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POST UTME LEAD CITY UNIVERSITY 2022 Mathematics | Objective

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Question 1

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

Correct A. \( x^2 + y^2 - 6x + 2y + 7 = 0 \)

B. \( x^2 + y^2 - 4x - 2y + 3 = 0 \)

C. \( x^2 + y^2 + 2x - 4y + 5 = 0 \)

D. \( x^2 + y^2 - 2x + 4y + 3 = 0 \)

Correct Answer: A

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Question 2

A random variable ( X ) has a probability distribution given by \( P\( X=x \ \) = \frac{1}{2^x} ) for \( x = 1, 2, 3, ldots \). Find ( P(X geq 3) ).

Correct A. \( \frac{1}{4} \)

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

C. \( \frac{3}{4} \)

D. \( \frac{7}{8} \)

Correct Answer: A

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Question 3

Solve the system of equations \( egin{cases} x + y + z = 6 \ 2x + 2y + 3z = 12 \ 3x + 2y + z = 9 \end{cases} \).

Correct A. \( x = 1, y = 2, z = 3 \)

B. \( x = 2, y = 1, z = 3 \)

C. \( x = 3, y = 2, z = 1 \)

D. \( x = 1, y = 3, z = 2 \)

Correct Answer: A

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Question 4

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

D. \( y = -2x - 1 \)

Correct Answer: A

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Question 5

A sequence is defined by \( a_n = 2n + 1 \) for \( n = 1, 2, 3, ldots \). Find the sum of the first five terms of the sequence.

Correct A. ( 15 )

B. ( 21 )

C. ( 25 )

D. ( 30 )

Correct Answer: A

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Question 6

Determine 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 = 4 )

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

Correct Answer: A

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Question 7

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

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

Correct Answer: A

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Question 8

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \( \frac{1}{4} \)

Correct B. \( \frac{3}{8} \)

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

D. \( \frac{3}{4} \)

Correct Answer: B

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Question 9

Simplify the expression \( \sqrt[3]{64x^3y^3} \).

Correct A. \( 4x^1y^1 \)

B. \( 4x^3y^3 \)

C. \( 64x^3y^3 \)

D. \( 4x^3y^1 \)

Correct Answer: A

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Question 10

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, what is their total daily profit?

A. ₦1250

Correct B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: B

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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. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 12

Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 13

A histogram of exam scores has a mean of 80 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 70 and 90?

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 14

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

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 15

A circle has a radius of 4 cm. What is the area of the circle?

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 16

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 17

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

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 18

Solve the inequality \( x^2 - 4x + 4 > 0 \).

Correct A. \( -\infty, 2 \) \cup \( 2, \infty \)

B. \( -\infty, 0 \) \cup \( 0, \infty \)

C. \( -\infty, 1 \) \cup \( 1, \infty \)

D. \( -\infty, 3 \) \cup \( 3, \infty \)

Correct Answer: A

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Question 19

Find the value of \( \sqrt{\frac{16}{25}} \).

A. 2

Correct B. 4

C. 8

D. 16

Correct Answer: B

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Question 20

Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 21

Find the sum of the first 10 terms of the arithmetic sequence with first term 2 and common difference 3.

Correct A. 155

B. 165

C. 175

D. 185

Correct Answer: A

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Question 22

A circle with center (2, 3) passes through the point (7, 6). Find the equation of the circle.

A. \( x - 2 \)^2 + \( y - 3 \)^2 = 25

Correct B. \( x - 2 \)^2 + \( y - 3 \)^2 = 36

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 49

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 64

Correct Answer: B

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Question 23

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

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 24

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

A. 16

B. 32

Correct C. 48

D. 64

Correct Answer: C

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Question 25

A set of exam scores has a mean of 80 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 90.

A. 0.1587

Correct B. 0.3413

C. 0.4772

D. 0.6745

Correct Answer: B

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