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POST UTME UI 2018 Mathematics | Objective

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Question 1 View Details

Find the derivative of the function ( f(x) = $\frac{1}${\sqrt{$x^2 + 1}}$\) ) using the chain rule.

Correct A. ( f'$(x) =$$\frac{-x}${ $x^2 + 1$ \)^{$3/2$}}\) )

B. ( f'$(x) =$$\frac{x}${ $x^2 + 1$ \)^{$3/2$}}\) )

C. ( f'$(x) =$$\frac{1}${ $x^2 + 1$ \)^{$3/2$}}\) )

D. ( f'$(x) =$$\frac{-1}${ $x^2 + 1$ \)^{$3/2$}}\) )

Correct Answer: A

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Question 2 View Details

Solve the system of equations using matrices:$egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}$.

Correct A. $egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix}$

B. $egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix}$

C. $egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}$

D. $egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix}$

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

D. $\frac{1}{4}$

Correct Answer: A

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Question 4 View Details

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

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

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

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

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

Correct Answer: A

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Question 5 View Details

Find the derivative of the function ( f(x) = $\frac{1}{x^2}$\)\) ) using the chain rule.

A. ( f'$(x) =$$\frac{-2}{x^3}$\)\) )

Correct B. ( f'$(x) =$$\frac{2}{x^3}$\)\) )

C. ( f'$(x) =$$\frac{-1}{x^3}$\)\) )

D. ( f'$(x) =$$\frac{1}{x^3}$\)\) )

Correct Answer: B

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Question 6 View Details

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

Correct A. $x^2$ + \$(y^2 - 6x - 4y + 12$$= 0$\)

B. $x^2$ + \$(y^2 - 8x - 2y + 16$$= 0$\)

C. $x^2$ + \$(y^2 - 4x - 6y + 20$$= 0$\)

D. $x^2$ + \$(y^2 - 2x - 4y + 8$$= 0$\)

Correct Answer: A

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Question 7 View Details

Evaluate the integral \int_$0^1$ $x^2$ \ln x \, dx.

Correct A. $\frac{1}{3}$\) - $\frac{1}{4}$\)

B. $\frac{1}{2}$\) - $\frac{1}{3}$\)

C. $\frac{1}{3}$\) + $\frac{1}{4}$\)

D. $\frac{1}{2}$\) + $\frac{1}{3}$\)

Correct Answer: A

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Question 8 View Details

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

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

B. $\frac{2}{3}$\)

Correct C. $\frac{5}{8}$\)

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

Correct Answer: C

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Question 9 View Details

Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...

A. 3120

B. 3240

Correct C. 3360

D. 3480

Correct Answer: C

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Question 10 View Details

Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 11 View Details

Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.

A. 64π cm³

Correct B. 128π cm³

C. 256π cm³

D. 512π cm³

Correct Answer: B

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Question 12 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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Question 13 View Details

Find the area of the region bounded by the parabola (y = $x^2 + 1$\) and the line $y = 2x + 1\\((y = x^2 + 1) and the line$.

A. $3/2$

B. $5/2$

Correct C. $7/2$

D. $9/2$

Correct Answer: C

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Question 14 View Details

Solve the equation $x^2 + 2x - 6 = 0$.

A. $-3, 2$

Correct B. $-2, 3$

C. $1, -2$

D. $-1, 2$

Correct Answer: B

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Question 15 View Details

Find the value of (x) in the equation $2^x + 2^x = 64$.

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 16 View Details

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

Correct A. $\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \$ )

B. $\frac{1}{2} \left \frac{0^3}{3} + 3 \cdot 0^2 - 2 \cdot 0 \right \$ )

C. $\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \$ + $\frac{1}{2}$\) left$\frac{0^3}{3} + 3 \cdot 0^2 - 2 \cdot 0 \right$ )

D. $\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \$ - $\frac{1}{2}$\) left$\frac{0^3}{3} + 3 \cdot 0^2 - 2 \cdot 0 \right$ )

Correct Answer: A

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Question 17 View Details

A rectangular box has dimensions ( x ) cm by ( 2x ) cm by ( 3x ) cm. If its surface area is 264 cm², find the value of ( x ).

A. $x = 4$

Correct B. $x = 6$

C. $x = 8$

D. $x = 10$

Correct Answer: B

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Question 18 View Details

Solve the equation $\sin^2 x + \cos^2 x = 1$ for ( x ) in the interval ( [0, 2pi] ).

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

B. $x = \frac{3\pi}{2}$

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

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

Correct Answer: C

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Question 19 View Details

A circle has a diameter of 10 cm. Find the area of the sector formed by a central angle of 60°.

Correct A. $\frac{1}{6} \pi \cdot 5^2$

B. $\frac{1}{6} \pi \cdot 10^2$

C. $\frac{1}{6} \pi \cdot 5^2 \cdot \frac{3}{2}$

D. $\frac{1}{6} \pi \cdot 10^2 \cdot \frac{3}{2}$

Correct Answer: A

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Question 20 View Details

Find the value of $int_{0}^{1} x^2 , dx$.

Correct A. $\frac{1}{3}$

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

C. $\frac{2}{3}$

D. ( 1 )

Correct Answer: A

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Question 21 View Details

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 22 View Details

Find the volume of the sphere $V = \frac{4}{3} \pi r^3$ if the radius is 6 cm.

Correct A. 904.778

B. 904.779

C. 904.780

D. 904.781

Correct Answer: A

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Question 23 View Details

Solve the quadratic equation $x^2 + 5x + 6 = 0$ using the quadratic formula.

A. -2

Correct B. -3

C. -4

D. -5

Correct Answer: B

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Question 24 View Details

Find the equation of the circle with center ( (3, 4) ) and radius 5.

Correct A. $x - 3$^2 + $y - 4$^$2 = 25$

B. $x - 4$^2 + $y - 3$^$2 = 25$

C. $x - 3$^2 + $y - 4$^$2 = 30$

D. $x - 4$^2 + $y - 3$^$2 = 30$

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. $-∞, -2$ ∪ (2, ∞)

D. $-∞, -4$ ∪ (4, ∞)

Correct Answer: A

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