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POST UTME FUTO 2023 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 matrix equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

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

B. \(x = 2\), \(y = 3\)

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

D. \(x = 4\), \(y = 5\)

Correct Answer: A

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Question 3 View Details

Find the area of the triangle with vertices (1, 2), (3, 4), and (5, 6).

Correct A. 10

B. 20

C. 30

D. 40

Correct Answer: A

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Question 4 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\).

Correct A. \(x = 0\)

B. \(x = 90\)

C. \(x = 180\)

D. \(x = 270\)

Correct Answer: A

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Question 5 View Details

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

Correct A. 1200

B. 1300

C. 1400

D. 1500

Correct Answer: A

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Question 6 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

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

Correct B. 64\pi \(cm^3\)

C. 128\pi \(cm^3\)

D. 256\pi \(cm^3\)

Correct Answer: B

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Question 7 View Details

Solve the inequality \(\frac{x}{x-2}\)\\() > 1.\)

A. \(x < 2\)

B. \(x > 2\)

Correct C. \(x < 0\) or \(x > 2\)

D. \(x > 0\) or \(x < 2\)

Correct Answer: C

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Question 8 View Details

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

A. 36

B. 48

Correct C. 60

D. 72

Correct Answer: C

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Question 9 View Details

Solve the equation \\((x^2 + 4x - 5\)\(= 0.\)\)

Correct A. x = -5 or \(x = 1\)

B. x = -1 or \(x = 5\)

C. x = -2 or \(x = 3\)

D. x = -3 or \(x = 2\)

Correct Answer: A

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Question 10 View Details

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

Correct A. 242

B. 242.5

C. 243

D. 243.5

Correct Answer: A

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Question 11 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).

A. 24

B. 28

Correct C. 32

D. 36

Correct Answer: C

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Question 12 View Details

Solve for ( x ) in the equation \(\sin^2 x + \cos^2 x = 1 \\).

Correct A. \(x =\)\(\frac{\pi}{4}\)\)

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

C. \(x =\)\(\frac{3\pi}{4}\)\)

D. \(x =\)\(\frac{5\pi}{4}\)\)

Correct Answer: A

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Question 13 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. \(\frac{-x}{x^2 + 1\) ^2}\)\)

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

Correct Answer: B

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Question 14 View Details

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

A. \(x < -1\)

Correct B. \(x > -1\)

C. \(x < 3\)

D. \(x > 3\)

Correct Answer: B

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Question 15 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 16 View Details

Find the volume of the solid formed by rotating the region bounded by the curves \(y = x^2\) and \(y = 4x\) about the x-axis.

Correct A. \(\frac{32}{15}\)\)\pi

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

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

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

Correct Answer: A

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Question 17 View Details

Solve the inequality \(\log_2 x^2+1\)\(> 2\)\).

Correct A. \(x<-1\)\lor \(x > 1\)

B. \(x>-1\)\lor \(x > 1\)

C. \(x<-1\)\lor \(x < 1\)

D. \(x>-1\)\lor \(x < 1\)

Correct Answer: A

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Question 18 View Details

Find the area of the region bounded by the curves \(y = x^2+1\) and \(y = 2x+1\).

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

Correct B. \(\frac{5}{2}\)\)

C. \(\frac{7}{2}\)\)

D. \(\frac{9}{2}\)\)

Correct Answer: B

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Question 19 View Details

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

A. \(x=-2\)

B. \(x=-1\)

Correct C. \(x = 1\)

D. \(x = 2\)

Correct Answer: C

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Question 20 View Details

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

Correct A. \(y=-x+5\)

B. \(y = x-1\)

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

D. \(y = x+1\)

Correct Answer: A

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Question 21 View Details

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 3 \end{array} ].

A. 5

Correct B. -2

C. 10

D. 0

Correct Answer: B

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Question 22 View Details

A histogram is constructed with the following data: [ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ]. If the width of each bar is 2, what is the area of the histogram?

Correct A. 100

B. 200

C. 50

D. 150

Correct Answer: A

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Question 23 View Details

Solve the equation [ \\((x^2 + 5x + 6\)\(= 0\)\) ].

Correct A. -2

B. -3

C. 2

D. 3

Correct Answer: A

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Question 24 View Details

Find the value of [ sin(2x) \] when [ \\(sin(x) =\)\\(sin(2x) ] when [ \(\frac{1}{2}\)\) \].

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

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

C. \(\frac{\sqrt{3}}{2}\)

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

Correct Answer: A

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Question 25 View Details

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?

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

Correct B. \(\frac{2}{5}\)\)

C. \(\frac{4}{12}\)\)

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

Correct Answer: B

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