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Grade 11 Challenge: Algebra Puzzles Worksheet with Answers

Grade 11 (US) · Year 12 (UK) · Class 11 (India) · Math

Unit 8: Going FurtherChallenge PuzzlesChallenge

Algebra problems that look hard until you spot the trick — identities, consecutive numbers and exponents. This free high 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.

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Challenge: Algebra Puzzles

Grade 11 · 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 a + b = 3 and ab = 1, what is a^2 + b^2?

Answer: 7

1
Without a calculator: 85^2 - 71^2 = ?
Answer
2
If x + 1/x = 9, what is x^2 + 1/x^2?
Answer
3
If a + b = 20 and a - b = 7, what is a^2 - b^2?
Answer
4
The sum of 9 consecutive integers is 396. What is the largest of them?
Answer
5
If x + 1/x = 6, what is x^2 + 1/x^2?
Answer
6
If 2^x = 4, what is 4^x?
Answer
7
If x + 1/x = 3, what is x^2 + 1/x^2?
Answer
8
Without a calculator: 25^2 - 23^2 = ?
Answer
9
Without a calculator: 69^2 - 51^2 = ?
Answer
10
Without a calculator: 59^2 - 55^2 = ?
Answer
11
If 2^x = 64, what is 4^x?
Answer
12
If 2^x = 16, what is 4^x?
Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/11/challenge_algebra

Answer key (click to show)

1.2184
2.79
3.140
4.48
5.34
6.16
7.7
8.96
9.2160
10.456
11.4096
12.256

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Does this Grade 11 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?

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