FTCE Mathematics 2 — Questions and Answers
Question 1: A student simplifies the expression (3x²y)(4xy³) and gets 12x³y⁴. Which property justifies combining the exponents?
- Distributive property
- Product of powers property (Correct answer)
- Power of a power property
- Quotient of powers property
Correct answer: Product of powers property
The product of powers property states that when multiplying like bases, you add the exponents (x² · x = x³ and y · y³ = y⁴).
Question 2: A teacher wants students to understand that √(a²+b²) ≠ a+b. Which counterexample best demonstrates this?
- a=1, b=0
- a=3, b=4 (Correct answer)
- a=0, b=0
- a=2, b=2
Correct answer: a=3, b=4
With a=3 and b=4: √(9+16)=√25=5, but 3+4=7, clearly showing 5≠7.
Question 3: Which of the following best describes the graph of f(x) = -2|x - 3| + 4?
- V-shaped, opens upward, vertex at (3,4)
- V-shaped, opens downward, vertex at (3,4) (Correct answer)
- V-shaped, opens upward, vertex at (-3,4)
- V-shaped, opens downward, vertex at (-3,-4)
Correct answer: V-shaped, opens downward, vertex at (3,4)
The negative coefficient makes the absolute value graph open downward, and the vertex is at (h,k)=(3,4).
Question 4: A rectangular garden has a perimeter of 54 feet and an area of 180 square feet. What are the dimensions?
- 12 ft × 15 ft (Correct answer)
- 10 ft × 18 ft
- 9 ft × 20 ft
- 6 ft × 30 ft
Correct answer: 12 ft × 15 ft
Setting up 2(l+w)=54 and l·w=180 gives l+w=27; solving the system yields l=12 and w=15.
Question 5: What is the sum of the interior angles of a regular hexagon?
- 540°
- 720° (Correct answer)
- 900°
- 1080°
Correct answer: 720°
Using the formula (n-2)×180° with n=6 gives (6-2)×180°=4×180°=720°.
Question 6: A data set has a mean of 50 and a standard deviation of 5. Approximately what percentage of values fall between 40 and 60?
- 68%
- 95% (Correct answer)
- 99.7%
- 75%
Correct answer: 95%
The range 40–60 spans 2 standard deviations on each side of the mean, so approximately 95% by the empirical rule.
Question 7: Which transformation maps triangle ABC onto triangle A'B'C' if every coordinate (x,y) becomes (-x, y)?
- Reflection over the x-axis
- Reflection over the y-axis (Correct answer)
- 180° rotation about the origin
- Translation 2 units left
Correct answer: Reflection over the y-axis
Negating only the x-coordinate reflects the figure across the y-axis.
FTCE Mathematics 2
A student simplifies the expression (3x²y)(4xy³) and gets 12x³y⁴.
Which property justifies combining the exponents?