POST UTME LASU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle pas\sing through the points (2,3), (4,5), and \( -1,2 \).
A. \( x^2 + y^2 + 6x - 4y - 12 = 0 \)
B. \( x^2 + y^2 - 6x + 4y - 12 = 0 \)
C. \( x^2 + y^2 + 6x + 4y - 12 = 0 \)
D. \( x^2 + y^2 - 6x - 4y - 12 = 0 \)
Question 2
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \).
A. -2
B. 2
C. 4
D. 6
Question 3
Solve for x in the equation \( \frac{x}{2} + 3 = 7 \).
A. 4
B. 6
C. 8
D. 10
Question 4
Solve the matrix equation $\begin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 4 \end{pmatrix}$.
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 1, y = 1
D. x = 2, y = 2
Question 5
A right-angled triangle has a hypotenuse of length 10cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. ( 5cm )
B. ( 7.5cm )
C. ( 10cm )
D. ( 12.5cm )
Question 6
Find the value of $\overrightarrow{a} \cdot \overrightarrow{b}$ if $\overrightarrow{a} = \begin{pmatrix} 2 \ 3 \ -1 \end{pmatrix}$ and $\overrightarrow{b} = \begin{pmatrix} 1 \ -2 \ 4 \end{pmatrix}$.
A. 13
B. 15
C. 17
D. 19
Question 7
Find the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \).
A. ( ln(2) - ln(1) )
B. ( ln(2) + ln(1) )
C. ( ln(1) - ln(2) )
D. ( ln(1) + ln(2) )
Question 8
Find the volume of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = 4 \) about the x-axis.
A. \( \frac{32}{3} pi \)
B. \( \frac{64}{3} pi \)
C. \( \frac{128}{3} pi \)
D. \( \frac{256}{3} pi \)
Question 9
Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).
A. \( x^2 + y^2 + 2gx + 2fy + c = 0 \)
B. \( x^2 + y^2 + 2gx - 2fy + c = 0 \)
C. \( x^2 + y^2 - 2gx + 2fy + c = 0 \)
D. \( x^2 + y^2 - 2gx - 2fy + c = 0 \)
Question 10
Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 12
B. 14
C. 16
D. 18
Question 11
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the quotient 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 12
In a circle with center O and radius 6, chord AB is 8 units long. If point P is the midpoint of AB, find the area of triangle OAP.
A. 12\sqrt{3}
B. 16\sqrt{3}
C. 20\sqrt{3}
D. 24\sqrt{3}
Question 13
A rec\tangular block measures 5cm by 3cm by 2cm. Find the volume of the block.
A. 30cm^3
B. 60cm^3
C. 90cm^3
D. 120cm^3
Question 14
A histogram is constructed with the following data: 2, 4, 6, 8, 10. What is the class width?
A. 2
B. 4
C. 6
D. 8
Question 15
Let $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$. Find the inverse of $A$.
A. \begin{bmatrix} 4 & -2 \\ -3 & 1 \end{bmatrix}
B. \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}
C. \begin{bmatrix} 2 & -1 \\ -3 & 1 \end{bmatrix}
D. \begin{bmatrix} 1 & -2 \\ 3 & -4 \end{bmatrix}

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