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POST UTME ELIZADE UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.

A. 200\pitext{ cm}^3

Correct B. 300\pitext{ cm}^3

C. 400\pitext{ cm}^3

D. 500\pitext{ cm}^3

Correct Answer: B

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Question 2 View Details

Solve for x in the equation \(\frac{1}{x+1} + \frac{1}{x-2} = \frac{3}{x^2-3x-2}\\).

A. \(x = 1\)

B. \(x = -1\)

Correct C. \(x = 2\)

D. \(x = -2\)

Correct Answer: C

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Question 3 View Details

A set of 5 consecutive integers has a median of 10. What is the sum of the integers?

A. 250

B. 260

Correct C. 270

D. 280

Correct Answer: C

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Question 4 View Details

A bakery sells 480 loaves of bread per day. If they make a profit of ₦2.50 per loaf, how much profit do they make in a day?

Correct A. ₦1200

B. ₦1200.00

C. ₦1200.00

D. ₦1200.00

Correct Answer: A

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Question 5 View Details

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

Correct A. 288\pitext{ cm}^2

B. 288\pitext{ cm}^2

C. 288\pitext{ cm}^2

D. 288\pitext{ cm}^2

Correct Answer: A

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Question 6 View Details

Let \(\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 1 \ -2 end{pmatrix}\). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula \(\\(end{pmatrix}). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula \mathrm{proj}_{\mathbf{a}} \mathbf{b} = \frac{\mathbf{a} \cdot \mathbf{b}}{| \mathbf{a} |^2} \mathbf{a}\).

A. 0

Correct B. \begin{pmatrix} \(\frac{4}{13}\)\) \\ \(\frac{6}{13}\)\) \end{pmatrix}

C. \begin{pmatrix} \(\frac{2}{13}\)\) \\ \(\frac{3}{13}\)\) \end{pmatrix}

D. \begin{pmatrix} \(\frac{1}{13}\)\) \\ \(\frac{-2}{13}\)\) \end{pmatrix}

Correct Answer: B

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Question 7 View Details

A fair six-sided die is rolled. What is the probability that the number appearing on the die is even?

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 8 View Details

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

A. \left\(-\frac{5}{4}, \frac{3}{2} \right\)

B. \left\(-\frac{3}{2}, \frac{5}{4} \right\)

Correct C. \left\(-\infty, -\frac{3}{2} \right\) \cup \left\(\frac{5}{4}, \infty \right\)

D. \left\(-\infty, \frac{5}{4} \right\) \cup \left\(-\frac{3}{2}, \infty \right\)

Correct Answer: C

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Question 9 View Details

Find the area under the curve \(y = x^2 - 4x + 3\) from \(x = 1\) to \(x = 3\) using the definite integral.

Correct A. \(\frac{20}{3}\)\)

B. \(\frac{22}{3}\)\)

C. \(\frac{24}{3}\)\)

D. \(\frac{26}{3}\)\)

Correct Answer: A

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Question 10 View Details

A sequence is defined recursively as \(a_n = 2a_{n-1} + 1\) with initial term \(a_1 = 3\). Find the sum of the first 5 terms of the sequence.

A. 63

Correct B. 65

C. 67

D. 69

Correct Answer: B

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Question 11 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 12 View Details

Solve the system of linear equations using matrices: \begin{align*} x + y &= 4 \ 2x - y &= 3 \end{align*}

Correct A. \text{Solution: } \(x = 2\), \(y = 2\)

B. \text{Solution: } \(x = 1\), \(y = 3\)

C. \text{Solution: } \(x = 3\), \(y = 1\)

D. \text{Solution: } \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 13 View Details

Find the volume of the sphere with radius 6.

Correct A. 904.778

B. 904.778

C. 904.778

D. 904.778

Correct Answer: A

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Question 14 View Details

Solve the quadratic equation: \begin{align*} \(x^2 + 5x + 6\) &= 0 \end{align*}

Correct A. \text{Solution: }\(x = -2\),\(x = -3\)

B. \text{Solution: } \(x = 2\), \(x = 3\)

C. \text{Solution: }\(x = -1\),\(x = -6\)

D. \text{Solution: } \(x = 1\), \(x = 6\)

Correct Answer: A

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Question 15 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

Correct A. \text{Equation: } \(y = 2x - 1\)

B. \text{Equation: } \(y = 2x + 1\)

C. \text{Equation: }\(y = -2x + 1\)

D. \text{Equation: }\(y = -2x - 1\)

Correct Answer: A

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Question 16 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 17 View Details

A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & text{if } \(X = 1\) \\(text{if} (X = 1\ 0.3 & text{if} \(X = 2\) \\(text{if} (X = 2\ 0.5 & text{if} \(X = 3\) \\(text{if}\((X = 3\)\end{cases} ). Find the expected value of X.

Correct A. 1.5

B. 2

C. 2.5

D. 3

Correct Answer: A

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Question 18 View Details

Find the derivative of the function ( f(x) = \\(\sin^2\) x ) using the chain rule.

Correct A. 2\sin x \cos x

B. \\(\cos^2\) x

C. \\(\sin^2\) x

D. \tan x

Correct Answer: A

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Question 19 View Details

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

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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Question 20 View Details

Solve the equation \(\sin^2 x + \cos^2 x = 1\) for x.

A. 0

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

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

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

Correct Answer: C

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Question 21 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\).

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 22 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 1\) ∪ (3, ∞)

Correct Answer: A

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Question 23 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If 80% of the scores are above 60, what is the value of the lower limit of the interval?

A. 50

Correct B. 55

C. 60

D. 65

Correct Answer: B

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Question 24 View Details

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

A. 16

Correct B. 32

C. 64

D. 128

Correct Answer: B

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Question 25 View Details

A survey of 100 students found that 60% of them preferred Mathematics, 20% preferred Science, and 20% preferred both. What is the number of students who prefer only Mathematics?

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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