POST UTME NOUN 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = 1 \)
D. \( x = 2, y = 2 \)
Question 2
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 3
Solve the trigonometric equation: \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = 90
C. x = 180
D. x = 270
Question 4
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 5
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4 \)
Question 6
A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even, the coin is flipped twice. Otherwise, the coin is flipped only once. What is the probability that the number of heads observed is odd?
A. 1/4
B. 1/2
C. 3/4
D. 2/3
Question 7
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 8
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 9
The mean of a set of 5 numbers is 10. If one of the numbers is 15, find the sum of the remaining 4 numbers.
A. 40
B. 50
C. 60
D. 70
Question 10
Find the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 12
B. 14
C. 16
D. 18
Question 11
Evaluate the definite integral \int_0^1 \frac{1}{x^2 + 1} dx.
A. \frac{1}{2} \ln(2)
B. \frac{1}{2} \ln\( 1 + \sqrt{2} \)
C. \frac{1}{2} \ln\( 1 - \sqrt{2} \)
D. \frac{1}{2} \ln\( 1 + \sqrt{2} \)
Question 12
Solve the equation \( 2^x + 2^{-x} = 10 \).
A. \( x = 2 \)
B. \( x = -2 \)
C. \( x = 3 \)
D. \( x = -3 \)
Question 13
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \) or \( x = -3 \)
D. \( x = 1 \) or \( x = 3 \)
Question 14
Find the volume of the frustum of a cone with height 6 cm, radius of the larger base 4 cm, and radius of the smaller base 2 cm.
A. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 \times 2 \times 4 \ \) )
B. \( \frac{1}{3} pi \( 4^2 + 2^2 - 4 \times 2 \times 4 \ \) )
C. \( \frac{1}{3} pi \( 4^2 + 2^2 + 2 \times 4 \times 2 \ \) )
D. \( \frac{1}{3} pi \( 4^2 + 2^2 - 2 \times 4 \times 2 \ \) )
Question 15
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

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