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POST UTME LAUTECH 2021 Mathematics | Objective

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Question 1 View Details

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

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

B. $\frac{1}{3}$

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

D. $\frac{1}{5}$

Correct Answer: A

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Question 2 View Details

In the diagram below, identify the part labeled A.

Correct A. Beaker

B. Burette

C. Test Tube

D. Cell

Correct Answer: A

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Question 3 View Details

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

A. $x = 10^2$

Correct B. $x = 10^4$

C. $x = 10^{-2}$

D. $x = 10^{-4}$

Correct Answer: B

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Question 4 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = $x^2$\) and the line $x = 2\\((y = x^2) and the line$ about the x-axis.

A. $\frac{32}{3} \pi$

Correct B. $\frac{64}{3} \pi$

C. $\frac{128}{3} \pi$

D. $\frac{256}{3} \pi$

Correct Answer: B

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Question 5 View Details

In the diagram below, identify the part labeled B.

Correct A. Plant

B. Animal

C. Cell

D. Graph

Correct Answer: A

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Question 6 View Details

Find the area under the curve $y = x\^2 + 2x + 1$ from $x = 0$ to $x = 3$.

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 7 View Details

Solve the equation $\frac{1}{x + 1}$\) + $\frac{1}{x - 1}$\) = $\frac{1}{2}$\)

A. $x = 2$

Correct B. $x = 3$

C. $x = 4$

D. $x = 5$

Correct Answer: B

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Question 8 View Details

Find the value of \log_{10} (1000)

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 9 View Details

Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix}

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 10 View Details

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

A. 104

B. 105

Correct C. 106

D. 107

Correct Answer: C

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Question 11 View Details

If P(A) = 0.4,$P(B) = 0.5$, and P((A \cap B\$)) = 0.15$, find P\$(A cap B\(A|B$.

A. 0.3

Correct B. 0.6

C. 0.8

D. 1.0

Correct Answer: B

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Question 12 View Details

Solve the equation: $\frac{1}{2} \sin^2 x + \frac{1}{4} \cos^2 x = \frac{1}{4}$

Correct A. $x =$$\frac{\pi}{6}$\)

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

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

D. $x =$$\frac{\pi}{2}$\)

Correct Answer: A

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Question 13 View Details

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

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 14 View Details

If f(x) = $2x^2 + 3x - 1$, find f'(x).

Correct A. 4x + 3

B. $2x^2 + 3$

C. 2x + 3

D. 4x - 3

Correct Answer: A

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Question 15 View Details

Find the sum of the first 5 terms of the geometric series 2, 6, 18, ...

A. 62

B. 64

Correct C. 66

D. 68

Correct Answer: C

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Question 16 View Details

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

Correct A. $-∞, -2$ ∪ (2, ∞)

B. $-∞, -2$ \cup $-2, 2$\)∪ (2, ∞)

C. $-∞, -2$ ∩ (2, ∞)

D. $-∞, 2$ ∪ (2, ∞)

Correct Answer: A

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Question 17 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 18 View Details

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

Correct A. $x = 0$, \$\pi/2$, \pi, 3\$\pi/2$

B. $x = 0$, \$\pi/2$, \pi, 3\$\pi/2$, 2\pi

C. $x = 0$, \$\pi/2$, \pi, 3\$\pi/2$, 5\$\pi/2$

D. $x = 0$, \$\pi/2$, \pi, 3\$\pi/2$, 4\pi

Correct Answer: A

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Question 19 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. $x - 3$^2 + $y - 2$^$2 = 16$

C. $x + 2$^2 + $y + 3$^$2 = 16$

D. $x - 2$^2 + $y + 3$^$2 = 16$

Correct Answer: A

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Question 20 View Details

Solve the system of equations $x + y = 3$ and $x - y = 1$.

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

B. $x = 1$, $y = 2$

C. $x = 2$, $y = 2$

D. $x = 1$, $y = 1$

Correct Answer: A

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Question 21 View Details

Determine the value of x in the equation $\sin^2 x \$ + \$\cos^2(x)$ = 1 ) if $$1x \$ = $\frac{3}{4}$\) ).

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

B. $\frac{3\pi}{4}$

C. $\frac{5\pi}{4}$

D. $\frac{7\pi}{4}$

Correct Answer: A

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Question 22 View Details

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

A. $\frac{64}{3}$

B. $\frac{128}{3}$

Correct C. $\frac{256}{3}$

D. $\frac{512}{3}$

Correct Answer: C

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Question 23 View Details

Solve the equation $x^3 - 6x^2 + 11x - 6 = 0$ using the factor theorem.

A. $x = 1$

B. $x = 2$

Correct C. $x = 3$

D. $x = 6$

Correct Answer: C

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Question 24 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 - 3 \$^2 + $y - 2$^$2 = 16$ )

C. $x - 2 \$^2 + $y - 3$^$2 = 9$ )

D. $x - 3 \$^2 + $y - 2$^$2 = 9$ )

Correct Answer: A

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Question 25 View Details

A particle moves in a straight line with an initial velocity of (5 , \text{$m/s$}\) and an acceleration of \$(5 , text{m/s}\(2 , \text{m/s}^2$. Find its velocity after ( 3 ) seconds.

A. $13 , \text{m/s}$

B. $15 , \text{m/s}$

Correct C. $17 , \text{m/s}$

D. $19 , \text{m/s}$

Correct Answer: C

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