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POST UTME ACHIEVERS UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 2 View Details

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

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 3 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. $x = 1$, $y = 2$

B. $x = 2$, $y = 3$

C. $x = 3$, $y = 4$

D. $x = 4$, $y = 5$

Correct Answer: A

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Question 4 View Details

A circle has a radius of 5 cm. Find the area of the circle.

Correct A. 25\pi

B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: A

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Question 5 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.

A. 4 cm

B. 6 cm

Correct C. 8 cm

D. 12 cm

Correct Answer: C

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Question 6 View Details

A random sample of 25 students from a university had a mean height of 175.5 cm with a standard deviation of 5.2 cm. If the population standard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.

Correct A. 170.3 cm, 180.7 cm

B. 168.1 cm, 182.9 cm

C. 169.5 cm, 181.5 cm

D. 171.1 cm, 179.9 cm

Correct Answer: A

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Question 7 View Details

Find the area under the curve of the function $f(x) = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.

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

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

C. $\frac{\pi}{6}$\)

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

Correct Answer: A

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Question 8 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. $x = 4$

Correct Answer: C

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Question 9 View Details

A binary operation (\ast\) on the set \$(ast\({1, 2, 3, 4 \}$ is defined as \${1, 2, 3, 4}\(a ast b = a + b$. Find the value of $2 \\(ast b = a + b). Find the value of \ast 3$.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 10 View Details

A histogram of exam scores is shown below. If the mean score is 75 and the standard deviation is 10, find the area under the curve between 60 and 80.

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 11 View Details

Solve for x in the equation $\frac{1}{2}x^2 + 5x - 3 = 0$.

A. $x = -10$

B. $x = 3$

Correct C. $x = -3$

D. $x = 10$

Correct Answer: C

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Question 12 View Details

Find the determinant of the matrix $egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}$.

Correct A. ( 1 )

B. ( 2 )

C. ( 3 )

D. ( 4 )

Correct Answer: A

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Question 13 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 14 View Details

Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).

A. ( 6 )

Correct B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: B

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Question 15 View Details

Solve the system of equations $x + y = 4$ and $2x - y = 3$.

A. $x = 1, y = 3$

B. $x = 2, y = 2$

Correct C. $x = 3, y = 1$

D. $x = 4, y = 0$

Correct Answer: C

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Question 16 View Details

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

Correct A. -4

B. 4

C. -2

D. 2

Correct Answer: A

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Question 17 View Details

Solve the equation [ \$\sin^2$ x + \$\cos^2$ $x = 1$ ].

Correct A. $x =$$\frac{\pi}{4}$\)

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

C. $x =$$\frac{\pi}{6}$\)

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

Correct Answer: A

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Question 18 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. $x - 5$^2 + $y - 3$^$2 = 25$

D. $x - 3$^2 + $y - 5$^$2 = 25$

Correct Answer: A

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Question 19 View Details

Find the derivative of the function [$f(x) =$$3x^2 + 2x - 5$ ].

Correct A. f'$(x) = 6x + 2$

B. f'$(x) = 6x - 2$

C. f'$(x) =$$3x^2 + 2$

D. f'$(x) =$$3x^2 - 2$

Correct Answer: A

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Question 20 View Details

Find the area under the curve [ $y = x\^2 + 2x - 3$ ] from $x = 0$ to $x = 4$.

Correct A. 20

B. 30

C. 40

D. 50

Correct Answer: A

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Question 21 View Details

Find the value of $\int_0^1 x^2 \ln(x) dx$.

Correct A. $1/3$

B. $1/2$

C. $2/3$

D. 1

Correct Answer: A

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Question 22 View Details

Solve the inequality $|x^2 - 4| > 2$.

Correct A. $-∞, -2$ ∪ (2, ∞)

B. $-∞, -1$ ∪ (1, ∞)

C. $-∞, -3$ ∪ (3, ∞)

D. $-∞, -4$ ∪ (4, ∞)

Correct Answer: A

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Question 23 View Details

Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.

A. $2/3$

B. $1/2$

C. 1

Correct D. $4/3$

Correct Answer: D

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Question 24 View Details

Solve the system of equations $x + y = 2$ and $xy = 1$.

Correct A. (1, 1)

B. $1, -1$

C. $-1, 1$

D. $-1, -1$

Correct Answer: A

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Question 25 View Details

Find the derivative of the function $f(x) = $1x^2$\).

Correct A. $2/x$

B. $1/x$

C. $2/x\^2$

D. $1/x\^2$

Correct Answer: A

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