POST UTME LASU 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of \( \sin \( 2x \ \) ) given that \( \sin x = \frac{3}{5} \) and \( \cos x = \frac{4}{5} \).
A. \frac{24}{25}
B. \frac{16}{25}
C. \frac{12}{25}
D. \frac{8}{25}
Question 2
Solve the inequality $|x - 2| > 3$.
A. \( -\infty, -1 \) \cup \( 4, \infty \)
B. \( -\infty, 1 \) \cup \( 4, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( 2, \infty \)
Question 3
Determine the value of $\frac{1}{2} \int_{0}^{\pi} \sin^2 x \, dx$.
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. 1
Question 4
A binary operation $\oplus$ is defined by $a \oplus b = a^2 + b^2$. Find $2 \oplus 3$.
A. 13
B. 14
C. 15
D. 16
Question 5
Find the area under the curve \( y = x^3 - 6x^2 + 9x + 2 \) from \( x = 0 \) to \( x = 2 \).
A. 14
B. 16
C. 18
D. 20
Question 6
A histogram of exam scores for a class of 50 students is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 7
Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.
A. \( \frac{1}{3} pi \( 6^2 + 4^2 + 6 cdot 4 \ \) \times 10 )
B. \( \frac{1}{3} pi \( 6^2 + 4^2 - 6 cdot 4 \ \) \times 10 )
C. \( \frac{1}{3} pi \( 6^2 + 4^2 + 6 cdot 4 \ \) \times 5 )
D. \( \frac{1}{3} pi \( 6^2 + 4^2 - 6 cdot 4 \ \) \times 5 )
Question 8
Solve the equation \( 2^x + 3^x = 5^x \ \) for \( x \ \).
A. 1
B. 2
C. 3
D. 4
Question 9
Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. \( \sin\( x \ \) = 1 )
B. \( \cos\( x \ \) = 1 )
C. \( \sin\( x \ \) = \cos(x) )
D. \( \sin\( x \ \) = -\cos(x) )
Question 10
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. ( f'(x) = 6x + 2 )
B. ( f'(x) = 6x - 2 )
C. ( f'(x) = 3x^2 + 2 )
D. ( f'(x) = 3x^2 - 2 )
Question 11
Let ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ). Find the value of \( f\( -2 \ \) ) u\sing the given function.
A. \frac{1}{3}
B. -\frac{1}{3}
C. \frac{1}{2}
D. -\frac{1}{2}
Question 12
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} ].
A. -2
B. 4
C. 6
D. 8
Question 13
A sequence is defined as: 2, 6, 12, 20, ... . Find the next term in the sequence.
A. 30
B. 32
C. 34
D. 36
Question 14
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 15
Find 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

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