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POST UTME LASU 2020 Mathematics | Objective

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Question 1

Find the equation of the circle pas\sing through the points (2,3), (4,5), and $ -1,2 $.

Correct A. $ x^2 + y^2 + 6x - 4y - 12 = 0 $

B. $ x^2 + y^2 - 6x + 4y - 12 = 0 $

C. $ x^2 + y^2 + 6x + 4y - 12 = 0 $

D. $ x^2 + y^2 - 6x - 4y - 12 = 0 $

Correct Answer: A

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Question 2

A rec\tangular block measures 5cm by 3cm by 2cm. Find the volume of the block.

A. 30cm^3

B. 60cm^3

Correct C. 90cm^3

D. 120cm^3

Correct Answer: C

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Question 3

Find the area under the curve $ y = \frac{1}{x} $ from $ x = 1 $ to $ x = 2 $.

Correct A. ( ln(2) - ln(1) )

B. ( ln(2) + ln(1) )

C. ( ln(1) - ln(2) )

D. ( ln(1) + ln(2) )

Correct Answer: A

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Question 4

Solve the equation $ 2^x + 2^{-x} = 10 $.

A. $ x = 2 $

B. $ x = -2 $

Correct C. $ x = \log_2\( 5 \ $ )

D. $ x = -\log_2\( 5 \ $ )

Correct Answer: C

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Question 5

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. $ -1 $

D. ( 2 )

Correct Answer: A

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Question 6

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

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

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

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

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

Correct Answer: A

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Question 7

Solve the system of equations u\sing matrices: $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} $.

Correct A. $ x = 2, y = 3 $

B. $ x = 3, y = 2 $

C. $ x = 4, y = 5 $

D. $ x = 5, y = 4 $

Correct Answer: A

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Question 8

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

A. $ \frac{32}{3} pi $

Correct B. $ \frac{64}{3} pi $

C. $ \frac{128}{3} pi $

D. $ \frac{256}{3} pi $

Correct Answer: B

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Question 9

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

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

B. $ 2\cos\( x \ $ )

C. $ 2\sin\( x \ $ )

D. $ 2\sin\( x $\cos(x \) + \sin^2(x) )

Correct Answer: A

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Question 10

Find the determinant of the matrix $ egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} $.

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 11

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 12

Solve for x in the equation $ \frac{x}{2} + 3 = 7 $.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 13

Find the determinant of the matrix $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} $.

Correct A. -2

B. 2

C. 4

D. 6

Correct Answer: A

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Question 14

A histogram is constructed with the following data: 2, 4, 6, 8, 10. What is the class width?

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 15

Solve the inequality $ x^2 + 4x + 4 > 0 $.

Correct A. $ -∞, -2 $ ∪ (2, ∞)

B. $ -∞, 2 $

C. $ -2, 2 $

D. (2, ∞)

Correct Answer: A

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Question 16

Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).

Correct A. $ x^2 + y^2 + 2gx + 2fy + c = 0 $

B. $ x^2 + y^2 + 2gx - 2fy + c = 0 $

C. $ x^2 + y^2 - 2gx + 2fy + c = 0 $

D. $ x^2 + y^2 - 2gx - 2fy + c = 0 $

Correct Answer: A

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Question 17

A rec\tangular water \tank with a length of 4m, a width of 3m, and a height of 2m is filled with water. Find the volume of water in the \tank.

A. $ 24m^3 $

B. $ 36m^3 $

Correct C. $ 48m^3 $

D. $ 60m^3 $

Correct Answer: C

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Question 18

Solve the equation $ x^3 - 6x^2 + 11x - 6 = 0 $ u\sing the factor theorem.

A. $ x = 1 $

B. $ x = 2 $

Correct C. $ x = 3 $

D. $ x = 4 $

Correct Answer: C

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Question 19

A right-angled triangle has a hypotenuse of length 10cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. ( 5cm )

Correct B. ( 7.5cm )

C. ( 10cm )

D. ( 12.5cm )

Correct Answer: B

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Question 20

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

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

B. ( f'(x) = \frac{2x}{$ x^2 + 1 $^2} )

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

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

Correct Answer: A

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Question 21

In a circle with center O and radius 6, chord AB is 8 units long. If point P is the midpoint of AB, find the area of triangle OAP.

A. 12\sqrt{3}

B. 16\sqrt{3}

Correct C. 20\sqrt{3}

D. 24\sqrt{3}

Correct Answer: C

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Question 22

Let $A = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}$. Find the determinant of $A^2$.

A. 0

B. 1

Correct C. 4

D. 9

Correct Answer: C

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Question 23

A binary operation $\circ$ on the set $\mathbb{Z}_4$ is defined by $a \circ b = a^2 + b^2$. Find the value of $1 \circ 2$.

A. 0

B. 1

C. 2

Correct D. 3

Correct Answer: D

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Question 24

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the die shows an even number and the coin lands heads up, what is the probability that the die shows a 4?

A. \frac{1}{6}

B. \frac{1}{3}

Correct C. \frac{1}{2}

D. \frac{2}{3}

Correct Answer: C

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Question 25

Let $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$. Find the inverse of $A$.

Correct A. \begin{bmatrix} 4 & -2 \\ -3 & 1 \end{bmatrix}

B. \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}

C. \begin{bmatrix} 2 & -1 \\ -3 & 1 \end{bmatrix}

D. \begin{bmatrix} 1 & -2 \\ 3 & -4 \end{bmatrix}

Correct Answer: A

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