POST UTME UNIOSUN 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations u\sing matrices: \[ \begin{array}{cc|c} 2x + 3y & = & 7 \ 4x - 2y & = & -3 \ \end{array} \]
A. \[ \begin{array}{c} x = 1 \ y = 2 \ \end{array} \]
B. \[ \begin{array}{c} x = 2 \ y = 1 \ \end{array} \]
C. \[ \begin{array}{c} x = 3 \ y = 4 \ \end{array} \]
D. \[ \begin{array}{c} x = 4 \ y = 3 \ \end{array} \]
Question 2
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 3
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 2040
B. 2050
C. 2060
D. 2070
Question 4
Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2 and the line y = 4 about the x-axis.
A. \boxed{\frac{32\pi}{3}}
B. \frac{16\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 5
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing integration.
A. 64
B. 32
C. 16
D. 8
Question 6
Find the determinant of the matrix \begin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{pmatrix} u\sing cofactor expansion.
A. 0
B. 1
C. -1
D. 2
Question 7
Find the equation of the circle with center at \( -2, 3 \) and radius 4.
A. \boxed{\( x + 2 \)^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 8
Solve for x in the equation 2^x + 3^x = 5^x.
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > 1 \)
C. \( x < -\frac{1}{2} \) or \( x > 3 \)
D. \( x < 1 \) or \( x > -3 \)
Question 10
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 12 \) and \( mathbf{a} cdot mathbf{c} = 20 \), where \( mathbf{b} = egin{bmatrix} 2 \ 3 \end{bmatrix} \) and \( mathbf{c} = egin{bmatrix} 4 \ 5 \end{bmatrix} \).
A. \( egin{bmatrix} 6 \ 4 \end{bmatrix} \)
B. \( egin{bmatrix} 4 \ 6 \end{bmatrix} \)
C. \( egin{bmatrix} 8 \ 6 \end{bmatrix} \)
D. \( egin{bmatrix} 6 \ 8 \end{bmatrix} \)
Question 11
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 12
If \( A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \), find \( AB \).
A. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}
B. \begin{bmatrix} 23 & 26 \ 47 & 54 \end{bmatrix}
C. \begin{bmatrix} 27 & 30 \ 51 & 58 \end{bmatrix}
D. \begin{bmatrix} 31 & 34 \ 55 & 62 \end{bmatrix}
Question 13
If \( y = \frac{1}{x^2 + 1} \) and \( x = \frac{1}{t^2 + 1} \), find \( \frac{dy}{dt} \) when \( t = 1 \).
A. 0
B. \frac{1}{2}
C. \frac{1}{4}
D. \frac{1}{6}
Question 14
Convert the decimal number 0.75 to a \fraction in its simplest form.
A. 3/4
B. 1/2
C. 3/8
D. 1/4
Question 15
Simplify the expression \( \sqrt{48} \ \)
A. 4\sqrt{3}
B. 6\sqrt{2}
C. 8\sqrt{3}
D. 12\sqrt{2}

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