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POST UTME REDEEMERS UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

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

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 2 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. \(x < 1\) or \(x > 3\)

C. x < -1 or \(x < 3/2\)\)

D. \(x < 1\) or \(x > 3/2\)\)

Correct Answer: A

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Question 3 View Details

Find the value of x in the equation \(x^3\) - \\((6x^2 + 11x - 6\)\(= 0.\)\)

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 4 View Details

A set A has 5 elements, and a set B has 3 elements. What is the number of elements in the union of sets A and B?

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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Question 5 View Details

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

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 6 View Details

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

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

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

C. \(x-4 \\)^2 + \(y-2\)^\(2 = 16\) )

D. \(x-2 \\)^2 + \(y-4\)^\(2 = 16\) )

Correct Answer: A

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Question 7 View Details

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

Correct A. \(x > -\frac{5}{4}\) or \(x < \frac{3}{2}\)

B. \(x < -\frac{5}{4}\) or \(x > \frac{3}{2}\)

C. \(x > -\frac{5}{4}\) and \(x < \frac{3}{2}\)

D. \(x < -\frac{5}{4}\) and \(x > \frac{3}{2}\)

Correct Answer: A

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Question 8 View Details

Find the value of \(\log_{10} x^2 \\) ) given that \(\log_{10} x = 2\).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 9 View Details

A car travels from city A to city B at an average speed of 60 \((km/h\)\) and returns at an average speed of 40 \(km/h\\((km/h) and returns at an average speed of 40\). Using the concept of variation, find the ratio of the time taken for the return journey to the time taken for the outward journey.

A. 1:2

Correct B. 2:1

C. 3:2

D. 4:3

Correct Answer: B

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Question 10 View Details

Solve the quadratic 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 11 View Details

Find the equation of the circle with center \(-2, 3\) and radius 4.

Correct A. \boxed{ 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 12 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If 75% of the scores fall below 80, what is the z-score corresponding to 80?

Correct A. \boxed{0.5}

B. 1.0

C. 1.5

D. 2.0

Correct Answer: A

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Question 13 View Details

Solve the equation \\(\tan^2\) x + 2 tan \(x - 6 = 0\) for x in the interval [0, \\(tan (x - 6 = 0\\(\pi/2\)].

Correct A. \boxed{\(x =\)\arctan(3)}

B. \(x =\)\arctan\(-2\)

C. \(x =\)\arctan(2)

D. \(x =\)\arctan\(-3\)

Correct Answer: A

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Question 14 View Details

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

Correct A. \boxed{\(\frac{16\pi}{15}\)\)}

B. \(\frac{32\pi}{15}\)\)

C. \(\frac{64\pi}{15}\)\)

D. \(\frac{128\pi}{15}\)\)

Correct Answer: A

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Question 15 View Details

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

Correct A. \boxed{0}

B. 2

C. 4

D. 6

Correct Answer: A

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Question 16 View Details

Find the value of ( lambda ) such that the quadratic equation \(x^2 + 4x + \lambda = 0\) has equal roots.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 17 View Details

Solve the system of linear equations using matrices: \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

Correct A. \(egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix}\)

B. \(egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 3 \end{bmatrix}\)

C. \(egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix}\)

D. \(egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 5 \end{bmatrix}\)

Correct Answer: A

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Question 18 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 - 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

C. \(x - 4 \\)^2 + \(y - 5\)^\(2 = 16\) )

D. \(x - 5 \\)^2 + \(y - 4\)^\(2 = 16\) )

Correct Answer: A

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Question 19 View Details

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

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

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

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

D. \(x < 1\) or \(x > 2\)

Correct Answer: A

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Question 20 View Details

Find the value of ( k ) such that the equation \(x^2 + kx + 6 = 0\) has a discriminant of ( 12 ).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 21 View Details

Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.

A. 32\pi \(cm^3\)

Correct B. 48\pi \(cm^3\)

C. 64\pi \(cm^3\)

D. 80\pi \(cm^3\)

Correct Answer: B

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Question 22 View Details

Solve the inequality \(\frac{x-1}{x+1}\)\\()>0.\)

Correct A. \(-\infty,-1)\cup 1,\infty \\)

B. \(-\infty,-1)\cup 0,\infty \\)

C. \(-\infty,0)\cup 1,\infty \\)

D. \(-\infty,0)\cup 1,\infty \\)

Correct Answer: A

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Question 23 View Details

A die is rolled twice. Find the probability that the sum of the numbers on the two dice is 7.

A. \(\frac{1}{6}\)\)

Correct B. \(\frac{1}{12}\)\)

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

D. \(\frac{5}{6}\)\)

Correct Answer: B

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Question 24 View Details

Simplify the expression \sqrt[3]{\(64x^6y\)^3}.

Correct A. \(4x^2\)\sqrt[3]{\(y^3}\)

B. \(4x^2y\)\sqrt[3]{\(y^3}\)

C. \(4x^3y\)\sqrt[3]{\(y^3}\)

D. \(4x^3y\)^2\sqrt[3]{\(y^3}\)

Correct Answer: A

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Question 25 View Details

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

Correct A. y-3=\(\frac{2}{2}\)\)\(x-2\)

B. y-3=\(\frac{2}{2}\)\)\(x-4\)

C. y-5=\(\frac{2}{2}\)\)\(x-2\)

D. y-5=\(\frac{2}{2}\)\)\(x-4\)

Correct Answer: A

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