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POST UTME IMS U 2018 Mathematics | Objective

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Question 1 View Details

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

Correct A. ( 12 )

B. ( 20 )

C. ( 30 )

D. ( 40 )

Correct Answer: A

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Question 2 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 3 View Details

Find the vector ( mathbf{a} ) given that $\mathbf{a} \cdot \mathbf{b} = 6$ and $\mathbf{a} \cdot \mathbf{c} = 3$, where $\mathbf{b} = egin{pmatrix} 2 \ 1 \end{pmatrix}$ and $\mathbf{c} = egin{pmatrix} 1 \ 2 \end{pmatrix}$.

Correct A. $egin{pmatrix} 3 \ 2 \end{pmatrix}$

B. $egin{pmatrix} 2 \ 3 \end{pmatrix}$

C. $egin{pmatrix} 1 \ 1 \end{pmatrix}$

D. $egin{pmatrix} 4 \ 3 \end{pmatrix}$

Correct Answer: A

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Question 4 View Details

Find the sum of the first 10 terms of the geometric series $2 + 6 + 18 + ldots$.

Correct A. ( 3094 )

B. ( 3095 )

C. ( 3096 )

D. ( 3097 )

Correct Answer: A

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Question 5 View Details

Solve the equation $x^3 + 2x^2 - 7x + 12 = 0$.

Correct A. $x = -3$

B. $x = -1$

C. $x = 2$

D. $x = 3$

Correct Answer: A

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Question 6 View Details

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

Correct A. $\frac{4}{5}$

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

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

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

Correct Answer: A

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Question 7 View Details

A cylindrical \tank with a radius of 5m and height of 10m is filled with water. Find the volume of water in the \tank.

A. $785.4 , \text{m}^3$

Correct B. $1570.8 , \text{m}^3$

C. $3141.6 , \text{m}^3$

D. $6283.2 , \text{m}^3$

Correct Answer: B

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Question 8 View Details

Find the derivative of the function ( f(x) = \sin(2x) ) using the chain rule.

Correct A. ( f'$(x) =$\cos(2x) cdot 2 )

B. ( f'$(x) =$\sin(2x) cdot 2 )

C. ( f'$(x) =$\cos(2x) cdot 4 )

D. ( f'$(x) =$\sin(2x) cdot 4 )

Correct Answer: A

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Question 9 View Details

A set of exam scores has a mean of 80 and a standard deviation of 10. What is the z-score of a score of 90?

A. $z = 0.5$

Correct B. $z = 1.0$

C. $z = 1.5$

D. $z = 2.0$

Correct Answer: B

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Question 10 View Details

Simplify the expression $\frac{2^3 \cdot 3^2}{2^2 \cdot 3}$.

Correct A. $2 \cdot 3 = 6$

B. $2^3 \cdot 3^2 = 72$

C. $2^2 \cdot 3 = 12$

D. $\frac{2^3 \cdot 3^2}{2^2 \cdot 3} = 4$

Correct Answer: A

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Question 11 View Details

Let ( f(x) = $\frac{x^2 - 4}{x - 2}$\)) ). Find lim_{x \to 2} f\( x \\() ). Find lim_{x to 2} f\ ) using the chain rule.

A. $\frac{0}{0} \$

B. $4 \$

Correct C. $2 \$

D. $\frac{4}{2} \$

Correct Answer: C

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Question 12 View Details

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

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 13 View Details

Find the sum of the first 5 terms of the geometric series $2 + 6 + 18 + \ldots$.

A. $62 \$

Correct B. $64 \$

C. $66 \$

D. $68 \$

Correct Answer: B

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Question 14 View Details

Let $S = \{1, 2, 3, \ldots, 10 \}$. Find the number of subsets of S that contain exactly 3 elements.

Correct A. $120 \$

B. $126 \$

C. $132 \$

D. $140 \$

Correct Answer: A

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Question 15 View Details

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

Correct A. $x = -2 \$

B. $x = -1 \$

C. $x = 0 \$

D. $x = 1 \$

Correct Answer: A

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Question 16 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 48\pi $cm^3$

B. 64\pi $cm^3$

Correct C. 80\pi $cm^3$

D. 96\pi $cm^3$

Correct Answer: C

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Question 17 View Details

Solve the inequality $\frac{x^2 - 4x - 5}{x^2 - 4x + 3}$\)\$) > 0.$

Correct A. \left$-\infty, -1\right$ \cup \left$3, \infty\right$

B. \left$-\infty, -1\right$ \cup \left$1, 3\right$

C. \left$-\infty, 1\right$ \cup \left$3, \infty\right$

D. \left$-\infty, -1\right$ \cup \left$1, \infty\right$

Correct Answer: A

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Question 18 View Details

A firm produces two products, A and B. The profit function is given by \pi(x,$y) = 2x + 3y - 0.$$5x^2 - 2y^2$, where x and y are the quantities of products A and B, respectively. Find the critical points of the profit function.

Correct A. \left$4, 2\right$

B. \left$2, 4\right$

C. \left$1, 3\right$

D. \left$3, 1\right$

Correct Answer: A

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Question 19 View Details

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8 cm

B. 6 cm

C. 4 cm

D. 2 cm

Correct Answer: A

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Question 20 View Details

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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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 \$ = $\frac{3}{5}$\) ).

Correct A. $\frac{4\pi}{3}$

B. $\frac{5\pi}{3}$

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

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

Correct Answer: A

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Question 22 View Details

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

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

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

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

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

Correct Answer: A

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Question 23 View Details

Solve the equation $2x^2 + 5x - 3 = 0$ using the quadratic formula.

Correct A. $x = \frac{-5 \pm \sqrt{109}}{4}$

B. $x = \frac{5 \pm \sqrt{109}}{4}$

C. $x = \frac{-5 \pm \sqrt{109}}{2}$

D. $x = \frac{5 \pm \sqrt{109}}{2}$

Correct Answer: A

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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 - 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 25 View Details

Find the vector ( mathbf{v} ) such that $\mathbf{v} \cdot \mathbf{i} = 3$ and $\mathbf{v} \cdot \mathbf{j} = 4$.

Correct A. $\mathbf{v} = 3\mathbf{i} + 4\mathbf{j}$

B. $\mathbf{v} = 4\mathbf{i} + 3\mathbf{j}$

C. $\mathbf{v} = 3\mathbf{i} - 4\mathbf{j}$

D. $\mathbf{v} = 4\mathbf{i} - 3\mathbf{j}$

Correct Answer: A

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