POST UTME LAUTECH 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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. 1.5
B. 2
C. 2.5
D. 3
Question 2
A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has 10 bars, find the sum of the products of the heights of the bars and their respective midpoints.
A. 2500
B. 3000
C. 3500
D. 4000
Question 3
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 6 \) and \( mathbf{a} cdot mathbf{c} = 3 \), given that \( mathbf{b} = 2mathbf{i} + 3mathbf{j} \) and \( mathbf{c} = mathbf{i} - 2mathbf{j} \).
A. 3mathbf{i} + 2mathbf{j}
B. 2mathbf{i} + 3mathbf{j}
C. 4mathbf{i} + mathbf{j}
D. 5mathbf{i} - 2mathbf{j}
Question 4
A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 3. If a_1 = 2, find the sum of the first 5 terms of the sequence.
A. 2 + 7 + 17 + 37 + 79
B. 2 + 5 + 13 + 29 + 61
C. 2 + 7 + 15 + 31 + 63
D. 2 + 5 + 13 + 27 + 55
Question 5
A rec\tangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. What is the volume of the prism?
A. 120 cm^3
B. 160 cm^3
C. 200 cm^3
D. 240 cm^3
Question 6
A rec\tangular garden measures 15 meters by 8 meters. If a path that is 2 meters wide is built around the garden, what is the area of the path?
A. 40
B. 50
C. 60
D. 70
Question 7
Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, ... ).
A. 62
B. 64
C. 66
D. 68
Question 8
Determine the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 60\pi cm^3
D. 72\pi cm^3
Question 9
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 10
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 = 4
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
Question 11
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) in the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ).
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 12
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?
A. \frac{2}{3}
B. \frac{3}{4}
C. \frac{4}{5}
D. \frac{5}{6}
Question 13
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. What is the length of the other leg?
A. 8 cm
B. 6 cm
C. 10 cm
D. 12 cm
Question 14
A circle has a radius of 4cm. If a chord is drawn from the center of the circle to a point on the circumference, find the length of the chord.
A. 8cm
B. 6cm
C. 4cm
D. 2cm
Question 15
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
A. 0
B. -2
C. 2
D. -4

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