POST UTME LASU 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A particle moves along the curve y = x^2 + 2x - 3. Find the equation of the \tangent line at the point where x = 1.
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 2
Solve for x in the equation \( 2^x + 2^{x+1} = 2^{x+2} + 1 \).
A. \( x = -1 \)
B. \( x = 0 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 3
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. \( -1 \)
D. ( 2 )
Question 4
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1, 2, 3
B. 1, 2, 4
C. 1, 3, 4
D. 2, 3, 4
Question 5
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{4} \)
B. \( \frac{pi}{2} \)
C. \( \frac{2pi}{3} \)
D. \( \frac{3pi}{4} \)
Question 6
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 7
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 8
Let X be a random variable with probability density function (pdf) given by f(x) = \( \frac{1}{2} e^{-|x|} \) for -\( infty < x < infty \). Find the probability that X lies between -1 and 1.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 9
Find the vector ( mathbf{v} ) such that \( mathbf{v} cdot mathbf{i} = 3 \) and \( mathbf{v} cdot mathbf{j} = 4 \).
A. \( mathbf{v} = 3mathbf{i} + 4mathbf{j} \)
B. \( mathbf{v} = 4mathbf{i} + 3mathbf{j} \)
C. \( mathbf{v} = 3mathbf{i} - 4mathbf{j} \)
D. \( mathbf{v} = 4mathbf{i} - 3mathbf{j} \)
Question 10
Find the area under the curve \( y = x^3 - 6x^2 + 9x + 2 \) from \( x = 0 \) to \( x = 2 \).
A. ( 4 )
B. ( 6 )
C. ( 8 )
D. ( 10 )
Question 11
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 12
Let A be a 2x2 matrix given by [A = egin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix}]. Find the determinant of A.
A. 1
B. 2
C. 3
D. 4
Question 13
A bakery sells 250 loaves of bread per day. If they make a profit of ₦2 per loaf, how much profit do they make in a day?
A. ₦500
B. ₦5000
C. ₦50000
D. ₦500000
Question 14
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. \( \frac{2}{3} \)
C. \( \frac{3}{4} \)
D. \( \frac{4}{5} \)
Question 15
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 5x - 3} ) u\sing the quotient rule.
A. \( \frac{-2x + 5}{\( 2x^2 + 5x - 3 \ \)^2} )
B. \( \frac{2x + 5}{\( 2x^2 + 5x - 3 \ \)^2} )
C. \( \frac{2x - 5}{\( 2x^2 + 5x - 3 \ \)^2} )
D. \( \frac{-2x - 5}{\( 2x^2 + 5x - 3 \ \)^2} )

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