FTCE Mathematics 4 — Questions and Answers
Question 1: A teacher graphs y = 2sin(3x). Compared to y = sin(x), what changes are made?
- Amplitude doubles, period triples
- Amplitude doubles, period is one-third as long (Correct answer)
- Amplitude is halved, period triples
- Amplitude triples, period doubles
Correct answer: Amplitude doubles, period is one-third as long
The coefficient 2 doubles the amplitude to 2, while the coefficient 3 compresses the period to 2π/3.
Question 2: Which expression is equivalent to (2/3)⁻²?
- 4/9
- 9/4 (Correct answer)
- -4/9
- −9/4
Correct answer: 9/4
A negative exponent means take the reciprocal: (2/3)⁻² = (3/2)² = 9/4.
Question 3: Two lines are represented by y = 2x + 1 and y = -½x + 4. Which statement is true about these lines?
- They are parallel
- They are perpendicular (Correct answer)
- They are the same line
- They have the same y-intercept
Correct answer: They are perpendicular
Their slopes are 2 and -½; since 2 × (-½) = -1, the lines are perpendicular.
Question 4: A box contains 4 red, 3 blue, and 5 green marbles. If one marble is selected at random, what is the probability it is NOT green?
- 5/12
- 7/12 (Correct answer)
- 1/2
- 5/7
Correct answer: 7/12
There are 12 marbles total and 7 non-green (4 red + 3 blue), so P(not green) = 7/12.
Question 5: When solving 3(x - 4) = 2x + 5, a student distributes first and gets 3x - 12 = 2x + 5. What is x?
- 7
- 17 (Correct answer)
- 1
- -7
Correct answer: 17
Subtracting 2x from both sides gives x - 12 = 5, so x = 17.
Question 6: Which of the following is the correct description of a function that is one-to-one?
- Every x-value maps to the same y-value
- Every y-value corresponds to exactly one x-value (Correct answer)
- The domain equals the range
- The graph passes the vertical line test
Correct answer: Every y-value corresponds to exactly one x-value
A one-to-one function means each output value is produced by exactly one input value, which it passes the horizontal line test.
Question 7: A school surveys 200 students: 120 prefer math and 90 prefer science. If 40 prefer both, how many prefer neither?
- 10
- 30 (Correct answer)
- 50
- 70
Correct answer: 30
By inclusion-exclusion: |Math ∪ Science| = 120+90-40 = 170; those preferring neither = 200-170 = 30.
FTCE Mathematics 4
A teacher graphs y = 2sin(3x).
Compared to y = sin(x), what changes are made?