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POST UTME WELLSPRING UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 104,783

B. 104,783

C. 104,783

D. 104,783

Correct Answer: A

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Question 2 View Details

A circle has a diameter of 10 cm. Find the area of the circle.

Correct A. 78.5

B. 78.5

C. 78.5

D. 78.5

Correct Answer: A

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Question 3 View Details

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

Correct A. \(-∞, -3\) ∪ (1, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, -3\) ∪ (1, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 4 View Details

Find the volume of the cylinder with radius 4 cm and height 10 cm.

Correct A. 251.2

B. 251.2

C. 251.2

D. 251.2

Correct Answer: A

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Question 5 View Details

A set of 5 numbers has a mean of 10. Find the sum of the numbers.

Correct A. 50

B. 50

C. 50

D. 50

Correct Answer: A

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Question 6 View Details

Determine the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 2

B. 61

Correct C. 62

D. 63

Correct Answer: C

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Question 7 View Details

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

A. -1

B. 1

Correct C. 2

D. -2

Correct Answer: C

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Question 8 View Details

Find the derivative of the function f(x) = \(\frac{x^2}{x\)^2 + 1}\)\).

Correct A. \(\frac{2x}{x^2 + 1\) ^2}\)\)

B. \(\frac{2x^2}{\) \(x^2 + 1\) ^2}\)\)

C. \(\frac{2x^3}{\) \(x^2 + 1\) ^2}\)\)

D. \(\frac{2x^4}{\) \(x^2 + 1\) ^2}\)\)

Correct Answer: A

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Question 9 View Details

Solve the system of equations \begin{align*} x + y &= 2 \ x - y &= 1 \end{align*}.

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

B. \(x = 1\), \(y = 2\)

Correct C. \(x = 2\), \(y = 1\)

D. \(x = 2\), \(y = 2\)

Correct Answer: C

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Question 10 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 11 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{\(x^2 + 1}}\)\) ) using the chain rule.

A. \(\frac{-x}{x^2 + 1 \\)^{\(3/2\)}} )

Correct B. \(\frac{x}{x^2 + 1 \\)^{\(3/2\)}} )

C. \(\frac{1}{x^2 + 1 \\)^{\(3/2\)}} )

D. \(\frac{-1}{x^2 + 1 \\)^{\(3/2\)}} )

Correct Answer: B

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Question 12 View Details

Solve the inequality \(2^x + 2^{x+1} > 2^{x+2}\).

A. \(x < -2\)

Correct B. \(x > -2\)

C. \(x < 0\)

D. \(x > 0\)

Correct Answer: B

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Question 13 View Details

Find the area of the region bounded by the curves \(y = x^2\) and \(y = 2x\).

Correct A. \(\frac{4}{3}\)

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

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

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

Correct Answer: A

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Question 14 View Details

A vector ( mathbf{a} ) has magnitude 5 and direction \(30^circ\) north of east. Find the vector ( mathbf{a} ).

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

B. \(egin{pmatrix} 2.5 \ 4.33 \end{pmatrix}\)

C. \(egin{pmatrix} 3.54 \ 3.54 \end{pmatrix}\)

D. \(egin{pmatrix} 2.5 \ -2.5 \end{pmatrix}\)

Correct Answer: A

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Question 15 View Details

A histogram has a mean of 25 and a standard deviation of 5. Find the probability that a randomly selected value is between 20 and 30.

Correct A. ( 0.8 )

B. ( 0.6 )

C. ( 0.4 )

D. ( 0.2 )

Correct Answer: A

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Question 16 View Details

Let X be a random variable with probability density function (pdf) given by f(x) = (\(\frac{1}{2}\\()e^{-\)|x|}\) for -∞\(< x\)< ∞. Find the probability that X lies in the interval \\((frac{1}{2}e^{-|x|}\(-1, 2\).

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 17 View Details

Find the area under the curve y = \(\frac{1}{x^2 + 1}\) from \(x = 0\) to \(x = 1\).

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 18 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\).

Correct A. \(-∞, -3\) ∪ (2, ∞)

B. \(-3, 2\)

C. \(-∞, -3\) ∪ (2, ∞) ∪ (3, 4)

D. \(-∞, -3\) ∪ (2, 4)

Correct Answer: A

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Question 19 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 20 View Details

Find the mean and standard deviation of the data set {1, 2, 3, 4, 5}.

Correct A. Mean: 3, Standard Deviation: 1

B. Mean: 2, Standard Deviation: 1

C. Mean: 3, Standard Deviation: 2

D. Mean: 2, Standard Deviation: 2

Correct Answer: A

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Question 21 View Details

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

Correct A. 13

B. 15

C. 17

D. 19

Correct Answer: A

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Question 22 View Details

Solve the system of linear equations using the method of substitution: \(x + y = 3\) and 2x - 3y = -5.

Correct A. \(x = 2\), \(y = 1\)

B. \(x = 1\), \(y = 2\)

C. \(x = 3\), \(y = 0\)

D. \(x = 0\), \(y = 3\)

Correct Answer: A

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Question 23 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. \(y = x - 2\)

D. \(y = x + 2\)

Correct Answer: A

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Question 24 View Details

A binary operation star is defined as a \star \(b = a\\(star is defined as a star \^2 + b^2\). Find the value of 2 \star 3.

Correct A. 13

B. 15

C. 17

D. 19

Correct Answer: A

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Question 25 View Details

A histogram is shown below. Find the mean of the data.

Correct A. 10

B. 12

C. 14

D. 16

Correct Answer: A

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