The Heartland Institute

# Test Yourself: NAEP’s ‘Hard’ 8th-Grade ‘Algebra and Functions’ Questions

Published January 1, 2005

The National Assessment of Educational Progress Web site offers the following questions as examples of “hard” eighth-grade “algebra” problems. Answers are on page 18.

1. The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work.

2. If the pattern shown in the table were continued, what number would appear in the box at the bottom of column B next to 14?

 A B 2 5 4 9 6 13 8 17 14 ?

a) 19
b) 21
c) 23
d) 25
e) 29

3. The length of a rectangle is 3 more than its width. If L represents the length, what is an expression for the width?
a) 3 ÷ L
b) L ÷ 3
c) L x 3
d) L + 3
e) L – 3

4. While she was on vacation, Tara sent 14 friends either a letter or a postcard. She spent \$3.84 on postage. If it costs \$0.20 to mail a postcard and \$0.33 to mail a letter, how many letters did Tara send? Show what you did to get your answer.

5. Evaluate the expression: 3^3 + 4(8 – 5) ÷ 6 = ?
a) 6.5
b) 11
c) 27.5
d) 29
e) 34.16