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POST UTME ABU 2018 Mathematics | Objective

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Question 1 View Details

Find the equation of the circle with center $-2, 3$ and radius 4.

Correct A. $x^2$ + \$(y^2 + 4x - 6y + 13$$= 0$\)

B. $x^2$ + \$(y^2 - 4x + 6y + 13$$= 0$\)

C. $x^2$ + \$(y^2 + 4x + 6y + 13$$= 0$\)

D. $x^2$ + \$(y^2 - 4x - 6y + 13$$= 0$\)

Correct Answer: A

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Question 2 View Details

Solve the inequality $\frac{x - 2}{x + 1}$\$) > 0.$

Correct A. $-\infty, -1$ \cup $2, \infty$

B. $-\infty, -1$ \cup $-1, 2$

C. $-\infty, 2$ \cup $2, \infty$

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

Correct Answer: A

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Question 3 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 59048

Correct B. 59049

C. 59050

D. 59051

Correct Answer: B

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Question 4 View Details

Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= 3 \end{align*}

Correct A. \begin{align*} x &= 7 \ y &= -3 \end{align*}

B. \begin{align*} x &= 3 \ y &= 1 \end{align*}

C. \begin{align*} x &= 1 \ y &= 3 \end{align*}

D. \begin{align*} x &= -1 \ y &= -3 \end{align*}

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. $y = x - 1$

D. $y = x + 1$

Correct Answer: A

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Question 6 View Details

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

Correct A. $\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4$

B. $\frac{1}{2} \times 4^2 + 3 \times 4 - 2$

C. $\frac{1}{2} \times 4^3 - 3 \times 4^2 - 2 \times 4$

D. $\frac{1}{2} \times 4^2 - 3 \times 4 + 2$

Correct Answer: A

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Question 7 View Details

Solve the inequality $\frac{x}{x-1} > 2$.

A. $x < -1$ or $x > 2$

Correct B. $x < 1$ or $x > 2$

C. $x < -1$ or $x < 2$

D. $x > 1$ or $x < 2$

Correct Answer: B

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Question 8 View Details

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

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

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

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

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

Correct Answer: C

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Question 9 View Details

A vector ( mathbf{a} ) has magnitude 5 and direction $30^circ$ from the positive x-axis. Find the unit vector in the direction of ( mathbf{a} ).

Correct A. $egin{pmatrix} \frac{5}{\sqrt{3}} \ \frac{5}{\sqrt{3}} \end{pmatrix}$

B. $egin{pmatrix} \frac{5}{\sqrt{2}} \ \frac{5}{\sqrt{2}} \end{pmatrix}$

C. $egin{pmatrix} \frac{5}{\sqrt{3}} \ -\frac{5}{\sqrt{3}} \end{pmatrix}$

D. $egin{pmatrix} \frac{5}{\sqrt{2}} \ -\frac{5}{\sqrt{2}} \end{pmatrix}$

Correct Answer: A

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Question 10 View Details

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

A. ( 16 pi )

B. ( 32 pi )

Correct C. ( 64 pi )

D. ( 128 pi )

Correct Answer: C

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Question 11 View Details

In a circle of radius 10 cm, a chord of length 8 cm subtends an angle of 60° at the centre. Find the area of the sector.

Correct A. $\frac{1}{6} \pi 10 \$^2 )

B. $\frac{1}{6} \pi 8 \$^2 )

C. $\frac{1}{6} \pi 10 \$^2 - $\frac{1}{6}$\) pi $(8)^2$ )

D. $\frac{1}{6} \pi 10 \$^2 + $\frac{1}{6}$\) pi $(8)^2$ )

Correct Answer: A

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Question 12 View Details

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

A. $x = 1$

Correct B. $x = 2$

C. $x = 3$

D. $x = 4$

Correct Answer: B

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Question 13 View Details

A set A contains 5 elements and a set B contains 3 elements. Find the number of elements in the union of sets A and B.

Correct A. $5 + 3 - 2$

B. $5 + 3 + 2$

C. ( 5 cdot 3 )

D. $5 \cdot 3 + 2$

Correct Answer: A

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Question 14 View Details

Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ... .

A. ( 55 )

B. ( 65 )

Correct C. ( 75 )

D. ( 85 )

Correct Answer: C

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Question 15 View Details

A circle passes through the points (1, 2) and (3, 4). Find the equation of the circle.

Correct A. $x^2 + y^2 - 4x - 6y + 9 = 0$

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

C. $x^2 + y^2 - 4x - 6y + 7 = 0$

D. $x^2 + y^2 - 4x - 6y + 11 = 0$

Correct Answer: A

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Question 16 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 6 cm, and upper base radius 4 cm. The frustum is cut off by a plane parallel to the base of the cone.

A. 256\pitext{ cm}^3

B. 512\pitext{ cm}^3

Correct C. 768\pitext{ cm}^3

D. 1024\pitext{ cm}^3

Correct Answer: C

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Question 17 View Details

Differentiate the function $f(x) = \frac{$1x}{x^2}$ with respect to x.

Correct A. $\frac{1 - 2$1x}{x^3}$\)\)

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

C. $\frac{1}{x^3}$\)\)

D. $\frac{2}{x^3}$\)\)

Correct Answer: A

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Question 18 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 50 and 70?

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 19 View Details

Simplify the expression $\sqrt{\frac{16x^2y^2}{25}}$ and express it in the form $ax^by^c$.

A. $\frac{4x}{5y}$\)

Correct B. $\frac{4xy}{5}$\)

C. $\frac{4x^2y}{5}$\)\)

D. $\frac{4xy^2}{5}$\)\)

Correct Answer: B

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Question 20 View Details

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

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 21 View Details

Let X and Y be independent events with P(X) = 0.4 and P(Y) = 0.6. Find P($X \cap Y$).

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.8

Correct Answer: A

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Question 22 View Details

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

A. \$\frac{-5 \pm \sqrt{109}$}{4}\)

B. \$\frac{-5 \pm \sqrt{121}$}{4}\)

Correct C. \$\frac{-5 \pm \sqrt{169}$}{4}\)

D. \$\frac{-5 \pm \sqrt{225}$}{4}\)

Correct Answer: C

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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. $x - 3$^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 24 View Details

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

Correct A. $-∞, -3$ ∪ (1, ∞)

B. $-∞, -1$ ∪ (3, ∞)

C. $-∞, 1$ ∪ (3, ∞)

D. $-∞, -3$ ∪ (1, 3)

Correct Answer: A

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Question 25 View Details

Find the value of (\sin(2x)\) when \$(sin(2x)\(\cos(x) = \frac{1}{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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