Number Sense and Algebraic Thinking Flashcards

If f(x) = 2x² - 3x + 1, what is f(2)?

Answer: 3

Substituting x = 2: f(2) = 2(4) - 3(2) + 1 = 8 - 6 + 1 = 3.

Which property is demonstrated by: 5(3 + 4) = 5(3) + 5(4)?

Answer: Distributive property

The distributive property states that a(b + c) = ab + ac, which is exactly what is shown here.

What is the greatest common factor (GCF) of 36 and 48?

Answer: 12

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and factors of 48 include 12 and 24; the greatest shared factor is 12.

A car travels 180 miles in 3 hours. What is the average speed in miles per hour?

Answer: 60 mph

Average speed = distance ÷ time = 180 ÷ 3 = 60 mph.

Simplify: (x³y²)(x²y⁴)

Answer: x⁵y⁶

Multiply by adding exponents of like bases: x^(3+2) = x⁵ and y^(2+4) = y⁶, giving x⁵y⁶.

Which of the following represents a linear equation?

Answer: y = 2x + 5

y = 2x + 5 is linear because the variable x is raised only to the first power and the graph is a straight line.

If a rectangle has a length of 9 cm and a width of 5 cm, what is the area?

Answer: 45 cm²

Area of a rectangle = length × width = 9 × 5 = 45 cm².