POST UTME LASU 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Given that \( \tan \theta = \frac{1}{3} \), find the value of \( \sin \theta \cos \theta \) u\sing the identity \( \tan \theta = \frac{\sin \theta}{\cos \theta} \).
A. 1/6
B. 1/2
C. 2/3
D. 3/4
Question 2
Find the sum of the first 10 terms of the geometric progression with first term 2 and common ratio 3.
A. 59049
B. 59048
C. 59050
D. 59051
Question 3
Solve the system of equations: \[ \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*} \].
A. \[ x = 3, y = 1 \]
B. \[ x = 1, y = 3 \]
C. \[ x = 2, y = 2 \]
D. \[ x = 4, y = 0 \]
Question 4
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).
A. \left\( -\infty, -1 \right] \cup \left[ 3, \infty \right \)
B. \left\( -\infty, -3 \right] \cup \left[ 1, \infty \right \)
C. \left\( -\infty, -3 \right] \cup \left[ 1, \infty \right \)
D. \left\( -\infty, -1 \right] \cup \left[ 3, \infty \right \)
Question 5
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. 0.25
B. 0.5
C. 0.75
D. 1
Question 6
Find the value of ( mathbf{a} cdot mathbf{b} ) if \( mathbf{a} = egin{pmatrix} 2 \ 3 \ -1 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \ 4 \end{pmatrix} \).
A. 10
B. -10
C. 5
D. -5
Question 7
Solve for x in the equation \( \log_{2} \( x^2 \) = 4 \).
A. 4
B. 8
C. 16
D. 32
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. x < -1 or x > 3/2
B. x < 1 or x > -3/2
C. x < -3/2 or x > 1
D. x < 3/2 or x > -1
Question 9
Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.
A. 121
B. 143
C. 165
D. 187
Question 10
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 8
C. 10
D. 12
Question 11
In the diagram below, ( overrightarrow{AB} ) and ( overrightarrow{AC} ) are two vectors with magnitudes 5 and 7 respectively. If ( overrightarrow{AB} ) is perp\endicular to ( overrightarrow{AC} ), find the magnitude of \( overrightarrow{AB} + overrightarrow{AC} \).
A. 8
B. 10
C. 12
D. 14
Question 12
Solve the equation \( x^2 + 2x - 6 = 0 \) u\sing the quadratic formula.
A. \( x = -3 \ \) or \( x = 2 \ \)
B. \( x = -2 \ \) or \( x = 3 \ \)
C. \( x = -1 \ \) or \( x = 6 \ \)
D. \( x = 1 \ \) or \( x = -6 \ \)
Question 13
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} \) u\sing the chain rule.
A. \( -\frac{2x}{\( x^2 + 1 \ \)^2} \)
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} \)
C. \( -\frac{2}{\( x^2 + 1 \ \)^2} \)
D. \( \frac{2}{\( x^2 + 1 \ \)^2} \)
Question 14
Solve for x in the equation \[ \log_{10} \( x^2 \) = 4 \].
A. 10^4
B. 10^8
C. 10^12
D. 10^16
Question 15
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing integration.
A. 64
B. 32
C. 16
D. 8

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