POST UTME LASU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes a value between 0.5 and 1.
A. \frac{1}{2}
B. \frac{3}{4}
C. \frac{7}{8}
D. \frac{5}{6}
Question 2
Find the value of \( \log_{10} \( 1000 \ \) ).
A. 3
B. 4
C. 5
D. 6
Question 3
Find the equation of the \tangent to the curve y = x^2 at the point where x = 2.
A. y = 4x - 4
B. y = 4x + 4
C. y = 2x - 2
D. y = 2x + 2
Question 4
Solve the system of equations \( egin{cases} x + y = 2 \ x - y = 1 \end{cases} \) u\sing substitution.
A. \( x = 1, y = 1 \)
B. \( x = 1, y = 3 \)
C. \( x = 3, y = 1 \)
D. \( x = 3, y = 3 \)
Question 5
Solve the inequality \( x^2 - 4x + 3 > 0 \).
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 6
A quadratic equation has roots at x = 2 and x = -3. Write the equation in factored form.
A. \( x - 2 \)\( x + 3 \)
B. \( x + 2 \)\( x - 3 \)
C. \( x - 3 \)\( x + 2 \)
D. \( x + 3 \)\( x - 2 \)
Question 7
A set of 5 consecutive integers has a median of 8. What is the sum of the integers?
A. 120
B. 125
C. 130
D. 135
Question 8
Find the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).
A. \( \frac{pi}{4} \)
B. \( \frac{3pi}{4} \)
C. \( \frac{5pi}{4} \)
D. \( \frac{7pi}{4} \)
Question 9
A vector \overrightarrow{a} has magnitude 5 and direction 60^\circ. Find the vector \overrightarrow{b} such that \overrightarrow{a} \cdot \overrightarrow{b} = 10.
A. \overrightarrow{b} = \left< \frac{5}{2}, \frac{5\sqrt{3}}{2} \right>
B. \overrightarrow{b} = \left< \frac{5\sqrt{3}}{2}, \frac{5}{2} \right>
C. \overrightarrow{b} = \left< \frac{5}{2}, -\frac{5\sqrt{3}}{2} \right>
D. \overrightarrow{b} = \left< -\frac{5}{2}, \frac{5\sqrt{3}}{2} \right>
Question 10
Solve for x: 2^x + 3^x = 5^x.
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 11
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{3} \)
D. \( \frac{pi}{6} \)
Question 12
Determine the sum of the infinite geometric series with first term \( a = \frac{1}{2} \) and common ratio \( r = \frac{1}{3} \).
A. \( \frac{1}{2} \)
B. \( \frac{1}{3} \)
C. \( \frac{3}{4} \)
D. \( \frac{2}{3} \)
Question 13
Evaluate the definite integral \( int_{0}^{1} x^2 , dx \).
A. \( \frac{1}{3} \)
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)
D. \( \frac{1}{4} \)
Question 14
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. \( x = -2 \)
B. \( x = -3 \)
C. \( x = 2 \)
D. \( x = 3 \)
Question 15
Find the mean and s\tandard deviation of the data set: ( { 2, 4, 6, 8, 10 } ).
A. Mean: 6, S\tandard Deviation: 2
B. Mean: 6, S\tandard Deviation: 4
C. Mean: 6, S\tandard Deviation: 6
D. Mean: 6, S\tandard Deviation: 8

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