POST UTME OAU 2018 Mathematics | Objective

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Question 1 View Details
In a survey of 100 students, the mean height of the students is 175 cm. If the standard deviation of the heights is 5 cm, what is the probability that a randomly selected student will have a height between 170 cm and 180 cm?
Correct A. 0.6915
B. 0.3085
C. 0.5
D. 0.8413

Correct Answer: A

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Question 2 View Details
Solve for 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 3 View Details
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. What is the length of the third side?
A. 8
B. 10
Correct C. 12
D. 14

Correct Answer: C

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Question 4 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 of the car for the entire trip?
A. 48
Correct B. 50
C. 52
D. 54

Correct Answer: B

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Question 5 View Details
A basket contains 5 red apples and 3 green apples. If 2 apples are drawn at random, what is the probability that both apples are red?
Correct A. 0.25
B. 0.5
C. 0.75
D. 0.9

Correct Answer: A

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Question 6 View Details
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm. The frustum is cut off by a plane parallel to the base of the cone.
Correct A. 48\pi \(cm^3\)
B. 64\pi \(cm^3\)
C. 80\pi \(cm^3\)
D. 96\pi \(cm^3\)

Correct Answer: A

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Question 7 View Details
Solve the equation \(x^2 + 4x + 4 = 0\) using the quadratic formula.
Correct A. \(x = -2\)
B. \(x = 2\)
C. \(x = -1\)
D. \(x = 1\)

Correct Answer: A

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Question 8 View Details
Find the derivative of the function \(f(x) = 3x^2 + 2x - 5\) using the power rule.
Correct A. f'\((x) = 6x + 2\)
B. f'\((x) = 6x - 2\)
C. f'\((x) = 6x + 1\)
D. f'\((x) = 6x - 1\)

Correct Answer: A

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Question 9 View Details
A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a score range. The heights of the bars are 8, 12, 15, 10, and 5 units, respectively. What is the mean score of the class?
Correct A. 11.2
B. 12.1
C. 13.5
D. 14.8

Correct Answer: A

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Question 10 View Details
Find the determinant of the matrix \(\begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\) using the formula for 2x2 matrices.
Correct A. 1
B. 2
C. 3
D. 4

Correct Answer: A

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Question 11 View Details
Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)
Correct A. 10
B. 100
C. 1000
D. 10000

Correct Answer: A

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Question 12 View Details
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
Correct C. 80
D. 90

Correct Answer: C

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Question 13 View Details
Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).
A. 32
B. 64
Correct C. 128
D. 256

Correct Answer: C

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Question 14 View Details
A vector ( mathbf{a} ) has a magnitude of 5 and is directed at an angle of 30° to the x-axis. Find the x and y components of ( mathbf{a} ).
Correct A. 3, 4
B. 4, 3
C. 5, 5
D. 6, 6

Correct Answer: A

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Question 15 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. 0.12
B. 0.24
C. 0.36
D. 0.48

Correct Answer: A

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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. 0
B. 1
C. 2
D. 3

Correct Answer: A

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Question 17 View Details
A histogram of exam scores is shown below. What is the mean score?
A. 40
Correct B. 50
C. 60
D. 70

Correct Answer: B

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Question 18 View Details
Find the derivative of the function [\(f(x) =\)\(\frac{1}{x^2}\)\)\) \] using the chain rule.
A. \(\frac{-2}{x^3}\)\)\)
Correct B. \(\frac{2}{x^3}\)\)\)
C. \(\frac{-1}{x^3}\)\)\)
D. \(\frac{1}{x^3}\)\)\)

Correct Answer: B

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Question 19 View Details
Solve the inequality [ \(2x^2 + 5x - 3\) \geq 0 \].
Correct A. \left\(-\infty, -\frac{3}{2} \right\) \cup \left\(\frac{1}{2}, \infty \right\)
B. \left\(-\infty, -\frac{1}{2} \right\) \cup \left\(\frac{3}{2}, \infty \right\)
C. \left\(-\infty, \frac{1}{2} \right\) \cup \left\(-\frac{3}{2}, \infty \right\)
D. \left\(-\infty, \frac{3}{2} \right\) \cup \left\(-\frac{1}{2}, \infty \right\)

Correct Answer: A

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Question 20 View Details
Find the value of [ \log_{10} (1000) \].
A. 3
Correct B. 4
C. 5
D. 6

Correct Answer: B

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Question 21 View Details
Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)
Correct A. 10
B. 100
C. 1000
D. 10000

Correct Answer: A

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Question 22 View Details
A set of 10 numbers has a mean of 20 and a standard deviation of 5. What is the probability that a randomly selected number from this set is greater than 25?
A. 0.2
B. 0.3
Correct C. 0.4
D. 0.5

Correct Answer: C

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Question 23 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
Correct A. \(-∞, -1\) ∪ (3, ∞)
B. \(-∞, 1\) ∪ (3, ∞)
C. \(-∞, -3\) ∪ (1, ∞)
D. \(-∞, 3\) ∪ (1, ∞)

Correct Answer: A

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Question 24 View Details
Find the sum of the first 10 terms of the geometric series ( 2, 6, 18, ... ).
Correct A. 1950
B. 1960
C. 1970
D. 1980

Correct Answer: A

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Question 25 View Details
A polynomial function has a degree of 4 and has roots at x = -2, \(x = 1\), \(x = 3\), and \(x = 4\). What is the polynomial function?
Correct A. \(x + 2\), x - 1\)\(x - 3\), x - 4\)
B. \(x - 2\), x + 1\)\(x + 3\), x + 4\)
C. \(x + 2\), x - 1\)\(x + 3\), x - 4\)
D. \(x - 2\), x + 1\)\(x - 3\), x + 4\)

Correct Answer: A

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