POST UTME OSUSTECH 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix \begin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{pmatrix}.
A. 0
B. 1
C. 2
D. 3
Question 2
A circle with center ( C ) and radius ( r ) passes through the points ( A ) and ( B ). If \( CA = 5 \) and \( CB = 6 \), what is the value of ( r )?
A. 7
B. 5
C. 6
D. 4
Question 3
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
A. 2
B. -3
C. -2
D. 1
Question 4
Solve the system of linear equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).
A. \begin{cases} x = 2 \ y = 2 \end{cases}
B. \begin{cases} x = 3 \ y = 1 \end{cases}
C. \begin{cases} x = 1 \ y = 3 \end{cases}
D. \begin{cases} x = 4 \ y = 0 \end{cases}
Question 5
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 15
D. 20
Question 6
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.68
B. 0.84
C. 0.95
D. 0.99
Question 7
A car travels from city A to city B at an average speed of 60 km/h. On the return trip, the car travels at an average speed of 40 km/h. What is the average speed of the car for the entire trip?
A. 45 km/h
B. 50 km/h
C. 55 km/h
D. 60 km/h
Question 8
A polynomial function ( f(x) ) has zeros at \( x = -2 \) and \( x = 3 \). If \( f\( -1 \ \) = 4 ), what is the value of ( f(2) )?
A. 0
B. 2
C. 4
D. 6
Question 9
Find the volume of the solid formed by revolving the region bounded by the curves $y=x^2$ and $y=4x$ about the x-axis.
A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi
Question 10
Simplify the expression \( \frac{2^3 cdot 3^2}{2^2 cdot 3^4} \).
A. \( \frac{1}{3^2} \)
B. \( \frac{1}{3^4} \)
C. \( \frac{1}{2^2} \)
D. \( \frac{1}{2^4} \)
Question 11
Find the sum of the infinite geometric series \sum_{n=1}^\infty \frac{1}{2^n}.
A. 1
B. \frac{1}{2}
C. \frac{1}{3}
D. \frac{1}{4}
Question 12
Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 13
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{4} \)
B. \( \frac{pi}{2} \)
C. \( \frac{pi}{6} \)
D. \( \frac{pi}{8} \)
Question 14
Find the derivative of the function f(x) = \frac{1}{x^2 + 1}.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2x}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 15
Let ( f(x) = x^2 + 2x - 3 \). Find the equation of the \tangent line to the graph of \( f \ \) at the point where \( x = 1 \ \).
A. y = 2x - 1
B. y = 2x + 1
C. y = x + 1
D. y = x - 1

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