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POST UTME UI 2022 Mathematics | Objective

Prepare for your exams with POST UTME UI questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1 View Details

Find the equation of the circle passing through the points (2, 3), (4, 1), and \(-1, 2\).

Correct A. \boxed{\(x^2\) + \\((y^2 - 5x + 7y - 12\)\(= 0\)\)}

B. \boxed{\(x^2\) + \\((y^2 - 3x - 5y + 4\)\(= 0\)\)}

C. \boxed{\(x^2\) + \\((y^2 + 3x - 7y + 2\)\(= 0\)\)}

D. \boxed{\(x^2\) + \\((y^2 - x + 3y - 6\)\(= 0\)\)}

Correct Answer: A

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Question 2 View Details

Solve the equation \(2x^3 - 5x^2 + 3x - 1 = 0\) using the Rational Root Theorem.

Correct A. \boxed{\(r =\)\pm 1}

B. \boxed{\(r =\)\pm 2}

C. \boxed{\(r =\)\pm 3}

D. \boxed{\(r =\)\pm \(1/2\)}

Correct Answer: A

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Question 3 View Details

Find the derivative of the function \(f(x) = \frac{x^2 + 3x - 2}{x + 1}\) using the Quotient Rule.

Correct A. \boxed{f'\((x) =\)\(\frac{2x + 3}{x + 1 ^2}\)\)}

B. \boxed{f'\((x) =\)\(\frac{2x - 3}{x + 1 ^2}\)\)}

C. \boxed{f'\((x) =\)\(\frac{2x + 2}{x + 1 ^2}\)\)}

D. \boxed{f'\((x) =\)\(\frac{2x - 2}{x + 1 ^2}\)\)}

Correct Answer: A

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Question 4 View Details

Solve the system of equations \(x + y = 2\) and \(x - y = 1\) using the method of substitution.

Correct A. \boxed{\(x = 1\), \(y = 1\)}

B. \boxed{\(x = 2\), \(y = 0\)}

C. \boxed{\(x = 0\), \(y = 2\)}

D. \boxed{\(x = 1\), \(y = 2\)}

Correct Answer: A

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Question 5 View Details

Find the equation of the line passing through the points (1, 2) and (3, 4).

Correct A. \boxed{\(y = x + 1\)}

B. \boxed{\(y = x - 1\)}

C. \boxed{\(y = -x + 2\)}

D. \boxed{\(y = x - 2\)}

Correct Answer: A

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Question 6 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 7 View Details

Solve for x in the equation \(\log_{10} x^2\)\(= 4\)\).

Correct A. \(x = 10\^4\)

B. \(x = 10\^2\)

C. \(x = 10\^8\)

D. \(x = 10\^6\)

Correct Answer: A

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Question 8 View Details

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

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

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

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

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

Correct Answer: B

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Question 9 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

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

B. \(\frac{2}{6}\)\)

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

Correct D. \(\frac{4}{6}\)\)

Correct Answer: D

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Question 10 View Details

Find the vector \(\mathbf{a} \cdot mathbf{b}\) given \(\\(mathbf{b}) given \mathbf{a} = \begin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix} 4 \ 5 \end{pmatrix}\).

A. 23

Correct B. 29

C. 31

D. 37

Correct Answer: B

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Question 11 View Details

Solve for x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 12 View Details

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

A. 24π \(cm^3\)

B. 48π \(cm^3\)

Correct C. 72π \(cm^3\)

D. 96π \(cm^3\)

Correct Answer: C

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Question 13 View Details

If ( f(x) = \(\frac{x^2 - 4}{x - 2}\)\)) ), find \(f -2 \\\() ), find (f -2\) ).

A. 0

Correct B. 2

C. 4

D. 6

Correct Answer: B

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Question 14 View Details

A particle moves along the x-axis with its position given by ( s(t) = \((2t^3 - 5t^2 + 3t + 1\)\) ). Find the velocity of the particle at time \(t = 2\\((2t^3 - 5t^2 + 3t + 1) ). Find the velocity of the particle at time\) s.

A. 10 \(m/s\)

B. 20 \(m/s\)

Correct C. 30 \(m/s\)

D. 40 \(m/s\)

Correct Answer: C

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Question 15 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 16 View Details

Find the area under the curve \(y = \frac{1}{2}x^2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{16}{3}\)

B. ( 8 )

C. ( 12 )

D. ( 16 )

Correct Answer: A

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Question 17 View Details

Solve the system of linear equations using matrices: \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix}\).

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

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

C. \(x = 3, y = 4\)

D. \(x = 4, y = 3\)

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

D. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 16\) )

Correct Answer: A

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Question 19 View Details

Solve the inequality \(x^2 - 4x + 3 > 0\).

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

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

C. \(x < -3\) or \(x > 1\)

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

Correct Answer: A

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Question 20 View Details

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

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 21 View Details

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

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

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: A

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Question 22 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

Correct A. 0.8413

B. 0.8413

C. 0.8413

D. 0.8413

Correct Answer: A

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Question 23 View Details

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

A. -2

Correct B. -1

C. 0

D. 1

Correct Answer: B

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Question 24 View Details

Find the vector projection of \(\vec{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\) onto \(\vec{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}\).

Correct A. \(egin{pmatrix} 0.8 \ 1 \ 1.2 \end{pmatrix}\)

B. \(egin{pmatrix} 1 \ 1.2 \ 1.6 \end{pmatrix}\)

C. \(egin{pmatrix} 1.2 \ 1.6 \ 2 \end{pmatrix}\)

D. \(egin{pmatrix} 1.6 \ 2 \ 2.4 \end{pmatrix}\)

Correct Answer: A

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Question 25 View Details

A set ( S ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( S ) that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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