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Algebra Word Problems Practice Tests

These Grade 9 Math practice tests cover consecutive numbers, ages and averages, rates and distance, travel, money and percentages, tickets, commissions, interest, geometry, work rates, mixtures, growth, break-even models, and fixed-plus-variable costs.

Skills covered

  • Defining variables and translating words into equations
  • Solving number, average, rate, distance, and work problems
  • Modeling discounts, tax, tips, commissions, interest, tickets, and budgets
  • Using perimeter, area, volume, circles, triangles, and the Pythagorean theorem
  • Interpreting mixtures, percentages, growth, break-even points, and real-world units

How to use these practice tests

Read the question for quantities and units, define one unknown, write a relationship, solve step by step, and reject values that do not fit the situation. Include units in the final answer.

For more Grade 9 Math practice, return to the Grade 9 Math category.

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Grade 9 Algebra Word Problems Practice Tests

Practice Grade 9 Math questions about number problems, rates, distance, money, percentages, tickets, geometry, work, mixtures, growth, and algebraic models.

Choose the best answer. Define the unknown, write an equation or model, keep units consistent, solve, and check that the result makes sense in context.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

A rectangle has width 6 and perimeter 34. What is its length?

Please select an answer first.

Correct answer: A

The correct answer is 11.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Use 2l + 2(6) = 34. Then 2l = 22 and l = 11.
  3. Check the context: The correct choice is 11.

Use 2l + 2(6) = 34. Then 2l = 22 and l = 11.

2. QuestionMultiple choice

A triangle has base 12 and height 7. What is its area?

Please select an answer first.

Correct answer: B

The correct answer is 42 square units.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Use area = bh/2 = 12 × 7 / 2 = 42 square units.
  3. Check the context: The correct choice is 42 square units.

Use area = bh/2 = 12 × 7 / 2 = 42 square units.

3. QuestionMultiple choice

A rectangle has area 96 square units and width 8 units. What is its length?

Please select an answer first.

Correct answer: C

The correct answer is 12 units.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Use area = length × width, so length = 96/8 = 12 units.
  3. Check the context: The correct choice is 12 units.

Use area = length × width, so length = 96/8 = 12 units.

4. QuestionMultiple choice

A square has perimeter 44 units. What is the side length?

Please select an answer first.

Correct answer: D

The correct answer is 11 units.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: A square has four equal sides, so 44/4 = 11 units.
  3. Check the context: The correct choice is 11 units.

A square has four equal sides, so 44/4 = 11 units.

5. QuestionMultiple choice

A rectangle has length x + 4, width x, and perimeter 40. What is x?

Please select an answer first.

Correct answer: A

The correct answer is 8.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Set 2(x + 4) + 2x = 40. Then 4x + 8 = 40 and x = 8.
  3. Check the context: The correct choice is 8.

Set 2(x + 4) + 2x = 40. Then 4x + 8 = 40 and x = 8.

6. QuestionMultiple choice

A triangle has area 30 square units and base 10 units. What is its height?

Please select an answer first.

Correct answer: B

The correct answer is 6 units.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Use 30 = 10h/2, so 30 = 5h and h = 6.
  3. Check the context: The correct choice is 6 units.

Use 30 = 10h/2, so 30 = 5h and h = 6.

7. QuestionMultiple choice

A circle has circumference 18.84 units. Using pi = 3.14, what is its radius?

Please select an answer first.

Correct answer: C

The correct answer is 3 units.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Use C = 2πr: 18.84 = 6.28r, so r = 3.
  3. Check the context: The correct choice is 3 units.

Use C = 2πr: 18.84 = 6.28r, so r = 3.

8. QuestionMultiple choice

A right triangle has legs 6 and 8. What is its hypotenuse?

Please select an answer first.

Correct answer: D

The correct answer is 10.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Use the Pythagorean theorem: c squared = 36 + 64 = 100, so c = 10.
  3. Check the context: The correct choice is 10.

Use the Pythagorean theorem: c squared = 36 + 64 = 100, so c = 10.

9. QuestionMultiple choice

A rectangular garden has dimensions x and x + 5 and area 84. What is the positive value of x?

Please select an answer first.

Correct answer: A

The correct answer is 7.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Solve x(x + 5) = 84, or x squared + 5x - 84 = 0. Factoring gives (x + 12)(x - 7), so x = 7 is the positive value.
  3. Check the context: The correct choice is 7.

Solve x(x + 5) = 84, or x squared + 5x - 84 = 0. Factoring gives (x + 12)(x - 7), so x = 7 is the positive value.

10. QuestionMultiple choice

A rectangle has length twice its width and perimeter 60. What is its width?

Please select an answer first.

Correct answer: B

The correct answer is 10 units.

  1. Define the unknown: Choose a variable and identify the quantities, units, and relationships described in the problem.
  2. Build and solve the model: Let width be w and length 2w. Then 2(2w) + 2w = 60, so 6w = 60 and w = 10.
  3. Check the context: The correct choice is 10 units.

Let width be w and length 2w. Then 2(2w) + 2w = 60, so 6w = 60 and w = 10.

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