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POST UTME LEAD CITY UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME LEAD CITY UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

Correct A. $ x > 4 $

B. $ x < 4 $

C. $ x = 4 $

D. ( x leq 4 )

Correct Answer: A

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Question 2

A set of exam scores has a mean of 75 and a s\tandard deviation of 10. If a new score of 85 is added, what is the new mean?

Correct A. 80

B. 82

C. 84

D. 86

Correct Answer: A

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Question 3

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

Correct A. 0.083

B. 0.0833

C. 0.08333

D. 0.083333

Correct Answer: A

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Question 4

A sequence is defined by the formula $ a_n = 2n + 1 $. Find the sum of the first 5 terms.

Correct A. 30

B. 31

C. 32

D. 33

Correct Answer: A

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Question 5

Solve the equation $ x^2 + 4x + 4 = 0 $.

Correct A. $ x = -2 $

B. $ x = -1 $

C. $ x = 1 $

D. $ x = 2 $

Correct Answer: A

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Question 6

In a triangle $ABC$, if $\tan A = \frac{1}{3}$ and $\tan B = \frac{1}{2}$, find $\tan C$.

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 7

Solve the inequality $|x^2 - 4| geq 3$.

Correct A. x leq -1 \text{ or } x geq 2

B. x leq -2 \text{ or } x geq 1

C. x leq -3 \text{ or } x geq 2

D. x leq -1 \text{ or } x geq 3

Correct Answer: A

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Question 8

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

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 9

In a circle of radius 4, a chord of length 6 is drawn. Find the dis\tance from the center of the circle to the chord.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 10

A line passes through the points $(1, 2)$ and $(3, 4)$. Find the equation of the line in slope-intercept form.

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 3

D. y = x - 2

Correct Answer: A

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Question 11

Solve for x in the equation $ \sin^2 x + \cos^2 x = 1 $ u\sing the identity $ \sin^2 x + \cos^2 x = 1 $.

Correct A. $ x = \frac{pi}{2} $

B. $ x = \frac{pi}{4} $

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

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

Correct Answer: A

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Question 12

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

A. $ \log 2 - \log 1 $

Correct B. $ \frac{1}{2} \log 2 $

C. $ \frac{1}{2} \log 1 $

D. $ \log 1 - \log 2 $

Correct Answer: B

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Question 13

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

Correct A. $ x = 1, y = 2 $

B. $ x = 2, y = 1 $

C. $ x = 3, y = 4 $

D. $ x = 4, y = 3 $

Correct Answer: A

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Question 14

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 15

Solve the polynomial equation $ x^3 - 2x^2 + 3x - 4 = 0 $ u\sing synthetic division.

A. $ x = 1 $

Correct B. $ x = 2 $

C. $ x = 3 $

D. $ x = 4 $

Correct Answer: B

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Question 16

Let $ S = {1, 2, 3, 4, 5} $ be a set of integers. Find the number of subsets of ( S ) that contain exactly two elements.

Correct A. 10

B. 15

C. 20

D. 25

Correct Answer: A

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Question 17

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.

A. 30

B. 35

Correct C. 40

D. 45

Correct Answer: C

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Question 18

A binary operation ( ast ) is defined on the set of integers by $ a ast b = a^2 + b^2 $ for all integers ( a ) and ( b ). Find the value of ( 2 ast 3 ).

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 19

A polynomial ( p(x) ) is defined by ( p(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of ( p(2) ).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 20

A quadratic equation $ ax^2 + bx + c = 0 $ has roots $ x = 1 $ and $ x = 2 $. Find the value of ( a ).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 21

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

Correct A. 2 + 3 + 9/2 + 27/4 + 81/8 + 243/16 + 729/32 + 2187/64 + 6561/128 + 19683/256

B. 2 + 3 + 9/2 + 27/4 + 81/8 + 243/16 + 729/32 + 2187/64 + 6561/128 + 19683/256 + 59049/512

C. 2 + 3 + 9/2 + 27/4 + 81/8 + 243/16 + 729/32 + 2187/64 + 6561/128 + 19683/256 + 177147/1024

D. 2 + 3 + 9/2 + 27/4 + 81/8 + 243/16 + 729/32 + 2187/64 + 6561/128 + 19683/256 + 531441/2048

Correct Answer: A

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Question 22

Solve for x in the equation $ 2x^2 + 5x - 3 = 0 $.

Correct A. \frac{-5 + \sqrt{109}}{4}

B. \frac{-5 - \sqrt{109}}{4}

C. \frac{5 + \sqrt{109}}{4}

D. \frac{5 - \sqrt{109}}{4}

Correct Answer: A

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Question 23

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 24

A die is rolled 5 times. What is the probability that the sum of the 5 rolls is 20?

A. \frac{1}{6}

B. \frac{1}{12}

Correct C. \frac{1}{24}

D. \frac{1}{36}

Correct Answer: C

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Question 25

Solve for x in the equation $ x^2 + 4x + 4 = 0 $.

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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