PAT Algebraic Thinking 3

Question 1

Which graph shape would represent the equation y = x + 3?

Accepted Answer

A straight line with positive slope

Answer

y = x + 3 is a linear equation of the form y = mx + b, which always produces a straight line with slope 1.

Question 2

Two consecutive even numbers have a sum of 54. What are the numbers?

Accepted Answer

26 and 28

Answer

Let the numbers be n and n+2: n + (n+2) = 54, so 2n = 52, n = 26; the numbers are 26 and 28.

Question 3

What is the value of the expression 2m² when m = 3?

Accepted Answer

18

Answer

Substituting m = 3: 2(3²) = 2(9) = 18.

Question 4

A function machine multiplies the input by 4 and then subtracts 3. What output does an input of 7 produce?

Accepted Answer

25

Answer

Input 7 → multiply by 4 = 28 → subtract 3 = 25.

Question 5

Which of these is an algebraic expression (not an equation)?

Accepted Answer

4n − 7

Answer

4n − 7 is an algebraic expression because it has no equals sign; the others are equations.

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