POST UTME UNIPORT 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $\tan \frac{\pi}{4}$.
A. 1
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{3}{2}
Question 2
Solve the system of equations: \begin{align*} x + y + z &= 3 \ 2x + 2y + 2z &= 6 \ x + 2y + 4z &= 7 \end{align*}
A. x = 1, y = 1, z = 1
B. x = 2, y = 1, z = 1
C. x = 1, y = 2, z = 1
D. x = 1, y = 1, z = 2
Question 3
Solve the equation 2x + 5y = 11, where x and y are vectors.
A. x = 2, y = 1
B. x = 3, y = 2
C. x = 4, y = 3
D. x = 5, y = 4
Question 4
Determine the value of x in the equation \( \frac{1}{2}x + 5 = 11 \) in base 8.
A. 6
B. 7
C. 8
D. 9
Question 5
Solve the equation \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 6
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 7
Solve the equation $x^3 + 2x^2 - 5x - 6 = 0$.
A. x = -1
B. x = 2
C. x = -2
D. x = 3
Question 8
In a triangle $ABC$, if $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$, find $\tan C$.
A. \frac{11}{7}
B. \frac{7}{11}
C. \frac{5}{3}
D. \frac{3}{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. \( x < -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x < \frac{3}{2} \)
Question 10
Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.
A. \frac{4}{3}
B. \frac{2}{3}
C. \frac{1}{3}
D. \frac{1}{2}
Question 11
Express the number 456 in base 8.
A. 720
B. 721
C. 722
D. 723
Question 12
A histogram of exam scores is shown below. What is the mean score of the exam?
A. 60
B. 70
C. 80
D. 90
Question 13
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 10 \) and \( mathbf{a} cdot mathbf{c} = 5 \), where \( mathbf{b} = egin{bmatrix} 2 \ 3 \end{bmatrix} \) and \( mathbf{c} = egin{bmatrix} 1 \ 4 \end{bmatrix} \).
A. \( egin{bmatrix} 5 \ 2 \end{bmatrix} \)
B. \( egin{bmatrix} 2 \ 5 \end{bmatrix} \)
C. \( egin{bmatrix} 3 \ 4 \end{bmatrix} \)
D. \( egin{bmatrix} 4 \ 3 \end{bmatrix} \)
Question 14
Solve for x in the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )

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