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POST UTME PAN-ATLANTIC UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Determine 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 2 View Details

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 3 View Details

In the diagram below, identify the type of triangle formed by the points A(1, 2), B(3, 4), and C(5, 6).\nn{\n \n \n \n}

A. Isosceles

B. Scalene

C. Equilateral

Correct D. Right-angled

Correct Answer: D

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Question 4 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

C. 25

Correct D. 30

Correct Answer: D

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Question 5 View Details

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

A. 50

B. 100

C. 200

Correct D. 400

Correct Answer: D

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Question 6 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

Correct B. 7.5 cm

C. 10 cm

D. 12.5 cm

Correct Answer: B

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Question 7 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30 cm³

B. 40 cm³

C. 50 cm³

D. 60 cm³

Correct Answer: A

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Question 8 View Details

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

A. \(\frac{1}{3}\)\)

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

Correct C. \(\frac{2}{3}\)\)

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

Correct Answer: C

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Question 9 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 1\)

Correct Answer: A

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Question 10 View Details

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

Correct A. -120

B. -150

C. -180

D. -200

Correct Answer: A

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Question 11 View Details

Let ( X ) and ( Y ) be independent random variables with probability density functions \(f_X x \\) = egin{cases} 2x, & \(0 < x\)\(< 1\)\ 0, & \text{otherwise} \end{cases} ) and \(f_Y y \\) = egin{cases} \(3y^2\), & \(0 < y\)\(< 1\)\ 0, & text{otherwise} \end{cases} ). Find the probability that \(X + Y < 1\\(text{otherwise} end{cases} ). Find the probability that\).

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

B. \(\frac{1}{3}\)\)

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

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

Correct Answer: A

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Question 12 View Details

Solve for ( x ) in the equation \(2^x + 3^x = 5^x\).

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 13 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 14 View Details

Let ( f(x) = egin{cases} \(x^2\), & \(x < 0\) \ \(x^3\), & x \geq 0 end{cases} ). Find the value of \(\int_{-1}^{1} f x \\(end{cases} ). Find the value of (\\) \, dx ).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 15 View Details

Solve the system of equations: \(x + y = 2\) and \(xy = 1\).

Correct A. \(x = 1\), \(y = 1\)

B. \(x = 2\), \(y = 0\)

C. \(x = 0\), \(y = 2\)

D. \(x = -1\),\(y = -1\)

Correct Answer: A

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Question 16 View Details

Find the area under the curve of ( f(x) = \(2x^2 + 3x - 1\) ) from \(x = 0\) to \(x = 2\).

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 17 View Details

Solve the system of linear equations: \(\begin{cases} 2x + 3y = 7 \ 4x - 2y = - 3 \end{cases}\).

Correct A. \begin{cases} \(x = 1\) \ \(y = 2\) \end{cases}

B. \begin{cases} \(x = 2\) \ \(y = 1\) \end{cases}

C. \begin{cases} \(x = 3\) \ \(y = 0\) \end{cases}

D. \begin{cases} \(x = 0\) \ \(y = 3\) \end{cases}

Correct Answer: A

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Question 18 View Details

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

Correct A. \(\frac{\pi}{12}\)\)

B. \(\frac{\pi}{6}\)\)

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

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

Correct Answer: A

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Question 19 View Details

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

Correct A. \begin{cases}\(x = -2\)\end{cases}

B. \begin{cases} \(x = 2\) \end{cases}

C. \begin{cases}\(x = -1\)\end{cases}

D. \begin{cases} \(x = 1\) \end{cases}

Correct Answer: A

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Question 20 View Details

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

Correct A. \(\frac{\pi}{3}\)\)

B. \(\frac{\pi}{6}\)\)

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

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

Correct Answer: A

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Question 21 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 mean height of the university students.

A. 168.3 cm to 182.7 cm

Correct B. 170.1 cm to 180.9 cm

C. 172.9 cm to 178.1 cm

D. 174.7 cm to 176.3 cm

Correct Answer: B

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Question 22 View Details

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 23 View Details

A company produces two products, A and B. The profit from the production of product A is ₦120 per unit, while the profit from the production of product B is ₦180 per unit. If the company produces 200 units of product A and 300 units of product B, what is the total profit?

A. ₦48,000

B. ₦54,000

Correct C. ₦60,000

D. ₦66,000

Correct Answer: C

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Question 24 View Details

A right-angled triangle has a hypotenuse of 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

B. 7.5 cm

Correct C. 8.66 cm

D. 10 cm

Correct Answer: C

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Question 25 View Details

A vector (\(\vec{a}\)\) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x and y components of \\((vec{a}\(\vec{a}\).

Correct A. \(\begin{pmatrix} 2.5 \ 4.33 \end{pmatrix}\)

B. \(\begin{pmatrix} 3.54 \ 2.5 \end{pmatrix}\)

C. \(\begin{pmatrix} 4.33 \ 2.5 \end{pmatrix}\)

D. \(\begin{pmatrix} 2.5 \ 3.54 \end{pmatrix}\)

Correct Answer: A

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