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POST UTME OAU 2019 Mathematics | Objective

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Question 1 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 6.1 cm, calculate the 95% confidence interval for the population mean.

A. 168.3 cm, 182.7 cm

Correct B. 170.1 cm, 180.9 cm

C. 172.9 cm, 178.1 cm

D. 169.5 cm, 181.5 cm

Correct Answer: B

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Question 2 View Details

Solve the following system of linear equations using matrices:

Correct A. \(\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}\)

B. \(\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 2 \end{bmatrix}\)

C. \(\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 1 \\ 4 \end{bmatrix}\)

D. \(\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ 1 \end{bmatrix}\)

Correct Answer: A

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Question 3 View Details

A binary operation (*\) on the set \{0, 1\\((*) on the set \} is defined as follows: (0 * 0 = 0, 0 * 1 = 1, 1 * 0 = 1, 1 * 1 = 1\). Find the value of \(1 * 1 * 0)\\((0 * 0 = 0, 0 * 1 = 1, 1 * 0 = 1, 1 * 1 = 1). Find the value of \\).

A. 0

Correct B. 1

C. 10

D. 11

Correct Answer: B

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Question 4 View Details

A random variable X has a probability distribution given by the following table:

A. 0.2

Correct B. 0.3

C. 0.4

D. 0.5

Correct Answer: B

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Question 5 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

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Question 6 View Details

Find the value of x in the equation \(\frac{1}{2}x^2 + 5x - 3 = 0\).

A. 1

B. -2

Correct C. 3

D. -1

Correct Answer: C

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Question 7 View Details

Solve the inequality \(2x - 5 > 3\).

Correct A. \(x > 4\)

B. \(x < 4\)

C. \(x > 2\)

D. \(x < 2\)

Correct Answer: A

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Question 8 View Details

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If they sell 30 more whole wheat loaves than white bread loaves, and they sell a total of 240 whole wheat loaves per day, how many white bread loaves do they sell per day?

A. 120

Correct B. 140

C. 160

D. 180

Correct Answer: B

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Question 9 View Details

Find the value of x in the matrix equation \(egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 3 \ 3 \end{bmatrix}\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 10 View Details

A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 11 View Details

Determine the mean of the data set {2, 4, 6, 8, 10} using the formula for the mean of a finite set of numbers.

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 12 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\) using the quadratic formula.

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 13 View Details

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

Correct A. 288\pi

B. 288\sqrt{\pi}

C. 288\\(\pi^2\)

D. 288\\(\pi^3\)

Correct Answer: A

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Question 14 View Details

A set of 5 consecutive integers has a mean of 11. Find the sum of the integers.

Correct A. 55

B. 60

C. 65

D. 70

Correct Answer: A

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Question 15 View Details

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

Correct A. \(-\infty, -1\) \cup \(3, \infty\)

B. \(-\infty, 1\) \cup \(3, \infty\)

C. \(-\infty, -1\) \cup \(1, \infty\)

D. \(-\infty, 1\) \cup \(1, \infty\)

Correct Answer: A

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Question 16 View Details

Find the area under the curve \(y = \frac{1}{2}x^2\) from \(x = 0\) to \(x = 4\).

Correct A. 8

B. 16

C. 32

D. 64

Correct Answer: A

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Question 17 View Details

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

A. 2

Correct B. 4

C. 8

D. 16

Correct Answer: B

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Question 18 View Details

Find the value of (\(12x \\) ) given that \\((\)12x \(\(1x \\) = \(\frac{1}{2}\)\) ) and 1x \\) = \(\frac{\sqrt{3}}{2}\) ).

A. 1

Correct B. \(√3\)

C. 2

D. \\((√3/2\)\)

Correct Answer: B

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Question 19 View Details

A random variable ( X ) has a probability distribution given by \(P X = x \\) = \(frac{1}{2}\)\) ) for \\(frac{1}{2})\(x = 1, 2, 3\). Find the expected value of ( X ).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 20 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 70?

A. 0.25

B. 0.5

C. 0.75

Correct D. 0.9

Correct Answer: D

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Question 21 View Details

In the interval \([0, 2\pi]\), find the value of \(\int_0^{2\pi} \frac{\sin^2 x}{1 + \cos^2 x} dx\).

Correct A. \(\frac{\pi}{2}\)\)

B. \(\frac{\pi}{4}\)\)

C. \(\frac{\pi}{8}\)\)

D. \(\frac{\pi}{16}\)\)

Correct Answer: A

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Question 22 View Details

A random variable \(X\) has a probability density function \(f(x) = \begin{cases} frac{1}{2} & \text{if} 0 < x < 2, \\\(frac{1}{2} & text{if} 0 < x < 2, \ 0 & text{otherwise}. \end{cases}\) Find \\(text{otherwise}. end{cases}\(P 1 < X < 3\).\)

Correct A. \(\frac{1}{2}\)\)

B. \(\frac{1}{4}\)\)

C. \(\frac{3}{4}\)\)

D. \(\frac{1}{8}\)\)

Correct Answer: A

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Question 23 View Details

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

Correct A. \(\frac{\pi}{2}\)\)

B. \(\frac{\pi}{4}\)\)

C. \(\frac{\pi}{8}\)\)

D. \(\frac{\pi}{16}\)\)

Correct Answer: A

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Question 24 View Details

A population of bacteria is growing at a rate of 20% per hour. If there are initially 100 bacteria, how many bacteria will there be after 3 hours?

A. 1000

B. 1200

Correct C. 1500

D. 2000

Correct Answer: C

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Question 25 View Details

A car travels from city A to city B at an average speed of 60 \((km/h\)\) and returns at an average speed of 40 \(km/h\\((km/h) and returns at an average speed of 40\). What is the average speed for the round trip?

A. 45

B. 50

C. 55

Correct D. 60

Correct Answer: D

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