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

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

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

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

Correct Answer: A

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Question 2 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 + $y - 3$^$2 = 9$ )

D. $x - 3 \$^2 + $y - 2$^$2 = 9$ )

Correct Answer: A

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Question 3 View Details

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

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

B. $\frac{16}{3} \pi$

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

D. $\frac{128}{3} \pi$

Correct Answer: A

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Question 4 View Details

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

Correct A. ( 32 pi )

B. ( 16 pi )

C. ( 64 pi )

D. ( 128 pi )

Correct Answer: A

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Question 5 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 6 View Details

In a random sample of 100 students, the mean height is 175 cm with a standard deviation of 5 cm. If the mean height of the population is 180 cm, what is the probability that the sample mean is less than 170 cm?

A. 0.01

Correct B. 0.05

C. 0.10

D. 0.20

Correct Answer: B

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Question 7 View Details

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

Correct A. $$1x \$$= 0 )$

B. $$1x \$$= 0 )$

C. $$1x \$$= 1 )$

D. $$1x \$$= -1 )$

Correct Answer: A

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Question 8 View Details

A random experiment has two independent events A and B. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. What is the probability that both events A and B occur?

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 9 View Details

Find the derivative of the function ( f(x) = $3x^2$ \sin(x) ) using the product rule.

Correct A. $6x $1x \$ + $3x^2$ \cos(x) )

B. $6x $1x \$ - $3x^2$ \sin(x) )

C. $6x $1x \$ - $3x^2$ \cos(x) )

D. $6x $1x \$ + $3x^2$ \sin(x) )

Correct Answer: A

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Question 10 View Details

Solve the system of equations using matrices:

Correct A. $x = 2, y = 3$

B. $x = 3, y = 2$

C. $x = 1, y = 4$

D. $x = 4, y = 1$

Correct Answer: A

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Question 11 View Details

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

Correct A. 3,261

B. 3,261.25

C. 3,261.5

D. 3,261.75

Correct Answer: A

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Question 12 View Details

A particle moves along the x-axis with its position given by the equation x(t) = $(2t^2 - 5t + 1$\). Find the velocity of the particle at $t = 2\\((2t^2 - 5t + 1). Find the velocity of the particle at$.

Correct A. 1

B. -1

C. 3

D. -3

Correct Answer: A

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Question 13 View Details

A rectangular box has a length of 6 cm, a width of 4 cm, and a height of 2 cm. Find the volume of the box.

Correct A. 48

B. 50

C. 52

D. 54

Correct Answer: A

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Question 14 View Details

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

Correct A. $\frac{1}{3}$\)

B. $\frac{1}{2}$\)

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

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

Correct Answer: A

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Question 15 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 16 View Details

Let A be a 3x3 matrix with determinant 6. If A is transformed into B by multiplying each element by 2, what is the determinant of B?

A. 12

B. 24

Correct C. 48

D. 96

Correct Answer: C

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Question 17 View Details

A sequence is defined as: $a_n = \frac{1}{n} + \frac{1}{n+1}$. Find the sum of the first 5 terms of the sequence.

A. 1.8

B. 2.1

Correct C. 2.4

D. 2.7

Correct Answer: C

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Question 18 View Details

In the diagram below, ( O ) is the center of the circle and ( AB ) is a chord. If $OA = 5$ and $OB = 7$, find the length of ( AB ).

Correct A. $√(74)$

B. $√(50)$

C. $√(100)$

D. $√(200)$

Correct Answer: A

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Question 19 View Details

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. √$1/6$

Correct B. $1/6$

C. $1/3$

D. $1/2$

Correct Answer: B

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Question 20 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 21 View Details

In the diagram below, the graph of $y = \frac{1}{2} \tan^{-1} x$ is shown. What is the value of ( x ) at the point where the graph intersects the line $y = 1$?

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 22 View Details

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

Correct A. 2 + 5 + 13 + 29 + 61

B. 2 + 5 + 13 + 29 + 57

C. 2 + 5 + 13 + 27 + 57

D. 2 + 5 + 13 + 27 + 61

Correct Answer: A

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Question 23 View Details

In the diagram below, the circle with center ( O ) has equation $x^2 + y^2 = 4$. What is the length of the chord ( AB )?

A. $2√3$

Correct B. $2√2$

C. $2√5$

D. $2√6$

Correct Answer: B

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Question 24 View Details

A right-angled triangle has sides of length 3, 4, and 5. What is the area of the triangle?

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 25 View Details

A function is defined by ( f(x) = $\frac{1}{x^2 + 1}$\)) ). Find the value of $f -1 \\\() ). Find the value of (f -1$ ).

A. 0

B. 1

Correct C. $1/2$

D. $1/4$

Correct Answer: C

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