FTCE Mathematics 2

Question 1

A student simplifies the expression (3x²y)(4xy³) and gets 12x³y⁴. Which property justifies combining the exponents?

Accepted Answer

Product of powers property

Answer

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?

Accepted Answer

a=3, b=4

Answer

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?

Accepted Answer

V-shaped, opens downward, vertex at (3,4)

Answer

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?

Accepted Answer

12 ft × 15 ft

Answer

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?

Accepted Answer

720°

Answer

Using the formula (n-2)×180° with n=6 gives (6-2)×180°=4×180°=720°.

FTCE Practice Test