POST UTME LASU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
Find the derivative of the function ( f(x) = \sin^2(x) ) u\sing the chain rule.
A. \( 2\sin\( x \)\cos(x \) )
B. \( 2\cos\( x \ \) )
C. \( 2\sin\( x \ \) )
D. \( 2\sin\( x \)\cos(x \) + \sin^2(x) )
Question 4
A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the die shows an even number and the coin lands heads up, what is the probability that the die shows a 4?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{1}{2}
D. \frac{2}{3}
Question 5
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 6
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 7
Let $A = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}$. Find the determinant of $A^2$.
A. 0
B. 1
C. 4
D. 9
Question 8
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the factor theorem.
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 4 \)
Question 9
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 10
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )
Question 11
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 12
A rec\tangular water \tank with a length of 4m, a width of 3m, and a height of 2m is filled with water. Find the volume of water in the \tank.
A. \( 24m^3 \)
B. \( 36m^3 \)
C. \( 48m^3 \)
D. \( 60m^3 \)
Question 13
Solve the equation \( 2^x + 2^{-x} = 10 \).
A. \( x = 2 \)
B. \( x = -2 \)
C. \( x = \log_2\( 5 \ \) )
D. \( x = -\log_2\( 5 \ \) )
Question 14
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 15
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}

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