MAKE IT YOURS

A world for every learner

Choose a grade to discover its colours and creative world.

Your grade

Grade 8 Challenge: Algebra Puzzles Worksheet with Answers

Grade 8 (US) · Year 9 (UK) · Class 8 (India) · Math

Unit 7: Going FurtherChallenge PuzzlesChallenge

Algebra problems that look hard until you spot the trick — identities, consecutive numbers and exponents. This free middle school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

Save to Pinterest Jump to answer key

Answer keys checked by code
No ads, ever
No student accounts needed
Safety & privacy

Practice Sheetaethelsystems.com

Challenge: Algebra Puzzles

Grade 8 · Math

Score___ / 12

Name

Class

Date

Learning goal: Challenge Puzzles

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

If x + 1/x = 9, what is x^2 + 1/x^2?

Answer: 79

1
If a + b = 10 and ab = 18, what is a^2 + b^2?
Answer
2
Without a calculator: 76^2 - 64^2 = ?
Answer
3
The sum of 9 consecutive integers is 387. What is the largest of them?
Answer
4
The sum of 4 consecutive integers is 106. What is the largest of them?
Answer
5
Without a calculator: 38^2 - 26^2 = ?
Answer
6
Without a calculator: 51^2 - 33^2 = ?
Answer
7
The sum of 4 consecutive integers is 58. What is the largest of them?
Answer
8
If 2^x = 32, what is 4^x?
Answer
9
If a + b = 10 and ab = 22, what is a^2 + b^2?
Answer
10
If a + b = 6 and a - b = 3, what is a^2 - b^2?
Answer
11
If 2^x = 16, what is 4^x?
Answer
12
If a + b = 5 and a - b = 2, what is a^2 - b^2?
Answer

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/8/challenge_algebra

Answer key (click to show)

1.64
2.1680
3.47
4.28
5.768
6.1512
7.16
8.1024
9.56
10.18
11.256
12.10

Need another Challenge: Algebra Puzzles worksheet?

Generate unlimited fresh versions at easy, medium or hard difficulty, each with its own answer key. Free during our launch — no card needed.

Create a free account

How to use this worksheet

Works well as a bell-ringer, exit ticket, homework set or quick quiz.
Have students self-check with the answer key, then correct their own mistakes before you review.
Generate a new version of the same topic for a re-test, so students can't just memorise the answers.

Related worksheets

Challenge: Algebra Puzzles at other grades

Grade 9 Grade 11 Grade 12

More Grade 8 Math worksheets

Grade 8 Challenge: Counting & Arrangements Grade 8 Challenge: Number Theory Puzzles Grade 8 Polynomials Grade 8 Factoring Trinomials Grade 8 Quadratic Equations Grade 8 Find the Mistake Grade 8 Balance Scale Puzzles Grade 8 Reading Bar & Line Graphs

Guides for teaching Challenge: Algebra Puzzles

What Are the Common Core and NGSS Standards? A Parent's GuideWhat learning standards are, how to read a code like 3.NF.A.1 or MS-PS1-2, what each grade covers in Math, English and Science, and how to use them at home.

Can't find what you need? Tell us which worksheet to make next.

Frequently asked questions

Does this Grade 8 Challenge: Algebra Puzzles worksheet come with answers?

Yes. The full answer key is on this page, and it prints on its own page after the questions. Every answer is calculated or checked by code rather than written by an AI model, so the key is always correct.

How do I print it or save it as a PDF?

Click "Download PDF" to save a ready-to-print PDF with the answer key on the last page, or click "Print" to send the worksheet and answer key straight to your printer.

Can I get a different Challenge: Algebra Puzzles worksheet?

Yes. Create a free account to generate as many fresh Grade 8 Challenge: Algebra Puzzles worksheets as you like, at easy, medium or hard difficulty, each with its own answer key.

Is this worksheet free?

Yes. This worksheet is free to print, and Practice Sheet is free to use during our launch with no card needed.