B.L.A.; occasionally A.L.B. Bachelor of Liberal Arts Bachelor of Liberal Arts For Math 3 — Questions and Answers
Question 1: A bag contains 4 red, 3 blue, and 5 green marbles. What is the probability of drawing a blue marble?
- 1/4
- 3/12 (Correct answer)
- 3/11
- 1/3
Correct answer: 3/12
There are 3 blue marbles out of 4+3+5=12 total, so P(blue) = 3/12 = 1/4.
Question 2: What is the solution to the system: 2x + y = 7 and x - y = 2?
- x=3, y=1 (Correct answer)
- x=1, y=5
- x=2, y=3
- x=4, y=-1
Correct answer: x=3, y=1
Adding the equations gives 3x = 9, so x = 3; substituting back gives y = 1.
Question 3: Which of the following best describes an irrational number?
- A number that can be written as p/q where p and q are integers and q≠0
- A negative integer
- A number whose decimal expansion is non-terminating and non-repeating (Correct answer)
- A whole number that is not prime
Correct answer: A number whose decimal expansion is non-terminating and non-repeating
Irrational numbers have decimal expansions that neither terminate nor repeat, such as √2 or π.
Question 4: What is the area of a circle with diameter 10?
- 10π
- 25π (Correct answer)
- 100π
- 50π
Correct answer: 25π
Radius = 5, so Area = πr² = π(5²) = 25π.
Question 5: If f(x) = 2x + 1, what is f⁻¹(x)?
- (x - 1)/2 (Correct answer)
- 2x - 1
- x/2 + 1
- (x + 1)/2
Correct answer: (x - 1)/2
Swap x and y: x = 2y + 1, then solve for y: y = (x - 1)/2.
Question 6: What is the greatest common divisor (GCD) of 48 and 36?
- 6
- 9
- 12 (Correct answer)
- 18
Correct answer: 12
The prime factorizations are 48 = 2⁴×3 and 36 = 2²×3², so GCD = 2²×3 = 12.
Question 7: What is the value of the expression 4! + 3!?
- 30 (Correct answer)
- 30
- 30
- 30
Correct answer: 30
4! = 24 and 3! = 6, so 4! + 3! = 30.
B.L.A.; occasionally A.L.B. Bachelor of Liberal Arts Bachelor of Liberal Arts For Math 3
A bag contains 4 red, 3 blue, and 5 green marbles.
What is the probability of drawing a blue marble?