POST UTME NOUN 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, -3 \) ∪ (3, ∞)
Question 3
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 4
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 5
Solve the inequality 2x^2 + 5x - 3 > 0.
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -3 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 6
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 7
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 8
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 9
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} \( x^4 \)
Question 10
Find the surface area of the sphere with radius 5 cm.
A. 100\pi
B. 50\pi
C. 200\pi
D. 250\pi
Question 11
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 12
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 13
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 14
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 15
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}

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