POST UTME LAUTECH 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a quadratic equation of the form \( ax^2 + bx + c = 0 \), if the sum of the roots is 6 and the product of the roots is 12, find the value of ( a ) if \( b = 3 \).
A. -2
B. 2
C. 4
D. 6
Question 2
A curve is defined by the equation \( y = \frac{2x^2 - 3x + 1}{x^2 - 4x + 3} \). Find the derivative of the curve at the point where \( x = 1 \).
A. -1
B. 1
C. 2
D. 3
Question 3
Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).
A. x = -10
B. x = 2
C. x = -6
D. x = 6
Question 4
A polynomial function is defined by the equation ( f(x) = x^3 - 2x^2 + 3x - 1 ). Find the value of \( f\( -2 \ \) ).
A. -11
B. -9
C. -7
D. -5
Question 5
A vector ( vec{a} ) has components \( a_x = 2 \) and \( a_y = 3 \). Find the magnitude of the vector.
A. 5
B. 10
C. 15
D. 20
Question 6
A quadratic equation is defined by the equation \( x^2 + 4x + 4 = 0 \). Find the roots of the equation.
A. -2
B. -1
C. 1
D. 2
Question 7
Find the area under the curve \[ y = \frac{1}{x^2 + 1} \] from \[ x = 0 \] to \[ x = 1. \]
A. \frac{1}{2} \ln 2
B. \frac{1}{2} \ln 1
C. \frac{1}{2} \ln 3
D. \frac{1}{2} \ln 4
Question 8
Solve the inequality \[ 2x^2 + 5x - 3 \geq 0. \]
A. x \in \left[ -3, \frac{1}{2} \right]
B. x \in \left[ -3, \infty \right]
C. x \in \left[ -3, 0 \right]
D. x \in \left[ 0, \frac{1}{2} \right]
Question 9
A histogram of exam scores is shown below. If the mean score is 60, find the value of k.
A. 20
B. 30
C. 40
D. 50
Question 10
A random variable X has a probability distribution given by \[ P(X) = \begin{cases} 0.2 & \text{if } X = 1, \\ 0.3 & \text{if } X = 2, \\ 0.5 & \text{if } X = 3. \end{cases} \] Find the expected value of X.
A. 1
B. 2
C. 3
D. 4
Question 11
In the diagram below, a right-angled triangle has a hypotenuse of length 10 cm. If the ratio of the lengths of the two legs is 3:4, find the area of the triangle.
A. 24
B. 30
C. 40
D. 50
Question 12
A circle with center ( C(2, 3) ) and radius 4 passes through the point ( P(6, 7) ). Find the equation of the circle.
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 36 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 49 )
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3
B. x < 1 or x > 3
C. x < -1 or x < 3
D. x > 1 or x < 3
Question 14
A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 6m, find the volume of water in the \tank in cubic meters.
A. 120π
B. 240π
C. 360π
D. 480π
Question 15
Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} x = 2 \).
A. 4
B. 2
C. 6
D. 8

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