POST UTME BSU 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function \[f(x) = \frac{\log_2 \( x + 1 \)}{x^2 + 1}\].
A. \frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2}{\( x^2 + 1 \)^2}
C. \frac{2x + 2}{\( x^2 + 1 \)^2}
D. \frac{2x - 2}{\( x^2 + 1 \)^2}
Question 2
Solve the system of linear equations u\sing matrices: [ egin{array}{ccc|c} 2 & 1 & -1 & 3 \ 1 & -1 & 2 & 0 \ 3 & -2 & 1 & 5 \end{array} ]. Find the value of x.
A. 1
B. 2
C. 3
D. 4
Question 3
Solve the system of equations x + y = 4 and xy = 6.
A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (4, 0)
Question 4
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 3 \)^2 + \( y + 2 \)^2 = 16
Question 5
Determine the value of $\frac{d}{dx} \left\( \frac{1}{x^2} \right \)$ u\sing the quotient rule.
A. \frac{2}{x^3}
B. -\frac{2}{x^3}
C. \frac{1}{x^3}
D. -\frac{1}{x^3}
Question 6
Find the mean of the data set: ( 2, 4, 6, 8, 10 ).
A. 4
B. 6
C. 8
D. 10
Question 7
A circle with center $C$ and radius $r$ is shown below. If the area of the circle is $\pi r^2$, what is the value of $r$?
A. 2
B. 4
C. 6
D. 8
Question 8
Solve the equation $\sin^2 x + \cos^2 x = 1$ for $x$.
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{3\pi}{4}
Question 9
A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, with the heights of the bars being 8, 12, 15, 10, and 5. What is the mean score of the class?
A. 10
B. 12
C. 15
D. 18
Question 10
Solve the matrix equation \[\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix}\].
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 11
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. \frac{32\pi}{3}
B. \frac{64\pi}{3}
C. \frac{128\pi}{3}
D. \frac{256\pi}{3}
Question 12
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 10 \) and \( mathbf{a} cdot mathbf{c} = 5 \), where \( mathbf{b} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{c} = egin{pmatrix} 1 \ 4 \end{pmatrix} \).
A. \( egin{pmatrix} 5 \ 2 \end{pmatrix} \)
B. \( egin{pmatrix} 2 \ 5 \end{pmatrix} \)
C. \( egin{pmatrix} 3 \ 4 \end{pmatrix} \)
D. \( egin{pmatrix} 4 \ 3 \end{pmatrix} \)
Question 13
A quadratic equation is given by: [ x^2 + 4x + 4 = 0 ]. Find the value of x.
A. -2
B. -1
C. 1
D. 2
Question 14
Solve the equation $\log_2 \( x^2 \) = 4$ for $x$.
A. 2
B. 4
C. 8
D. 16
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 42
C. 44
D. 46

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