4 \ 2x - 3y &= -1 \end{align*}

Correct A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 1 \end{bmatrix}

B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 2 \end{bmatrix}

C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 3 \end{bmatrix}

D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 0 \end{bmatrix}

Correct Answer: A

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Question 25

Simplify the expression: \frac{2x^2 - 5x + 3}{x^2 - 2x - 3}

Correct A. \frac{\( 2x - 3 \)\( x - 1 \)}{\( x - 3 \)\( x + 1 \)}

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

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

D. \frac{\( 2x - 1 \)\( x + 3 \)}{\( x - 3 \)\( x + 1 \)}

Correct Answer: A

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