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Cambridge / IGCSE • Algebraic Thinking

Variables and Expressions

Algebra allows us to write general rules and solve puzzles where numbers are hidden behind letters like x or y.

Learning Objectives

  • Understand the concept of a variable as a unknown quantity
  • Write algebraic expressions from word descriptions
  • Evaluate expressions for given variable values

Lesson Explanation

Lesson Content

An expression like 3x + 4 means 3 times x, plus 4. If x = 2, we substitute 2 into the expression: 3(2) + 4 = 6 + 4 = 10.

💡 Key Takeaway

Take one step at a time, check your working carefully, and keep both sides balanced!

Worked Examples

Example 1

Evaluate 5y - 3 when y = 4

  1. Step 1

    Substitute y = 4: 5(4) - 3

  2. Step 2

    Multiply: 20 - 3

  3. Step 3

    Subtract: 17

Visual Method

Balance Every Step

Mathematics becomes much clearer when you can see the structure behind equations.

Watch Video Explanation

Practice Questions

Try solving each question on paper first. Tap below to check a helpful hint or solution!

Question 1

Write an expression for '6 more than a number n'

Show Hint / Solution 💡

Use + for 'more than'.

Question 2

Evaluate 2a + 7 when a = 5

Show Hint / Solution 💡

Substitute 5 into 2a.

Lesson Summary

What to Remember

Variables use letters to stand in for numbers that can change or are unknown.

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