POST UTME LAUTECH 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
If f(x) = 2x^2 + 3x - 1, find f'(x).
A. 4x + 3
B. 2x^2 + 3
C. 2x + 3
D. 4x - 3
Question 2
Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.
A. 62
B. 63
C. 64
D. 65
Question 3
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 4
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).
A. \( -∞, -2 \) ∪ (2, ∞)
B. \( -∞, -2 \) ∪ \( -2, 2 \) ∪ (2, ∞)
C. \( -∞, -2 \) ∩ (2, ∞)
D. \( -∞, 2 \) ∪ (2, ∞)
Question 5
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing the definite integral.
A. \( \frac{64}{3} \)
B. \( \frac{128}{3} \)
C. \( \frac{256}{3} \)
D. \( \frac{512}{3} \)
Question 6
Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).
A. \( \frac{1}{2} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{5} \)
Question 7
Find the sum of the first 5 terms of the geometric series 2, 6, 18, ...
A. 62
B. 64
C. 66
D. 68
Question 8
Solve the system of equations u\sing matrices: \begin{align*} x + y + z &= 6 \ 2x + 3y + z &= 11 \ x + 2y + 3z &= 7 \end{align*}
A. \begin{pmatrix} x \ y \ z \end{pmatrix} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}
B. \begin{pmatrix} x \ y \ z \end{pmatrix} = \begin{pmatrix} 2 \ 1 \ 3 \end{pmatrix}
C. \begin{pmatrix} x \ y \ z \end{pmatrix} = \begin{pmatrix} 3 \ 2 \ 1 \end{pmatrix}
D. \begin{pmatrix} x \ y \ z \end{pmatrix} = \begin{pmatrix} 1 \ 3 \ 2 \end{pmatrix}
Question 9
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} )
Question 10
In the diagram below, identify the part labeled A.
A. Beaker
B. Burette
C. Test Tube
D. Cell
Question 11
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. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
Question 12
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. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 13
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^2 \)
B. \( x = 10^4 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)
Question 14
A histogram of exam scores is shown. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 15
Find the area under the curve y = x^2 + 2x + 1 from x = 0 to x = 3.
A. 27
B. 30
C. 33
D. 36

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