POST UTME NILE UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with center \( -2, 3 \) and radius 4.
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
Question 2
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 1 \)
Question 3
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. \frac{128\pi}{15}
B. \frac{64\pi}{15}
C. \frac{32\pi}{15}
D. \frac{16\pi}{15}
Question 4
Solve the inequality $\frac{x}{2} + 3 > 7$.
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 5
Let \( S = {1, 2, 3, 4, 5} \). Find the number of subsets of ( S ) that contain exactly two elements.
A. ( 10 )
B. ( 15 )
C. ( 20 )
D. ( 25 )
Question 6
Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.
A. 14
B. 14
C. 14
D. 14
Question 7
A sequence is defined by the formula $a_n = 2n + 1$. Find the sum of the first 5 terms.
A. 15
B. 20
C. 25
D. 30
Question 8
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. ( 15 )
B. ( 25 )
C. ( 35 )
D. ( 45 )
Question 9
A histogram of exam scores is shown. Find the mean score.
A. ( 60 )
B. ( 70 )
C. ( 80 )
D. ( 90 )
Question 10
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the unit vector in the direction of \( mathbf{a} + mathbf{b} \).
A. \( egin{pmatrix} 0.6 \ 0.8 \end{pmatrix} \)
B. \( egin{pmatrix} 0.4 \ 0.6 \end{pmatrix} \)
C. \( egin{pmatrix} 0.2 \ 0.3 \end{pmatrix} \)
D. \( egin{pmatrix} 0.8 \ 0.2 \end{pmatrix} \)
Question 11
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{64}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{16}{3} \)
D. \( \frac{8}{3} \)
Question 12
Solve the inequality \( \frac{x}{x-1} > 2 \) for \( x > 1 \).
A. \( x > 3 \)
B. \( x < 3 \)
C. \( x > 1 \) and \( x < 3 \)
D. \( x > 3 \) and \( x < 5 \)
Question 13
A quadratic equation is given by $x^2 + 4x + 4 = 0$. Solve for $x$.
A. -2
B. -1
C. 1
D. 2
Question 14
A rec\tangular solid has dimensions 3 cm, 4 cm, and 5 cm. What is the volume of the solid in cubic centimeters?
A. 60
B. 60
C. 60
D. 60
Question 15
A vector →A = 2→i + 3→j + 4→k is given. What is the magnitude of the vector?
A. 5
B. 5
C. 5
D. 5

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