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POST UTME MADONNA UNIVERSITY 2017 Mathematics | Objective

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Question 1

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

Correct A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )

B. \( \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \ \) )

C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )

D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )

Correct Answer: A

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Question 2

Solve the system of equations \( egin{cases} x + y = 4 \ xy = 5 \end{cases} \).

Correct A. \( x = 5, y = 1 \)

B. \( x = 1, y = 5 \)

C. \( x = -1, y = -5 \)

D. \( x = 5, y = -1 \)

Correct Answer: A

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Question 3

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

Correct A. \( y = \frac{5-3}{4-2}x + \frac{3 cdot 4 - 5 cdot 2}{4-2} \)

B. \( y = \frac{3-5}{2-4}x + \frac{3 cdot 2 - 5 cdot 4}{2-4} \)

C. \( y = \frac{5-3}{4-2}x + \frac{3 cdot 2 - 5 cdot 4}{4-2} \)

D. \( y = \frac{3-5}{2-4}x + \frac{3 cdot 4 - 5 cdot 2}{4-2} \)

Correct Answer: A

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Question 4

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

Correct A. \( 2^2 + 3^2 \)

B. \( 2^3 + 3^2 \)

C. \( 2^2 + 3^3 \)

D. \( 2^3 + 3^3 \)

Correct Answer: A

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Question 5

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

Correct A. \( \frac{1}{2} cdot 3 cdot 4 \)

B. \( \frac{1}{2} cdot 3 cdot 3 \)

C. \( \frac{1}{2} cdot 4 cdot 4 \)

D. \( \frac{1}{2} cdot 3 cdot 4 \)

Correct Answer: A

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Question 6

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

Correct A. x^2 + y^2 - 6x - 4y + 5 = 0

B. x^2 + y^2 + 6x + 4y + 5 = 0

C. x^2 + y^2 - 6x + 4y + 5 = 0

D. x^2 + y^2 + 6x - 4y + 5 = 0

Correct Answer: A

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Question 7

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

Correct A. \( -3, -1 \) \cup (1, 3)

B. \( -3, -1 \) \cup (1, 3) \cup \( 3, \infty \)

C. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \)

D. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \) \cup (0, 1)

Correct Answer: A

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Question 8

A histogram of the heights of 100 students in a class is shown below. Find the mean height of the students.

A. 165 cm

Correct B. 170 cm

C. 175 cm

D. 180 cm

Correct Answer: B

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Question 9

Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P\( A \cap B \).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 10

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

A. 18

B. 20

Correct C. 22

D. 24

Correct Answer: C

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Question 11

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 12

Solve for x in the equation: \frac{1}{x+1} + \frac{1}{x-1} = \frac{1}{2}

Correct A. x = 1

B. x = -1

C. x = 2

D. x = -2

Correct Answer: A

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Question 13

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 14

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

Correct A. x = \frac{\pi}{2}

B. x = \frac{\pi}{4}

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

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

Correct Answer: A

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Question 15

Find the volume of the sphere with radius 6.

Correct A. 904.778

B. 904.778

C. 904.778

D. 904.778

Correct Answer: A

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Question 16

Find the equation of the circle with center at ((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 17

A rec\tangular box has dimensions 3 cm x 2 cm x 4 cm. Find the volume of the box.

A. ( 24 ) cm^3

B. ( 36 ) cm^3

Correct C. ( 48 ) cm^3

D. ( 60 ) cm^3

Correct Answer: C

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Question 18

Solve for x: \( 2^x = 32 \).

A. \( x = 4 \)

Correct B. \( x = 5 \)

C. \( x = 6 \)

D. \( x = 7 \)

Correct Answer: B

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Question 19

Find the determinant of the matrix [ egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} ].

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 20

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

A. ( 16 )

B. ( 20 )

Correct C. ( 24 )

D. ( 28 )

Correct Answer: C

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Question 21

In a 3x3 matrix, if the determinant is 24, and the elements of the first row are 2, 3, and 4, what is the value of the element in the second row and third column?

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 22

If the volume of a rec\tangular prism is 120 cubic units, and the length and width are in the ratio 3:2, what is the height of the prism?

A. 4

B. 5

Correct C. 6

D. 8

Correct Answer: C

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Question 23

If \sin(x) = 3/5, and \cos(x) = 4/5, what is the value of \tan(x)?

Correct A. 3/4

B. 4/3

C. 3/4

D. 4/3

Correct Answer: A

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Question 24

If the surface area of a cube is 486 square units, what is the length of one side of the cube?

A. 9

B. 10

Correct C. 12

D. 15

Correct Answer: C

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Question 25

If the derivative of a function f(x) is f'(x) = 2x + 1, what is the value of f(3)?

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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