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POST UTME LEAD CITY UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Find the value of x in the equation $\frac{1}{x} + \frac{1}{2} = \frac{3}{4}$.

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 2 View Details

A circle with center (0, 0) and radius 5 passes through the point (3, 4). Find the equation of the circle.

Correct A. $x^2 + y^2 = 25$

B. $x^2 + y^2 = 16$

C. $x^2 + y^2 = 9$

D. $x^2 + y^2 = 4$

Correct Answer: A

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Question 3 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$.

Correct A. $x < -1$ or $x > \frac{3}{2}$

B. $x < -1$ or $x < \frac{3}{2}$

C. $x > -1$ or $x > \frac{3}{2}$

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

Correct Answer: A

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Question 4 View Details

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

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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Question 5 View Details

A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 3$ with initial term $a_1 = 2$. Find the value of $a_{10}$.

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 6 View Details

Determine the value of k in the polynomial equation $x^3 + 2x^2 - 7x - 12 = k x + 3$, x - 1 \\) ).

Correct A. -3

B. -1

C. 1

D. 3

Correct Answer: A

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Question 7 View Details

Find the area under the curve $y = \frac{1}{2}x^2 + 2x - 3$ from $x = 0$ to $x = 4$.

A. 32

B. 40

Correct C. 48

D. 56

Correct Answer: C

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Question 8 View Details

A set of exam scores has a mean of 70 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 80?

A. 0.135

B. 0.25

Correct C. 0.5

D. 0.75

Correct Answer: C

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Question 9 View Details

Solve for x in the equation $2^x + 2^{x+1} = 3 \cdot 2^{x+1}$.

A. -1

Correct B. 0

C. 1

D. 2

Correct Answer: B

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Question 10 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 80?

A. 0.135

B. 0.25

Correct C. 0.5

D. 0.75

Correct Answer: C

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Question 11 View Details

Determine the value of x in the equation $\sin^2 x \$ + \$\cos^2(x)$ = 1 ) if $$1x \$ = $\frac{3}{5}$\) ).

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

B. $x = \frac{\pi}{2}$

Correct C. $x = \frac{\pi}{6}$

D. $x = \frac{\pi}{3}$

Correct Answer: C

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Question 12 View Details

A random variable X has a probability distribution given by $P X = x \$ = \begin{cases} $\frac{1}{2}$\) & text{if } $x = 1$ \$text{if} (x = 1\(\frac{1}{4}$\) & \text{if } $x = 2$ $\frac{1}{4})$ & \text{if } \$)) & \(x = 3$ \end{cases} ). Find the expected value of X.

Correct A. $( E(X) = 1.5 )$

B. $( E(X) = 2 )$

C. $( E(X) = 2.5 )$

D. $( E(X) = 3 )$

Correct Answer: A

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Question 13 View Details

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

Correct A. $x = -2 \pm 2i$

B. $x = -1 \pm i$

C. $x = -2 \pm i$

D. $x = -1 \pm 2i$

Correct Answer: A

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Question 14 View Details

A function f(x) is defined as ( f(x) = $\frac{x^2 - 4}{x + 2}$\)\) ). Find the domain of the function.

Correct A. x \in $-\infty, -2 \ \cup -2, \infty$ )

B. x \in $-\infty, 2 \ \cup 2, \infty$ )

C. x \in $-\infty, -2 \ \cup 2, \infty$ )

D. x \in $-\infty, 2 \ \cup -2, \infty$ )

Correct Answer: A

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Question 15 View Details

A curve is defined by the equation (y = $\frac{1}{x}$\). Find the equation of the \\$((y = frac${1}{x}\tangent line to the curve at the point (1, 1).

Correct A. $y = x - 1$

B. $y = x + 1$

C. $y = -x + 1$

D. $y = x - 2$

Correct Answer: A

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Question 16 View Details

Let ( S ) be the set of all ordered pairs ( (x, y) ) such that $x^2 + y^2 \leq 4$. Find the number of elements in the set ( S ).

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 17 View Details

A sequence is defined by $a_n = \frac{1}{n} + \frac{1}{n+1}$ for ( n geq 1 ). Find the sum of the first 5 terms of the sequence.

A. 1.5

Correct B. 2.5

C. 3.5

D. 4.5

Correct Answer: B

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Question 18 View Details

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

A. $1/2$

B. $1/3$

Correct C. $2/5$

D. $3/5$

Correct Answer: C

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Question 19 View Details

Let $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} 4 \ 5 end{pmatrix}$. Find the magnitude of the vector $\\(end{pmatrix}). Find the magnitude of the vector \mathbf{a} + \mathbf{b}$.

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 20 View Details

A polynomial ( p(x) ) is defined by ( p(x) = $(x^3 + 2x^2 - 5x + 1$\) ). Find the value of $p -1 \\((x^3 + 2x^2 - 5x + 1) ). Find the value of \$ ).

Correct A. -3

B. -2

C. -1

D. 0

Correct Answer: A

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Question 21 View Details

A solid right circular cone has a height of 8 cm and a base radius of 3 cm. Find the volume of the cone in cubic centimeters.

Correct A. 48\pi

B. 64\pi

C. 72\pi

D. 80\pi

Correct Answer: A

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Question 22 View Details

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

Correct A. 2x - 1

B. 2x + 1

C. x + 2

D. x - 2

Correct Answer: A

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Question 23 View Details

Find 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 + $y - 3$^$2 = 25$ \)

C. $x - 2$^2 + $y - 3$^$2 = 36$ \)

D. $x - 2$^2 + $y - 3$^$2 = 49$ \)

Correct Answer: A

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Question 24 View Details

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

A. 8

Correct B. 10

C. 12

D. 14

Correct Answer: B

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Question 25 View Details

Solve the inequality: $2x - 5 > 3x + 2$.

Correct A. $x < -\frac{7}{2}$

B. $x > -\frac{7}{2}$

C. $x < \frac{7}{2}$

D. $x > \frac{7}{2}$

Correct Answer: A

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