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MATHEMATICSAlgebra
CURRENT TOPICExpressions
x
2x+5
● Master Topic Guide Verified 11+ Curriculum

Algebra & Expressions Guide ⚖️

Master variables, expressions, evaluating expressions, basic algebraic operations, solving simple equations, simplifying expressions, expanding, factorising, and key vocabulary!

Practice Levels:Warm-UpCore ModePro Mode
Practice Papers
⚖️

1. INTRODUCTION TO ALGEBRA

Algebra uses letters to represent numbers.

"Algebra uses letters to stand for unknown numbers!"
1. VARIABLES

A variable is a letter that stands for a number.

Examples:
xyab
x could be 3, 7, 10 or any number!
2. EXPRESSIONS

An expression combines numbers, variables and operations.

2x
multiply
x + 5
add
3y - 2
subtract
a + b
add
3. EVALUATE EXPRESSIONS

Replace the variable with a value and simplify.

Example: x + 5
If x = 3 ➔ 3 + 5 ═ 8
If x = 7 ➔ 7 + 5 ═ 12
Try your own x value:
x =
x + 5 ➔ 4 + 5 ═ 9
2x ➔ 2 × 4 ═ 8
3x - 2 ➔ (3 × 4) - 2 ═ 10
x² ➔ 4 × 4 ═ 16
4. BASIC OPERATIONS WITH ALGEBRA

Addition

Combine like terms.

x + x ═ 2x
2x + 3x ═ 5x

Subtraction

Subtract like terms.

x - x ═ 0
5x - 2x ═ 3x

Multiplication

Multiply numbers. Keep variable.

3 × x ═ 3x
2 × 4x ═ 8x

Division

Divide numbers. Keep variable.

x ÷ 2 ═ x/2
6x ÷ 3 ═ 2x
5. SOLVE SIMPLE EQUATIONS

Find the value of the variable that makes the equation true.

Example 1:
x + 5 ═ 12
x ═ 12 - 5
x ═ 7
Example 2:
3x ═ 15
x ═ 15 ÷ 3
x ═ 5
6. THE EQUAL SIGN

The equal sign (=) means both sides are equal.

2x + 1══7
⚖️ If one side changes, do the exact same to the other side!
7. KEY WORDS
VariableA letter that stands for a number.
ExpressionCombines numbers, variables & operations.
EquationStatement that 2 expressions are equal.
TermNumber, variable or part separated by + or -.
CoefficientNumber in front of variable (In 3x, coefficient is 3).
⚡

2. SIMPLIFYING EXPRESSIONS

Simplify means write the expression in the simplest form.

3x + 2x ═ 5x ⚖️
Simplify = Combine like terms!
TYPES OF TERMS

Like terms have the same variable and the same power.

Like terms (can be +/-):
3x & 5x-2a & 7a4y² & -y²
Unlike terms (cannot combine):
3x & 2x & x²2a & 3b
Numbers on their own:
5-311
HOW TO SIMPLIFY EXPRESSIONS
1Remove brackets

Multiply term outside brackets by each term inside.

2(x + 3) ═ 2x + 6
2Collect like terms

Group terms with the same variable and power.

3x + 2x - x ═ (3 + 2 - 1)x
3Add/subtract numbers

Calculate numbers, keep variable part same.

(3 + 2 - 1)x ═ 4x
4Simplest form

Write expression in clear, neat order.

4x + 6
WORKED EXAMPLES & SOLUTIONS
Example 1
3x + 5x - 2x
═ (3 + 5 - 2)x
═ 6x
Example 2
4a - 7a + 2a
═ (4 - 7 + 2)a
═ -a
Example 3
2(x + 3) + x
═ 2x + 6 + x
═ 3x + 6
Example 4
3(2y - 4) + 5y
═ 6y - 12 + 5y
═ 11y - 12
Example 5
2a + 3b - a + 4b - 5
═ (2a - a) + (3b + 4b) - 5
═ a + 7b - 5
Example 6
5(x - 2) - 2(x + 4) + 3
═ 5x - 10 - 2x - 8 + 3
═ 3x - 15
TOP TIP

Write each step on a new line to stay organised and avoid calculation mistakes on 11+ exams!

IMPORTANT RULES
  • ★ Only combine like terms.
  • ★ Never add/subtract unlike terms.
  • ★ Keep the sign with each term.
  • ★ A term with no variable is a number.
Ex: 7x + 3 ➔ 7x is not like 3
REORDERING TERMS

You can change the order of terms. Write in alphabetical order!

2x + 5y - 3 + x
═ (2x + x) + 5y - 3
═ 3x + 5y - 3
COMMON MISTAKES
❌ 2x + 3 ≠ 5x (Unlike terms)
❌ 2(x + 3) ≠ 2x + 3 (Multiply all terms)
❌ -(x + 2) ═ -x - 2 (Not -x + 2)

INTERACTIVE ALGEBRA MODULES

Step-by-step interactive practice modules

1 / 4 explored

VISUAL LIKE TERMS SIMPLIFIER

Watch like terms animate and combine together

Expression

3x
+
2x

Worked Examples

Worked Example

Simplify 3x + 2x − x

1
3x + 2x − x
Start with the original expression.

Quick Check

Quick Check1 / 3

Simplify 4x + 3x

INTERACTIVE ALGEBRA CHAMPION QUIZ11+ Exam Practice
1. Simplify the expression 3x + 4x - 2x:
2. Evaluate 4a - 3 when a = 5:
3. Simplify 5(x - 2) - 2(x + 4) + 3:
4. Solve for y: 2y + 3 = 11

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