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Literal Equations - Worksheet 10 - 9th Grade

Hard

Rearrange literal equations to solve for a specified variable (Hard)

27 problems · 20-25 minutes · Skills: algebra, equation solving, formulas

About This Worksheet

This hard-level worksheet contains 27 problems designed for 9th Grade students practicing literal equations & formulas. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Literal equations make formulas flexible tools. Being able to rearrange any formula — whether in math, chemistry, or physics — is an essential skill for STEM coursework. It also deepens understanding of algebraic structure and inverse operations.

  • Isolate a specified variable in a formula by applying inverse operations
  • Rearrange geometry formulas like A = ½bh to solve for b or h
  • Rearrange physics and science formulas to solve for desired variables
  • Distinguish between solving for a number and solving for a variable expression
  • Verify a rearranged formula by substituting known values into both forms

How to Solve: Worked Example

Example Problem: Solve for h: S = 2πr² + 2πrh
Solution Steps:
  1. Isolate the term containing h: subtract 2πr² from both sides to get S - 2πr² = 2πrh.
  2. The h is multiplied by 2πr, so divide both sides by 2πr.
  3. h = (S - 2πr²)/(2πr).
Answer: h = (S - 2πr²)/(2πr)
Tip: When the target variable appears in only one term, isolate that whole term first, then divide by everything attached to it.
1
Solve for r: V = (4/3)πr³
2
Solve for r: V = ⅓πr²h
3
Solve for h: A = ½h(b₁ + b₂)
4
Solve for b₂: A = ½h(b₁ + b₂)
5
Solve for c: a² + b² = c²
6
Solve for x: y - y₁ = m(x - x₁)
7
Solve for h: S = 2πr² + 2πrh
8
Solve for a: s = ut + ½at²
9
Solve for h: V = ⅓πr²h
10
Solve for r: A = P(1 + rt)
11
Solve for b: a² + b² = c²
12
Solve for v: 1/f = 1/u + 1/v
13
Solve for L: T = 2π√(L/g)
14
Solve for P: A = P(1 + r)ⁿ
15
Solve for m: y - y₁ = m(x - x₁)
16
Solve for r: V = (4/3)πr³
17
Solve for r: V = ⅓πr²h
18
Solve for h: A = ½h(b₁ + b₂)
19
Solve for b₂: A = ½h(b₁ + b₂)
20
Solve for c: a² + b² = c²
21
Solve for x: y - y₁ = m(x - x₁)
22
Solve for h: S = 2πr² + 2πrh
23
Solve for a: s = ut + ½at²
24
Solve for h: V = ⅓πr²h
25
Solve for r: A = P(1 + rt)
26
Solve for b: a² + b² = c²
27
Solve for v: 1/f = 1/u + 1/v

Answer Key

1. r = ∛(3V/(4π))2. r = √(3V/(πh))3. h = 2A/(b₁ + b₂)4. b₂ = 2A/h - b₁5. c = √(a² + b²)6. x = x₁ + (y - y₁)/m7. h = (S - 2πr²)/(2πr)8. a = 2(s - ut)/t²9. h = 3V/(πr²)10. r = (A/P - 1)/t11. b = √(c² - a²)12. v = uf/(u - f)13. L = g(T/(2π))²14. P = A/(1 + r)ⁿ15. m = (y - y₁)/(x - x₁)16. r = ∛(3V/(4π))17. r = √(3V/(πh))18. h = 2A/(b₁ + b₂)19. b₂ = 2A/h - b₁20. c = √(a² + b²)21. x = x₁ + (y - y₁)/m22. h = (S - 2πr²)/(2πr)23. a = 2(s - ut)/t²24. h = 3V/(πr²)25. r = (A/P - 1)/t26. b = √(c² - a²)27. v = uf/(u - f)

Frequently Asked Questions

How do I download this literal equations - worksheet 10 worksheet?

Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.

How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this linear equations & inequalities worksheet cover?

This worksheet focuses on algebra, equation solving, formulas. It is designed for 9th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 27 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.