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POST UTME UNIOSUN 2017 Mathematics | Objective

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Question 1

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 about the x-axis.

Correct A. \frac{32\pi}{5}

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

C. \frac{64\pi}{5}

D. \frac{128\pi}{5}

Correct Answer: A

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Question 2

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

Correct A. $ -\infty, -1 $ \cup $ 3, \infty $

B. $ -\infty, -3 $ \cup $ 1, \infty $

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

D. $ -\infty, 1 $ \cup $ 3, \infty $

Correct Answer: A

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Question 3

Find the derivative of the function f(x) = \frac{1}{x^2 + 1} u\sing the chain rule.

A. -\frac{2x}{$ x^2 + 1 $^2}

Correct B. \frac{2x}{$ x^2 + 1 $^2}

C. -\frac{2}{$ x^2 + 1 $^2}

D. \frac{2}{$ x^2 + 1 $^2}

Correct Answer: B

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Question 4

Solve the system of linear equations x + y = 2 and 2x - 3y = -3 u\sing the method of substitution.

Correct A. x = 1, y = 1

B. x = -1, y = 3

C. x = 2, y = 0

D. x = 0, y = 2

Correct Answer: A

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Question 5

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

A. \frac{16}{5}

Correct B. \frac{32}{5}

C. \frac{48}{5}

D. \frac{64}{5}

Correct Answer: B

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Question 6

Determine the value of $n$ in the arithmetic sequence $a_n = 2n + 5$, given that $a_1 = 9$ and $a_{10} = 47$.

A. 5

Correct B. 7

C. 9

D. 11

Correct Answer: B

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Question 7

A random variable $X$ has a probability distribution given by $P$ X = k $ = \frac{1}{2^k}$ for $k = 1, 2, 3, dots$. Find the expected value of $X$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 8

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

Correct A. 0.3413

B. 0.3415

C. 0.3417

D. 0.3419

Correct Answer: A

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Question 9

Solve for $x$ in the equation $2^x + 3^x = 5^x$.

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 10

A binary operation $ast$ on the set of integers is defined by $a ast b = a^2 + b^2$ for all integers $a$ and $b$. Find the value of $x$ such that $x ast 2 = 21$.

A. 3

B. 5

Correct C. 7

D. 9

Correct Answer: C

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Question 11

Let X be a random variable with probability density function (pdf) given by f(x) = $ \frac{1}{2}e^{-|x|} $ for -∞ < x < ∞. Find the probability that X lies between -1 and 1.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 12

A histogram of exam scores is given below. If the mean score is 60, find the value of k.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 13

Find the derivative of the function f(x) = $ \frac{1}{x^2 + 1} $ u\sing the chain rule.

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

B. $ \frac{2x}{\( x^2 + 1 \ $^2} )

C. $ \frac{1}{\( x^2 + 1 \ $^2} )

D. $ \frac{-1}{\( x^2 + 1 \ $^2} )

Correct Answer: A

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Question 14

Solve the equation $ x^3 - 6x^2 + 11x - 6 = 0 $ u\sing the factor theorem.

Correct A. $ x - 1 $$ x - 2 $$ x - 3 \ $ = 0 )

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

C. $ x + 1 $$ x - 2 $$ x - 3 \ $ = 0 )

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

Correct Answer: A

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Question 15

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

Correct A. $ egin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 0 $

B. $ egin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 1 $

C. $ egin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = -1 $

D. $ egin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 2 $

Correct Answer: A

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Question 16

Determine the value of x in the equation $ 2x^2 + 5x - 3 = 0 $.

Correct A. $ x = -1 $

B. $ x = 3 $

C. $ x = -3 $

D. $ x = 1 $

Correct Answer: A

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Question 17

Find the volume of the frustum of a cone with height 10cm, lower base radius 5cm, and upper base radius 3cm.

A. ( 100pi ) cm³

Correct B. ( 150pi ) cm³

C. ( 200pi ) cm³

D. ( 250pi ) cm³

Correct Answer: B

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Question 18

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

A. $ x = 10 $

B. $ x = 100 $

C. $ x = 1000 $

Correct D. $ x = 10000 $

Correct Answer: D

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Question 19

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

A. ( 8 )

Correct B. ( 10 )

C. ( 12 )

D. ( 14 )

Correct Answer: B

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Question 20

Find the surface area of the sphere with radius 6cm.

A. ( 288pi ) cm²

B. ( 360pi ) cm²

Correct C. ( 432pi ) cm²

D. ( 480pi ) cm²

Correct Answer: C

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Question 21

Find the sum of the infinite geometric series $ sum_{n=1}^{infty} \frac{1}{2^n} $.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 22

A set of 10 students scored the following marks in a mathematics test: 23, 21, 19, 24, 22, 20, 25, 18, 26, 17. Calculate the mean, median, and mode of the data.

A. Mean: 22, Median: 22, Mode: 23

B. Mean: 22, Median: 23, Mode: 22

C. Mean: 23, Median: 22, Mode: 22

Correct D. Mean: 22, Median: 22, Mode: 22

Correct Answer: D

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Question 23

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

Correct A. x < -1 or x > 3/2

B. x > -1 or x < 3/2

C. x < -1 or x < 3/2

D. x > -1 or x > 3/2

Correct Answer: A

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Question 24

A bag contains 5 red balls and 3 blue balls. A ball is drawn at random. What is the probability that it is red?

Correct A. 1/2

B. 2/3

C. 3/4

D. 4/5

Correct Answer: A

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Question 25

A sequence is defined by the formula $ a_n = 2n + 1 $. Find the 10th term of the sequence.

Correct A. 21

B. 22

C. 23

D. 24

Correct Answer: A

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