AQL Number Sense and Algebraic Thinking 2

Question 1

If f(x) = 2x² - 3x + 1, what is f(2)?

Accepted Answer

3

Answer

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

Question 2

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

Accepted Answer

Distributive property

Answer

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

Question 3

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

Accepted Answer

12

Answer

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.

Question 4

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

Accepted Answer

60 mph

Answer

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

Question 5

Simplify: (x³y²)(x²y⁴)

Accepted Answer

x⁵y⁶

Answer

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

AQL - Academic and Quantitative Literacy Practice Test