Algebra
Calculators, worked examples and guides — from solving basic equations through to quadratics, factorising and simultaneous equations.
Learning about Algebra
The key idea: algebra replaces unknown numbers with letters called variables. If you can solve "a box plus 5 equals 9, what is the box?", you can do algebra. The letter x is just the box.
Solving equations
"Solve 3x + 7 = 22"
Step 1: Subtract 7 from both sides: 3x = 15
Step 2: Divide both sides by 3: x = 5
Step 3: Check: 3(5) + 7 = 22 ✓
Shortcut: 'Whatever you do to one side, do to the other'
Expanding brackets
"Expand 3(2x + 5)"
Step 1: Multiply 3 by 2x: 6x
Step 2: Multiply 3 by 5: 15
Step 3: Answer: 6x + 15
Shortcut: Draw arrows from the outside term to each term inside
Factorising
"Factorise 6x + 9"
Step 1: Find HCF of 6 and 9 → 3
Step 2: Write 3 outside brackets: 3()
Step 3: 6x ÷ 3 = 2x, 9 ÷ 3 = 3 → Answer: 3(2x + 3)
Shortcut: Check by expanding — you should get back to the original
Algebra Formula Sheet & Rules
Need a printable revision sheet? Access expanding brackets, factorising, quadratic formula, sequences, and index laws with step-by-step worked examples and custom print export.
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Numbers & Arithmetic
Place value, operations, BODMAS, rounding, negatives
Fractions
Equivalent fractions, operations, mixed numbers, simplifying
Decimals
Place value, operations, rounding, recurring decimals
Percentages
% of a number, increase & decrease, reverse %, VAT
Geometry
Shapes, area, perimeter, volume, angles, Pythagoras
Ratio & Proportion
Simplifying, scaling, direct & inverse proportion
Factors & Multiples
HCF, LCM, prime factorisation, factor trees
Statistics & Data
Mean, median, mode, range, probability, graphs
Trigonometry
Sin, cos, tan, SOHCAHTOA, sine & cosine rules
Algebra Questions Answered
What is algebra?
Algebra is the branch of maths where letters (variables) represent unknown numbers. It lets us write general rules and solve problems where one or more values are not yet known.
How do I solve a simple linear equation?
Do the same operation to both sides to isolate the variable. For 3x + 7 = 22: subtract 7 from both sides to get 3x = 15, then divide by 3 to get x = 5.
What does expanding brackets mean?
Multiply everything inside the bracket by the term outside. For example: 3(x + 4) becomes 3x + 12.
What is factorising?
The reverse of expanding. You find the highest common factor and take it outside a bracket. For example: 6x + 9 = 3(2x + 3).
What are simultaneous equations?
Two equations with two unknowns that must both be true at the same time. Solving them finds the value of both unknowns — usually by substitution or elimination.