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POST UTME BOWEN UNIVERSITY 2023 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. \(\frac{1}{2} \times 4^3 + 3 \times 4 - 2 \times 4\)

Correct Answer: A

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Question 2 View Details

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

Correct A. \(x = 10^4\)

B. \(x = 10^2\)

C. \(x = 10^{-4}\)

D. \(x = 10^{-2}\)

Correct Answer: A

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Question 3 View Details

Find the magnitude of the vector \(\vec{a} = egin{pmatrix} 3 \ 4 \end{pmatrix}\).

Correct A. \(\sqrt{3^2 + 4^2}\)

B. \(3 + 4\)

C. \(3 \times 4\)

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

Correct Answer: A

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Question 4 View Details

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

Correct A. \(x < -\frac{5}{4}\) or \(x > \frac{3}{2}\)

B. \(x < -\frac{3}{2}\) or \(x > \frac{5}{4}\)

C. \(x < -\frac{5}{4}\) or \(x < \frac{3}{2}\)

D. \(x > -\frac{5}{4}\) or \(x < \frac{3}{2}\)

Correct Answer: A

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Question 5 View Details

Find the value of (\(12x\) given that 1x = \\((\(12x) given that \frac{3}{5}\) and 1x = \(\frac{4}{5}\)\).

Correct A. \(\frac{24}{25}\)

B. \(\frac{12}{25}\)

C. \(\frac{16}{25}\)

D. \(\frac{20}{25}\)

Correct Answer: A

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Question 6 View Details

A cylindrical \tank with a radius of 7m and height of 10m is filled with water. If the water level is raised by 2m, calculate the increase in volume of water in the \tank.

Correct A. 980\pi \text{ m}^3

B. 980\pi \text{ m}^3

C. 980\pi \text{ m}^3

D. 980\pi \text{ m}^3

Correct Answer: A

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Question 7 View Details

Solve for x in the equation \\(tan x =\)\(\sqrt{3}\) - \cot x.

Correct A. \(\frac{\pi}{6}\)\)

B. \(\frac{\pi}{3}\)\)

C. \(\frac{\pi}{2}\)\)

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

Correct Answer: A

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Question 8 View Details

A set of 5 numbers has a mean of 10. If 2 more numbers are added to the set, the new mean is 12. Find the sum of the original 5 numbers.

Correct A. 40

B. 50

C. 60

D. 70

Correct Answer: A

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Question 9 View Details

Solve the inequality \(\frac{x-2}{x+1}\)\\() > 0.\)

Correct A. \(x < -1\)\text{ or } \(x > 2\)

B. \(x < -1\)\text{ or } \(x < 2\)

C. \(x > -1\)\text{ or } \(x < 2\)

D. \(x > -1\)\text{ or } \(x > 2\)

Correct Answer: A

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Question 10 View Details

A circle has a radius of 4cm. Find the area of the circle.

Correct A. 16\pi \text{ cm}^2

B. 32\pi \text{ cm}^2

C. 64\pi \text{ cm}^2

D. 128\pi \text{ cm}^2

Correct Answer: A

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Question 11 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 unknown, calculate the 95% confidence interval for the mean height of all students in the university.

A. 168.3 cm, 182.7 cm

Correct B. 170.1 cm, 180.9 cm

C. 172.9 cm, 178.1 cm

D. 174.5 cm, 176.5 cm

Correct Answer: B

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Question 12 View Details

A company produces light bulbs with a mean lifespan of 1200 hours and a standard deviation of 120 hours. If a sample of 36 light bulbs is selected, what is the probability that the sample mean lifespan is less than 1150 hours?

A. 0.025

B. 0.05

Correct C. 0.10

D. 0.20

Correct Answer: C

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Question 13 View Details

A histogram of exam scores for a class of 50 students is shown below. If the mean score is 75 and the standard deviation is 10, what is the probability that a student scored above 85?

A. 0.15

B. 0.20

C. 0.25

Correct D. 0.30

Correct Answer: D

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Question 14 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

A. 0.12

Correct B. 0.20

C. 0.24

D. 0.30

Correct Answer: B

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Question 15 View Details

A function f(x) = \(2x^2 + 5x - 3\) has a local maximum at x = -1. Find the value of the function at this point.

A. -5

Correct B. -3

C. 1

D. 5

Correct Answer: B

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Question 16 View Details

A curve is defined by the equation (y = 2x\^3 - \(5x^2 + x + 1\)\). Find the area under the curve between \\((y = 2x^3 - 5x^2 + x + 1\(x = 0\) and \(x = 1\).

A. 0.5

B. 1.0

Correct C. 1.5

D. 2.0

Correct Answer: C

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Question 17 View Details

A polynomial function f(x) = \(x^4 - 2x^3 + x^2 - x + 1\) has a root at \(x = 1\). Find the other roots of the function.

A. \(x = 0\), \(x = 1\), \(x = 2\), \(x = 3\)

B. \(x = 0\), \(x = 1\),\(x = -1\), \(x = 2\)

C. \(x = 0\), \(x = 1\),\(x = -1\),\(x = -2\)

Correct D. \(x = 0\), \(x = 1\), \(x = 2\),\(x = -1\)

Correct Answer: D

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Question 18 View Details

A variation problem states that the cost of producing x units of a product is given by the equation C(x) = \(2x^2 + 5x + 1\). Find the marginal \\(cost of producing x units of a product is given by the equation C(x) = \((2x^2 + 5x + 1\)\cost function.

Correct A. 4x + 5

B. 2x + 5

C. \(x^2 + 5\)

D. \(2x^2 + 5\)

Correct Answer: A

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Question 19 View Details

Find the equation of the circle with center at \(-2, 3\) and radius 4.

Correct A. text{Equation: } \(x + 2\)^2 + \\(text{Equation:} (x + 2\(y - 3\)^\(2 = 16\)

B. text{Equation: } \(x - 2\)^2 + \\(text{Equation:} (x - 2\(y + 3\)^\(2 = 16\)

C. text{Equation: } \(x + 2\)^2 + \\(text{Equation:} (x + 2\(y + 3\)^\(2 = 16\)

D. text{Equation: } \(x - 2\)^2 + \\(text{Equation:} (x - 2\(y - 3\)^\(2 = 16\)

Correct Answer: A

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Question 20 View Details

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

A. \(S_{10} = 1230\)

B. \(S_{10} = 1240\)

Correct C. \(S_{10} = 1250\)

D. \(S_{10} = 1260\)

Correct Answer: C

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Question 21 View Details

Find the volume of the sphere with radius 6 cm.

Correct A. \(V = 904.778\) \(cm^3\)

B. \(V = 904.778\)

C. \(V = 904.778\) \(cm^3\)

D. \(V = 904.778\)

Correct Answer: A

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Question 22 View Details

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

Correct A. \(x = 10\^4\)

B. \(x = 10\^2\)

C. \(x = 10\^8\)

D. \(x = 10\^6\)

Correct Answer: A

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Question 23 View Details

Find the surface area of the cube with side length 8 cm.

Correct A. \(A = 256\) \(cm^2\)

B. \(A = 256\)

C. \(A = 256\) \(cm^2\)

D. \(A = 256\)

Correct Answer: A

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Question 24 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. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: A

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Question 25 View Details

Find the sum of the first 5 terms of the arithmetic sequence 2, 5, 8, ...

Correct A. \(S_5 = 30\)

B. \(S_5 = 25\)

C. \(S_5 = 20\)

D. \(S_5 = 15\)

Correct Answer: A

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