College Readiness Math Flashcards

What is the simplified form of (x² − 9) / (x − 3)?

Answer: x + 3

Factor the numerator as (x + 3)(x − 3); dividing by (x − 3) leaves x + 3.

If a triangle has legs of length 5 and 12, what is the length of the hypotenuse?

Answer: 13

By the Pythagorean theorem: √(25 + 144) = √169 = 13.

What is the slope-intercept form of a line with slope −3 passing through (0, 7)?

Answer: y = −3x + 7

With slope −3 and y-intercept 7, the equation is y = −3x + 7.

Which of the following is NOT a function?

Answer: {(1,2),(1,3),(2,4)}

The input 1 maps to two different outputs (2 and 3), violating the definition of a function.

Simplify: (3a²b³)² / (9a³b²)

Answer: a b⁴

Numerator = 9a⁴b⁶; dividing by 9a³b² gives a¹b⁴ = ab⁴.

A store sells items at 25% off. If an item originally costs $80, what is the sale price?

Answer: $60

Discount = 0.25 × 80 = $20; sale price = 80 − 20 = $60.

What is the vertex of the parabola y = x² − 6x + 8?

Answer: (3, −1)

x-coordinate of vertex = −b/(2a) = 6/2 = 3; y = 9 − 18 + 8 = −1.