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Grade 9 Challenge: Algebra Puzzles Worksheet with Answers

Grade 9 (US) · Year 10 (UK) · Class 9 (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 9 · 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 = 10 and ab = 21, what is a^2 + b^2?

Answer: 58

  1. 1

    If a + b = 7 and ab = 9, what is a^2 + b^2?

    Answer
  2. 2

    If a + b = 14 and a - b = 13, what is a^2 - b^2?

    Answer
  3. 3

    Without a calculator: 96^2 - 90^2 = ?

    Answer
  4. 4

    The sum of 9 consecutive integers is 153. What is the largest of them?

    Answer
  5. 5

    Without a calculator: 21^2 - 3^2 = ?

    Answer
  6. 6

    Without a calculator: 61^2 - 45^2 = ?

    Answer
  7. 7

    If 2^x = 32, what is 4^x?

    Answer
  8. 8

    If a + b = 6 and a - b = 1, what is a^2 - b^2?

    Answer
  9. 9

    If x + 1/x = 4, what is x^2 + 1/x^2?

    Answer
  10. 10

    If a + b = 8 and ab = 16, what is a^2 + b^2?

    Answer
  11. 11

    If a + b = 9 and a - b = 7, what is a^2 - b^2?

    Answer
  12. 12

    Without a calculator: 55^2 - 39^2 = ?

    Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/9/challenge_algebra

Answer key (click to show)
  1. 1.31
  2. 2.182
  3. 3.1116
  4. 4.21
  5. 5.432
  6. 6.1696
  7. 7.1024
  8. 8.6
  9. 9.14
  10. 10.32
  11. 11.63
  12. 12.1504

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Challenge: Algebra Puzzles at other grades

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Grade 9 Challenge: Counting & ArrangementsGrade 9 Quadratic Formula & VertexGrade 9 Completing the SquareGrade 9 Exponential Growth & DecayGrade 9 Linear EquationsGrade 9 Equations with Variables on Both SidesGrade 9 Literal Equations (Rearranging Formulas)Grade 9 Solving Two-Step Inequalities

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Does this Grade 9 Challenge: Algebra Puzzles worksheet come with answers?

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