POST UTME NOUN 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the surface area of the sphere with radius 5 cm.
A. 100\pi
B. 50\pi
C. 200\pi
D. 250\pi
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, -3 \) ∪ (3, ∞)
Question 3
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 4
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 2197
B. 2187
C. 2177
D. 2167
Question 5
Solve the system of linear equations u\sing matrices: \begin{align*} x + y + z &= 6 \ 2x - y + 3z &= 7 \ -x + 2y - z &= -2 \end{align*}
A. \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}
B. \begin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}
D. \begin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}
Question 6
Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].
A. -3
B. 0
C. 3
D. 6
Question 7
A circle with center (1, 2) and radius 3 passes through the point (6, 6). Find the equation of the circle.
A. \( x - 1 \)^2 + \( y - 2 \)^2 = 9
B. \( x - 2 \)^2 + \( y - 1 \)^2 = 9
C. \( x - 1 \)^2 + \( y - 2 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 1 \)^2 = 16
Question 8
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi
B. 48\pi
C. 96\pi
D. 192\pi
Question 9
Solve the quadratic equation \[ x^2 + 4x + 4 = 0 \] u\sing the quadratic formula.
A. \begin{pmatrix} -2 \ -2 \end{pmatrix}
B. \begin{pmatrix} -1 \ -4 \end{pmatrix}
C. \begin{pmatrix} -2 \ -2 \end{pmatrix}
D. \begin{pmatrix} -1 \ -4 \end{pmatrix}
Question 10
Find the derivative of the function \[ f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} \] u\sing the quotient rule.
A. \frac{2x + 2}{\( x^2 - 4 \)^2}
B. \frac{2x^2 + 4x - 6}{\( x^2 - 4 \)^2}
C. \frac{2x + 2}{x^2 - 4}
D. \frac{2x^2 + 4x - 6}{x^2 - 4}
Question 11
Find the value of x in the equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} \).
A. 3
B. 4
C. 5
D. 6
Question 12
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 13
Solve the inequality 2x^2 + 5x - 3 > 0.
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -3 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 14
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. \frac{2x\( x^2 + 1 \) - 2x^2}{\( x^2 + 1 \)^2}
B. \frac{2x\( x^2 + 1 \) - 2x^2}{\( x^2 + 1 \)^2}
C. \frac{2x\( x^2 + 1 \) + 2x^2}{\( x^2 + 1 \)^2}
D. \frac{2x\( x^2 + 1 \) - 2x^2}{\( x^2 + 1 \)^2}
Question 15
Simplify the expression \( \frac{1}{2} \log_{10} \( x^2 \ \) - \frac{1}{3} \log_{10} \( x^3 \) ).
A. \log_{10} (x)
B. \log_{10} \( x^2 \)
C. \log_{10} \( x^3 \)
D. \log_{10} \( x^4 \)

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