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POST UTME LEAD CITY UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

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

Correct A. $x > 4$

B. $x < 4$

C. $x = 4$

D. ( x leq 4 )

Correct Answer: A

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Question 2 View Details

A set of exam scores has a mean of 75 and a standard 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 View Details

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 View Details

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 View Details

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 View Details

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

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 7 View Details

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 View Details

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 View Details

In a circle of radius 4, a chord of length 6 is drawn. Find the distance 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 View Details

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 View Details

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

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

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

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

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

Correct Answer: A

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Question 12 View Details

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

A. $\(12 -$11\)

Correct B. $\frac{1}{2} $12$

C. $\frac{1}{2} $11$

D. $\(11 -$12\)

Correct Answer: B

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Question 13 View Details

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 View Details

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 View Details

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

A. $x = 1$

Correct B. $x = 2$

C. $x = 3$

D. $x = 4$

Correct Answer: B

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Question 16 View Details

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 View Details

A sequence is defined by (a_$n = 2n + 1$\) for $n = 1, 2, 3, ldots\\((a_n = 2n + 1) for$. 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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