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POST UTME SUMMIT UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

Find the equation of the circle with centre (2, 3) and radius 4.

Correct A. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

B. \(x + 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

C. \(x - 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

D. \(x + 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

Correct Answer: A

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Question 2 View Details

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

Correct A. \(x < -1\) or \(x > \frac{3}{2}\)

B. \(x < -1\) or \(x < \frac{3}{2}\)

C. \(x > -1\) or \(x < \frac{3}{2}\)

D. \(x > -1\) or \(x > \frac{3}{2}\)

Correct Answer: A

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Question 3 View Details

Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...

Correct A. ( 3054 )

B. ( 3056 )

C. ( 3058 )

D. ( 3060 )

Correct Answer: A

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Question 4 View Details

Solve the system of equations \(x + y = 3\) and \(xy = 2\).

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

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

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

D. \(x = -2, y = 1\)

Correct Answer: A

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Question 5 View Details

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

Correct A. ( 12 )

B. ( 14 )

C. ( 16 )

D. ( 18 )

Correct Answer: A

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Question 6 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 + \(y + 3\)^\(2 = 16\) )

C. \(x + 2 \\)^2 + \(y + 3\)^\(2 = 16\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 16\) )

Correct Answer: A

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Question 7 View Details

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

A. \(x = -1\)

B. \(x = 0\)

Correct C. \(x = 1\)

D. \(x = 2\)

Correct Answer: C

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Question 8 View Details

Find the value of \(\log_{10} 1000 \\) ).

A. ( 3 )

Correct B. ( 4 )

C. ( 5 )

D. ( 6 )

Correct Answer: B

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Question 9 View Details

Solve the system of equations \(x + y = 4\) and \(x - y = 2\).

Correct A. \(x = 3, y = 1\)

B. \(x = 1, y = 3\)

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

D. \(x = 4, y = 0\)

Correct Answer: A

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Question 10 View Details

Find the mean of the numbers 2, 4, 6, 8, 10.

A. ( 6 )

B. ( 7 )

Correct C. ( 8 )

D. ( 9 )

Correct Answer: C

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Question 11 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\), and P\(X = 3 = 0.3\). Find the expected value of X.

Correct A. 1.1

B. 1.2

C. 1.3

D. 1.4

Correct Answer: A

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Question 12 View Details

Solve the inequality \(x^2 + 4x - 5 \geq 0\).

Correct A. \(x \leq -5\) or \(x \geq 1\)

B. \(x \leq -1\) or \(x \geq 5\)

C. \(x \leq -5\) or \(x \geq -1\)

D. \(x \leq 1\) or \(x \geq 5\)

Correct Answer: A

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Question 13 View Details

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

Correct A. \(\frac{8}{3}\)

B. \(\frac{16}{3}\)

C. \(\frac{32}{3}\)

D. \(\frac{64}{3}\)

Correct Answer: A

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Question 14 View Details

A sequence is defined by \(a_n = \frac{1}{n}\). Find the sum of the first 5 terms of the sequence.

Correct A. \(\frac{121}{60}\)

B. \(\frac{241}{120}\)

C. \(\frac{421}{240}\)

D. \(\frac{521}{300}\)

Correct Answer: A

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Question 15 View Details

A set of numbers is defined as S = \{ x \in \mathbb{R} : \\((x^2 - 4x + 3\)\(= 0\)\) \}. Find the elements of the set S.

Correct A. \(\{1, 3 \}\)

B. \(\{-1, -3 \}\)

C. \(\{1, -3 \}\)

D. \(\{-1, 3 \}\)

Correct Answer: A

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Question 16 View Details

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

Correct A. \(x = -\frac{5}{2}\)

B. \(x = \frac{5}{2}\)

C. \(x = -\frac{1}{2}\)

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

Correct Answer: A

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Question 17 View Details

In a set of 10 integers, 3 are even and 7 are odd. If 2 integers are randomly selected, what is the probability that both integers are odd?

A. \(\frac{1}{10}\)

B. \(\frac{1}{5}\)

Correct C. \(\frac{7}{10}\)

D. \(\frac{9}{10}\)

Correct Answer: C

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Question 18 View Details

Find the sum of the infinite geometric series \(sum_{n = 1}^{\infty} \frac{2}{3^n}\).

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

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

C. \(\frac{6}{3}\)

D. \(\frac{8}{3}\)

Correct Answer: A

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Question 19 View Details

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

Correct A. \(x = -2\)

B. \(x = 2\)

C. \(x = -1\)

D. \(x = 1\)

Correct Answer: A

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Question 20 View Details

Find the value of \(\log_{10} 1000 \\) ).

A. ( 3 )

Correct B. ( 4 )

C. ( 5 )

D. ( 6 )

Correct Answer: B

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Question 21 View Details

Determine the value of (x\) in the equation \(2^x + 5^x = 7^x\\((x) in the equation\).

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 22 View Details

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 4

B. 5

Correct C. 6

D. 7

Correct Answer: C

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Question 23 View Details

Solve the system of equations: \(\begin{array}{ccc} x + y & = & 4 \ x - y & = & 2 \end{array}\)

Correct A. \(x = 1\), \(y = 3\)

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

C. \(x = 3\), \(y = 1\)

D. \(x = 4\), \(y = 0\)

Correct Answer: A

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Question 24 View Details

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 25 View Details

Solve the vector equation: \(\begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} \cdot \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} = 25\)

A. \(x = 5\)

B. \(x = 10\)

Correct C. \(x = 15\)

D. \(x = 20\)

Correct Answer: C

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