POST UTME UI 2019 Mathematics | Objective

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Question 1 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 2 View Details
Solve the quadratic equation \(x^2 + 5x + 6 = 0\).
A. -2
Correct B. -3
C. 1
D. 2

Correct Answer: B

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Question 3 View Details
A histogram is shown below. What is the mean of the data?
A. 10
B. 20
Correct C. 30
D. 40

Correct Answer: C

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Question 4 View Details
Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).
A. 16
B. 32
Correct C. 64
D. 128

Correct Answer: C

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Question 5 View Details
A circle with center ( C(0, 0) ) and radius \(r = 4\) is shown below. What is the equation of the circle?
Correct A. \(x^2\) + \\((y^2\)\(= 16\)\)
B. \(x^2\) + \\((y^2\)\(= 32\)\)
C. \(x^2\) + \\((y^2\)\(= 64\)\)
D. \(x^2\) + \\((y^2\)\(= 128\)\)

Correct Answer: A

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Question 6 View Details
Find the volume of the solid formed by revolving the region bounded by \(y = \sqrt{x}\), \(y = 0\)\), and \(x = 4\) about the \(x\)-axis.
Correct A. 128\pi
B. 256\pi
C. 512\pi
D. 1024\pi

Correct Answer: A

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Question 7 View Details
Solve the inequality \(\frac{1}{x^2-4x+3}\geq 0\).
Correct A. \(x\in -\infty, 1)\cup 3, \infty \\)\)
B. \(x\in -\infty, 1)\cup 1, 3)\cup (3, \infty \\)\)
C. \(x\in -\infty, 1)\cup 3, \infty \\)\)
D. \(x\in -\infty, 3)\cup 3, \infty \\)\)

Correct Answer: A

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Question 8 View Details
Find the derivative of \(f(x) = \frac{x^2}{x^2+1}\) using the quotient rule.
A. \(\frac{2x x^2+1 -2x^2x}{x^2+1 ^2}\)
B. \(\frac{2x x^2+1 +2x^2x}{x^2+1 ^2}\)
Correct C. \(\frac{2x x^2+1 -2x^2x}{x^2+1 ^2}\)
D. \(\frac{2x x^2+1 +2x^2x}{x^2+1 ^2}\)

Correct Answer: C

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Question 9 View Details
Solve the equation \(\log_{10} x^2\)\(= 4\)\).
A. \(x = \pm 10\)
Correct B. \(x = \pm 100\)
C. \(x = \pm 1000\)
D. \(x = \pm 10000\)

Correct Answer: B

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Question 10 View Details
Find the surface area of the solid formed by revolving the region bounded by \(y = x^2\) and \(y = 0\) about the \(x\)-axis.
A. \(\frac{4\pi}{3}\)
B. \(\frac{8\pi}{3}\)
Correct C. \(\frac{16\pi}{3}\)
D. \(\frac{32\pi}{3}\)

Correct Answer: C

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Question 11 View Details
Find the sum of the infinite geometric series \(sum_{n = 1}^{\infty} \frac{1}{2^n}\).
Correct A. 1
B. 2
C. 3
D. 4

Correct Answer: A

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Question 12 View Details
Solve the quadratic equation \(x^2 + 4x + 4 = 0\).
A. \(x = -2\)
Correct B. \(x = 2\)
C. \(x = -1\)
D. \(x = 1\)

Correct Answer: B

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Question 13 View Details
A set of 5 numbers has an average of 10. If one number is removed, the average becomes 12. What is the sum of the remaining 4 numbers?
A. 48
B. 50
Correct C. 52
D. 54

Correct Answer: C

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Question 14 View Details
A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?
Correct A. 18
B. 20
C. 22
D. 24

Correct Answer: A

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Question 15 View Details
A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?
Correct A. ₦1250
B. ₦1255
C. ₦1260
D. ₦1265

Correct Answer: A

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Question 16 View Details
Determine the value of \(\frac{d}{dx} \left \frac{1}{x^2 + 1} \right\)\) using the quotient rule.
Correct A. \(\frac{-2x}{x^2 + 1\) ^2}\)\)
B. \(\frac{2x}{x^2 + 1\) ^2}\)\)
C. \(\frac{2}{x^2 + 1\) ^2}\)\)
D. \(\frac{-2}{x^2 + 1\) ^2}\)\)

Correct Answer: A

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Question 17 View Details
A histogram is constructed with 5 classes of equal width. The first class has a frequency of 10, the second class has a frequency of 15, the third class has a frequency of 20, the fourth class has a frequency of 12, and the fifth class has a frequency of 8. What is the mean of the data?
A. 12.4
Correct B. 13.2
C. 14.1
D. 15.0

Correct Answer: B

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Question 18 View Details
Solve the inequality \(x^2 - 6x + 8 \geq 0\).
Correct A. x \in \(-\infty, 2 \cup 4, \infty\)\)
B. x \in \(-\infty, 4 \cup 2, \infty\)\)
C. x \in \(-\infty, 2 \cup 4, \infty\)\)
D. x \in \(-\infty, 4 \cup 2, \infty\)\)

Correct Answer: A

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Question 19 View Details
A binary operation (\star\) is defined as \\((star\(a star b = ab + 2\). Find the value of \(3 \\(star b = ab + 2). Find the value of \star 4\).
A. 14
B. 16
Correct C. 18
D. 20

Correct Answer: C

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Question 20 View Details
A quadratic equation is given by \((x^2 + 4x + 4\) = 0\). Solve for \(x\\((x^2 + 4x + 4 = 0). Solve for\).
Correct A. \(x = -2\)
B. \(x = -1\)
C. \(x = 1\)
D. \(x = 2\)

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 cm with a standard deviation of 5 cm. If the population standard deviation is 6 cm, calculate the standard error of the mean.
A. 2.5 cm
Correct B. 3.0 cm
C. 3.5 cm
D. 4.0 cm

Correct Answer: B

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Question 22 View Details
A rectangular solid has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Calculate the surface area of the solid.
A. 104 \(cm^2\)
Correct B. 120 \(cm^2\)
C. 140 \(cm^2\)
D. 160 \(cm^2\)

Correct Answer: B

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Question 23 View Details
If f(x) = \(3x^2 + 2x - 5\), find the derivative of the function.
Correct A. 6x + 2
B. 6x - 2
C. \(3x^2 + 2\)
D. \(3x^2 - 2\)

Correct Answer: A

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Question 24 View Details
Solve the equation: 2\\(\sin^2(x)\) + \\(cos(x) = 1.\)
A. \(\frac{\pi}{6}\)\)
Correct B. \(\frac{\pi}{4}\)\)
C. \(\frac{\pi}{3}\)\)
D. \(\frac{\pi}{2}\)\)

Correct Answer: B

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Question 25 View Details
Find the equation of the circle with center (2, 3) and radius 4.
Correct A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)
B. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)
C. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)
D. \(x - 2\)^2 + \(y - 3\)^\(2 = 49\)

Correct Answer: A

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