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POST UTME BELLS UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

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

Correct A. $x^2 + y^2 + 4x - 6y + 5 = 0$

B. $x^2 + y^2 - 4x + 6y + 5 = 0$

C. $x^2 + y^2 + 2x - 4y + 5 = 0$

D. $x^2 + y^2 - 2x + 4y + 5 = 0$

Correct Answer: A

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Question 2 View Details

Solve the equation $\frac{x}{2} + \frac{2}{x} = 5$ for ( x ).

Correct A. $x = \frac{10 \pm \sqrt{6}}{2}$

B. $x = \frac{10 \pm \sqrt{4}}{2}$

C. $x = \frac{10 \pm \sqrt{8}}{2}$

D. $x = \frac{10 \pm \sqrt{10}}{2}$

Correct Answer: A

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Question 3 View Details

Find the area under the curve $y = $1x$ from $x = 0$ to $x = \frac{\pi}{2}$.

Correct A. $\frac{1}{2}$

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

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

D. $\frac{\pi}{4}$

Correct Answer: A

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Question 4 View Details

Solve the inequality $|x - 2| > 3$.

Correct A. $x < -1$ or $x > 5$

B. $x < 1$ or $x > 5$

C. $x < -1$ or $x > 4$

D. $x < 1$ or $x > 4$

Correct Answer: A

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Question 5 View Details

Find the equation of the line passing through the points (1,2) and (3,4).

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 6 View Details

In the diagram below, a circle with center O and radius 6cm is tangent to the x-axis at point P. If the equation of the circle is $x - h \\\(tangent to the x-axis at point P. If the equation of the circle is (x - h$^2 + $y - k$^$2 = r\^2$ ), where ( (h, k) ) is the center of the circle, find the value of ( h ).

A. 0

B. 3

Correct C. 6

D. 9

Correct Answer: C

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Question 7 View Details

Solve the inequality ($\frac{\(x^2 - 4}{x^2 - 9}$$> 0$\) for x in \$(frac{\(x^2 - 4}{x^2 - 9}$$> 0$\mathbb{R} \setminus \{3\}\).

Correct A. $-\infty, -3$ \cup $3, \infty$\)

B. $-\infty, -3$ \cup $3, \infty$ \cup $0, \infty$\)

C. $-\infty, -3$ \cup $3, \infty$ \cup $-\infty, 0$\)

D. $-\infty, -3$ \cup $3, \infty$ \cup $-\infty, 0$ \cup $0, \infty$\)

Correct Answer: A

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Question 8 View Details

A vector $\mathbf{a}$ has magnitude 5 and direction $theta = 30^\circ$. Find the magnitude of the vector \$theta = 30^circ\(mathbf{a} + \mathbf{b}$, where \$mathbf{a} + mathbf{b}\(mathbf{b}$ is a unit vector in the direction of $\\(mathbf{b}) is a unit vector in the direction of \mathbf{a}$.

A. 6

B. 7

Correct C. 8

D. 9

Correct Answer: C

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Question 9 View Details

The mean of a set of 5 numbers is 10. If the largest number is 20, find the sum of the remaining 4 numbers.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 10 View Details

A circle with center O and radius 4cm is inscribed in a square with side length 8cm. Find the area of the shaded region.

A. 16\pi

B. 32\pi

Correct C. 48\pi

D. 64\pi

Correct Answer: C

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Question 11 View Details

Determine the value of lim_{x \to 0} $\frac{$1x}{x}$\) using the definition of a derivative.

A. 1

Correct B. 0

C. -1

D. undefined

Correct Answer: B

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Question 12 View Details

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) using the standard form of a circle's equation.

Correct A. $x - 2 \$^2 + $y - 3$^$2 = 16$ )

B. $x + 2 \$^2 + $y - 3$^$2 = 16$ )

C. $x - 2 \$^2 + $y + 3$^$2 = 16$ )

D. $x + 2 \$^2 + $y + 3$^$2 = 16$ )

Correct Answer: A

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Question 13 View Details

Solve the inequality $|2x - 3| > 5$ using the properties of absolute value.

Correct A. $x < -1$ or $x > 4$

B. $x < -4$ or $x > 1$

C. $x < 1$ or $x > 4$

D. $x < -4$ or $x > 1$

Correct Answer: A

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Question 14 View Details

Find the derivative of the function ( f(x) = $\frac{1}{x^2 + 1}$\)\) ) using 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 15 View Details

Solve the system of equations $egin{cases} x + y = 2 \ x - y = 1 \end{cases}$ using the method of substitution.

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

B. $x = 1, y = 3$

C. $x = 3, y = 1$

D. $x = 3, y = 3$

Correct Answer: A

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Question 16 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

A. -3

Correct B. 0

C. 3

D. 6

Correct Answer: B

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Question 17 View Details

Solve the equation [ \$(x^2 + 5x + 6$$= 0$\) ] using the quadratic formula.

Correct A. -2

B. -3

C. -1

D. 1

Correct Answer: A

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Question 18 View Details

A set of numbers has a mean of 10 and a standard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?

A. 0.25

B. 0.5

Correct C. 0.75

D. 1

Correct Answer: C

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Question 19 View Details

Find the derivative of the function [$f(x) =$$3x^2 + 2x - 5$ \] using the power rule.

Correct A. 6x + 2

B. 6x - 2

C. $3x^2 + 2$

D. $3x^2 - 2$

Correct Answer: A

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Question 20 View Details

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

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 21 View Details

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

Correct A. $10^4$

B. $10^2$

C. $10^8$

D. $10^12$

Correct Answer: A

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Question 22 View Details

A circle with center (0,0) has equation $x^2 + y^2 = 25$. Find the equation of the line perpendicular to the radius that passes through the point (3,4).

Correct A. $y = -$$\frac{4}{3}$\) x + 5

B. $y =$$\frac{4}{3}$\) x - 5

C. $y = -$$\frac{3}{4}$\) x + 5

D. $y =$$\frac{3}{4}$\) x - 5

Correct Answer: A

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Question 23 View Details

A quadratic equation has roots 2 and 5. Write the equation in factored form.

Correct A. $x - 2$, $x - 5 = 0$\)

B. $x - 5$, $x - 2 = 0$\)

C. $x + 2$, $x + 5 = 0$\)

D. $x + 5$, $x + 2 = 0$\)

Correct Answer: A

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Question 24 View Details

A random experiment has two independent events A and B. If P(A) = 0.4 and P(B) = 0.6, find P($A \cap B$).

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 25 View Details

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

Correct A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, -3$ ∪ (1, ∞)

C. $-∞, 1$ ∪ (3, ∞)

D. $-∞, -3$ ∪ (1, ∞)

Correct Answer: A

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