FTCE Mathematics 4

Question 1

A teacher graphs y = 2sin(3x). Compared to y = sin(x), what changes are made?

Accepted Answer

Amplitude doubles, period is one-third as long

Answer

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?

Accepted Answer

9/4

Answer

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?

Accepted Answer

They are perpendicular

Answer

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?

Accepted Answer

7/12

Answer

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?

Accepted Answer

17

Answer

Subtracting 2x from both sides gives x - 12 = 5, so x = 17.

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