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POST UTME EKSU 2017 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. $\frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4$

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

Correct Answer: A

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Question 2 View Details

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

Correct A. $x = \frac{-5 \pm \sqrt{25 + 24}}{4}$

B. $x = \frac{-5 \pm \sqrt{25 - 24}}{4}$

C. $x = \frac{-5 \pm \sqrt{25 + 12}}{4}$

D. $x = \frac{-5 \pm \sqrt{25 - 12}}{4}$

Correct Answer: A

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Question 3 View Details

Find the derivative of the function $y = \sin^2 x$ using the chain rule.

Correct A. $y' = 2 \(1x$1x\)

B. $y' = \(1x$1x\)

C. $y' = 2 $1x$

D. $y' = $1x$

Correct Answer: A

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Question 4 View Details

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

Correct A. $\vec{a} = 5 \(130^circ hat{i} + 5$$130^circ$ hat{j}\)

B. $\vec{a} = 5 \(130^circ hat{i} + 5$$130^circ$ hat{j}\)

C. $\vec{a} = 5 \(130^circ hat{j} + 5$$130^circ$ hat{i}\)

D. $\vec{a} = 5 \(130^circ hat{j} + 5$$130^circ$ hat{i}\)

Correct Answer: A

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Question 5 View Details

A binary operation ( ast ) is defined as $a ast b = a^2 + b^2$. Find the value of ( 2 ast 3 ).

Correct A. $2 ast 3 = 2^2 + 3^2 = 13$

B. $2 ast 3 = 2^2 - 3^2 = -5$

C. $2 ast 3 = 2^2 + 3^2 + 2 \times 2 \times 3 = 25$

D. $2 ast 3 = 2^2 + 3^2 - 2 \times 2 \times 3 = 1$

Correct Answer: A

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Question 6 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 7 View Details

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

Correct A. -2

B. -3

C. -1

D. 1

Correct Answer: A

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Question 8 View Details

Find the value of $\log_{10} x^2 \$ ) if $x = 10$.

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 9 View Details

A histogram is a graphical representation of the distribution of a set of data. What is the primary purpose of a histogram?

A. To show the mean of a data set

B. To show the median of a data set

Correct C. To show the distribution of a data set

D. To show the standard deviation of a data set

Correct Answer: C

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Question 10 View Details

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

Correct A. $x > -1$ or $x < 3$

B. $x > 1$ or $x < -3$

C. $x > 3$ or $x < -1$

D. $x > -3$ or $x < 1$

Correct Answer: A

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Question 11 View Details

Find the value of x in the equation $\log_{10} x^2 \$$= 4 ).$

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 12 View Details

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

A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, -3$ ∪ (1, ∞)

Correct C. $-∞, -1$ ∪ (1, ∞)

D. $-∞, 1$ ∪ (3, ∞)

Correct Answer: C

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Question 13 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 + $y + 3$^$2 = 16$

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

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

Correct Answer: A

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Question 14 View Details

Solve the system of equations $egin{cases} x + y = 4 \ 2x - y = 3 \end{cases}$.

Correct A. (1, 3)

B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: A

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Question 15 View Details

Find the value of x in the equation $x^3 - 6x^2 + 11x - 6 = 0$.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 16 View Details

Find the equation of the line passing through the points (2,3) and (4,5) in the vector form $\vec{r} = \vec{a} + tvec{b}$, where (vec{a}) is the position vector of the point (2,3) and (vec{b}) is a direction vector of the line.

Correct A. $\vec{r} = egin{pmatrix} 2 \ 3 \end{pmatrix} + t egin{pmatrix} 2 \ 2 \end{pmatrix}$

B. $\vec{r} = egin{pmatrix} 2 \ 3 \end{pmatrix} + t egin{pmatrix} 1 \ 1 \end{pmatrix}$

C. $\vec{r} = egin{pmatrix} 2 \ 3 \end{pmatrix} + t egin{pmatrix} 2 \ -1 \end{pmatrix}$

D. $\vec{r} = egin{pmatrix} 2 \ 3 \end{pmatrix} + t egin{pmatrix} 1 \ 2 \end{pmatrix}$

Correct Answer: A

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Question 17 View Details

Solve the system of equations $egin{cases} x + y + z = 6 \ 2x + 3y + z = 12 \ x + 2y + 3z = 8 \end{cases}$ using the method of elimination.

Correct A. $egin{cases} x = 2 \ y = 1 \ z = 3 \end{cases}$

B. $egin{cases} x = 1 \ y = 2 \ z = 3 \end{cases}$

C. $egin{cases} x = 3 \ y = 2 \ z = 1 \end{cases}$

D. $egin{cases} x = 2 \ y = 3 \ z = 1 \end{cases}$

Correct Answer: A

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Question 18 View Details

Find the equation of the circle with center at (2,3) and radius 4 in the form $x - h \$^2 + $y - k$^$2 = r\^2)$.

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

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

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

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

Correct Answer: A

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Question 19 View Details

A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.

Correct A. ( 24 )

B. ( 26 )

C. ( 28 )

D. ( 30 )

Correct Answer: A

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Question 20 View Details

A random experiment has 3 possible outcomes: A, B, and C. If the probability of outcome A is 0.4, the probability of outcome B is 0.3, and the probability of outcome C is 0.3, find the probability that outcome A occurs.

Correct A. ( 0.4 )

B. ( 0.3 )

C. ( 0.2 )

D. ( 0.1 )

Correct Answer: A

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Question 21 View Details

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

Correct A. $x < -1$\text{ or } $x > 5$

B. $x < 1$ \text{ or } $x > 5$

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

D. $x < 1$ \text{ or } $x > 2$

Correct Answer: A

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Question 22 View Details

Find the value of (x) in the equation $2^x = 16$.

A. ( 2 )

Correct B. ( 3 )

C. ( 4 )

D. ( 5 )

Correct Answer: B

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Question 23 View Details

A set of 4 numbers has a mean of 12 and a range of 8. If the largest number is 18, find the sum of the remaining 3 numbers.

Correct A. ( 36 )

B. ( 38 )

C. ( 40 )

D. ( 42 )

Correct Answer: A

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Question 24 View Details

Find the equation of the circle with center at ((2,3)) and radius (5).

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

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

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

D. $x^2 + y^2 + 4x + 6y + 9 = 0$

Correct Answer: A

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Question 25 View Details

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

Correct A. $x = 10^4$

B. $x = 10^2$

C. $x = 10^8$

D. $x = 10^6$

Correct Answer: A

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