POST UTME NOUN 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle with center ( (0, 0) ) and radius 4 passes through the point ( (3, 4) ). What is the equation of the circle?
A. \( x^2 + y^2 = 16 \)
B. \( x^2 + y^2 = 20 \)
C. \( x^2 + y^2 = 24 \)
D. \( x^2 + y^2 = 28 \)
Question 2
In the diagram below, ( ABC ) is a right-angled triangle with \( angle B = 90^{circ} \). If \( AB = 6 \) cm and \( BC = 8 \) cm, find the length of ( AC ).
A. 10 cm
B. 12 cm
C. 15 cm
D. 20 cm
Question 3
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).
A. x^2 + y^2 + 2x - 4y + 4 = 0
B. x^2 + y^2 - 2x + 4y - 4 = 0
C. x^2 + y^2 + 4x + 2y - 4 = 0
D. x^2 + y^2 - 4x - 2y + 4 = 0
Question 4
A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?
A. 17 days
B. 18 days
C. 19 days
D. 20 days
Question 5
Find the volume of the solid formed by revolving the region bounded by the curve y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. \frac{32}{3} \pi
B. \frac{64}{3} \pi
C. \frac{128}{3} \pi
D. \frac{256}{3} \pi
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. -1 < x < 3
B. x < -1 or x > 3
C. -3 < x < 1
D. x < -3 or x > 1
Question 7
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. 6x + 2
B. 6x - 2
C. 3x^2 + 2
D. 3x^2 - 2
Question 8
Find the derivative of the function ( f(x) = \sin (2x) ).
A. ( f'(x) = 2 \cos (2x) )
B. ( f'(x) = \cos (2x) )
C. ( f'(x) = 2 \sin (2x) )
D. ( f'(x) = \sin (2x) )
Question 9
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?
A. \( \frac{3}{8} \)
B. \( \frac{5}{8} \)
C. \( \frac{2}{5} \)
D. \( \frac{3}{5} \)
Question 10
Find the value of x in the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. 1
B. -2
C. -3
D. 4
Question 11
Solve the system of equations \( x + y = 4 \) and \( 2x - y = 3 \).
A. x = 1, y = 3
B. x = 2, y = 2
C. x = 3, y = 1
D. x = 4, y = 0
Question 12
The matrix \( A = egin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix} \) is multiplied by the matrix \( B = egin{bmatrix} 5 & 2 \ 1 & 3 \end{bmatrix} \). What is the value of the element in the first row and second column of the product matrix?
A. 17
B. 19
C. 21
D. 23
Question 13
Solve the equation \( 2^x + 2^{-x} = 10 \).
A. \( x = 2 \)
B. \( x = -2 \)
C. \( x = 3 \)
D. \( x = -3 \)
Question 14
Solve for x in the equation: \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 15
Find the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots \ \).
A. 2
B. 4
C. 8
D. 16

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