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POST UTME KSU 2019 Mathematics | Objective

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Question 1 View Details

Determine the volume of the solid formed by revolving the region bounded by the curves $y = x\^2$, $y = 0$, and $x = 2$ about the x-axis.

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

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

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

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

Correct Answer: A

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Question 2 View Details

A binary operation * on the set of real numbers is defined as follows:$(a * b = ab + 2$\). Find the value of $2 * 3\\((a * b = ab + 2). Find the value of$ * 4.

A. 40

Correct B. 42

C. 44

D. 46

Correct Answer: B

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Question 3 View Details

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment stops. What is the probability that the experiment will stop on the third roll?

A. $\frac{1}{6}$\)

B. $\frac{1}{12}$\)

Correct C. $\frac{1}{24}$\)

D. $\frac{1}{36}$\)

Correct Answer: C

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Question 4 View Details

Find the area under the curve $y = x\^3 - 6x^2 + 9x + 2$ from $x = 0$ to $x = 4$.

A. $\frac{256}{5}$\)

B. $\frac{512}{5}$\)

Correct C. $\frac{1024}{5}$\)

D. $\frac{2048}{5}$\)

Correct Answer: C

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Question 5 View Details

Solve the equation $x^4 - 6x^3$ + \$(11x^2 - 6x - 12$$= 0.$\)

Correct A. $x + 1$, x - 2\)$x^2 - 3x + 6 = 0$

B. $x - 1$, x + 2\)$x^2 - 3x + 6 = 0$

C. $x + 2$, x - 2\)$x^2 - 3x + 6 = 0$

D. $x - 2$, x + 1\)$x^2 - 3x + 6 = 0$

Correct Answer: A

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Question 6 View Details

Find the equation of the circle passing through the points (2, 3), (4, 1), and (6, 5).

Correct A. $x^2$ + \$(y^2 - 4x - 2y + 5$$= 0$\)

B. $x^2$ + \$(y^2 + 4x + 2y - 5$$= 0$\)

C. $x^2$ + \$(y^2 - 2x - 4y + 3$$= 0$\)

D. $x^2$ + \$(y^2 + 2x + 4y - 3$$= 0$\)

Correct Answer: A

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Question 7 View Details

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 8 View Details

Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, find P($A \cap B$).

Correct A. 0.2

B. 0.24

C. 0.28

D. 0.32

Correct Answer: A

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Question 9 View Details

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

Correct A. \$sin x =$\cos x

B. \$sin x = -$\cos x

C. \$cos x =$\sin x

D. \$cos x = -$\sin x

Correct Answer: A

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Question 10 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

Correct A. $y = 2x - 1$

B. $y = 2x + 1$

C. $y = -2x + 1$

D. $y = -2x - 1$

Correct Answer: A

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Question 11 View Details

In a triangle ABC, angle (A = 30\)°, angle $B = 90\\((A = 30)°, angle$°, and side $AB = 5$ cm. Find the length of side AC.

A. 10 cm

B. 12 cm

Correct C. 15 cm

D. 18 cm

Correct Answer: C

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Question 12 View Details

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

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

B. \begin{bmatrix} 2 \\ 1 \end{bmatrix}

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

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

Correct Answer: A

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Question 13 View Details

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 1230

B. 1240

Correct C. 1250

D. 1260

Correct Answer: C

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Question 14 View Details

In a circle with center O and radius 6 cm, chord $AB = 8$ cm. Find the length of the perpendicular from O to AB.

A. 4 cm

Correct B. 5 cm

C. 6 cm

D. 7 cm

Correct Answer: B

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Question 15 View Details

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

A. 10

B. 20

Correct C. 40

D. 80

Correct Answer: C

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Question 16 View Details

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

Correct A. ( f'$(x) =$$\frac{2x}${ 1 - $x^2$ \)^{$3/2$}}\) )

B. ( f'$(x) =$$\frac{-2x}${ 1 - $x^2$ \)^{$3/2$}}\) )

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

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

Correct Answer: A

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Question 17 View Details

Solve the system of equations using matrices:$egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix}$.

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

B. $x = 2, y = 1$

C. $x = 3, y = 4$

D. $x = 4, y = 3$

Correct Answer: A

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Question 18 View Details

Find the area of the triangle with vertices ( A(0, 0), B(3, 0), C(0, 4) ).

Correct A. ( 6 )

B. ( 12 )

C. ( 18 )

D. ( 24 )

Correct Answer: A

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Question 19 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. $\frac{1}{6}$

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

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

Correct D. $\frac{5}{6}$

Correct Answer: D

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Question 20 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?

A. ( 0.5 )

B. ( 0.6 )

Correct C. ( 0.7 )

D. ( 0.8 )

Correct Answer: C

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

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

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

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

Correct Answer: A

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Question 22 View Details

A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 1$ with initial term $a_1 = 3$. Find the sum of the first 5 terms of the sequence.

Correct A. $3 + 7 + 15 + 31 + 63$

B. $3 + 5 + 11 + 23 + 47$

C. $3 + 7 + 13 + 25 + 51$

D. $3 + 9 + 17 + 33 + 65$

Correct Answer: A

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Question 23 View Details

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

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

B. $\frac{32}{3}$

C. $\frac{16}{3}$

D. $\frac{8}{3}$

Correct Answer: A

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Question 24 View Details

Solve the system of equations $egin{cases} x + y = 2 \ 2x - 3y = -1 \end{cases}$ using matrices.

Correct A. $x = \frac{5}{7}, y = \frac{4}{7}$

B. $x = \frac{3}{5}, y = \frac{2}{5}$

C. $x = \frac{2}{3}, y = \frac{1}{3}$

D. $x = \frac{4}{5}, y = \frac{1}{5}$

Correct Answer: A

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Question 25 View Details

A random experiment consists of rolling a fair six-sided die. Find the probability that the sum of the numbers on the two dice is 7.

A. $\frac{1}{6}$

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

C. $\frac{1}{2}$

Correct D. $\frac{2}{3}$

Correct Answer: D

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