POST UTME LASU 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A curve is defined by the equation \( y = \frac{1}{x^2 + 1} \). Find the equation of the \tangent line to the curve at the point \( 1, \frac{1}{2} \ \)).
A. y = x - 1
B. y = x + 1
C. y = -x + 1
D. y = x - 2
Question 2
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 3
Find the value of \( \overrightarrow{a} \cdot \overrightarrow{b} \ \) given that \( \overrightarrow{a} = \begin{pmatrix} 2 \ 3 \ 1 \end{pmatrix} \ \) and \( \overrightarrow{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \ \).
A. 13
B. 14
C. 15
D. 16
Question 4
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = -1, 1 \ \). Find the probability that \( X \ \) is greater than 0.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. 1
Question 5
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 6
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 7
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \) u\sing the formula \( S = \frac{a}{1 - r} \), where (a) is the first term and (r) is the common ratio.
A. 1
B. 2
C. 3
D. 4
Question 8
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 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
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \frac{1}{2}
B. \frac{2}{5}
C. \frac{3}{8}
D. \frac{4}{9}
Question 11
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 12
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 13
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 14
Solve the equation \( 2^x + 3^x = 5^x \ \) for \( x \ \).
A. 1
B. 2
C. 3
D. 4
Question 15
Find the determinant of the following 3x3 matrix: \\[1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\].
A. 0
B. 1
C. -1
D. 2

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