Equations
Cambridge IGCSE Mathematics (0580) · Unit 2: Algebra and graphs · 9 flashcards
Equations is topic 2.2 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 2 — Algebra and graphs , alongside Algebraic notation and manipulation, Inequalities and Sequences. In one line: Inverse operations are operations that undo each other (.
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 9 flashcards — 3 definitions and 2 key concepts — covering the precise wording mark schemes reward. Use the 3 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
'inverse operations' and why are they important for solving equations
Inverse operations are operations that undo each other (
Questions this Equations deck will help you answer
- › What is the primary goal when solving an equation?
- › Explain the concept of 'balance' in the context of solving equations.
What is the primary goal when solving an equation?
The main goal is to isolate the unknown variable (
Solve the linear equation: 2x + 5 = 11
Subtract 5 from both sides: 2x = 6. Then, divide both sides by 2: x = 3. Therefore, the solution is x = 3.
Explain the concept of 'balance' in the context of solving equations.
The equation must remain equal. Any operation performed on one side of the equation must also be performed on the other side to maintain equality.
What are 'inverse operations' and why are they important for solving equations?
Inverse operations are operations that undo each other (
Define 'solution' in the context of an equation.
The solution is the value (or values) of the unknown variable that makes the equation true. Substituting the solution back into the original equation should result in a balanced equation.
Solve for x and y using elimination: x + y = 5, x - y = 1
Add the two equations: 2x = 6, so x = 3. Substitute x = 3 into the first equation: 3 + y = 5, so y = 2. Therefore, x=3 and y=2.
Explain the 'substitution' method for solving simultaneous equations.
Solve one equation for one variable, then substitute that expression into the other equation. This creates a single equation with one variable, which can then be solved. Finally, substitute the solved variable's value back to get the other variable.
When solving the equation 3(x - 2) = 9, what is the first step?
The first step is to either divide both sides of the equation by 3, or distribute the 3 into the parentheses to get 3x - 6 = 9. Both approaches are valid.
Solve the following: 5x - 3 = 12
Add 3 to both sides: 5x = 15. Divide both sides by 5: x = 3. Therefore the solution is x = 3.
Key Questions: Equations
What are 'inverse operations' and why are they important for solving equations?
Inverse operations are operations that undo each other (
Define 'solution' in the context of an equation.
The solution is the value (or values) of the unknown variable that makes the equation true. Substituting the solution back into the original equation should result in a balanced equation.
Explain the 'substitution' method for solving simultaneous equations.
Solve one equation for one variable, then substitute that expression into the other equation. This creates a single equation with one variable, which can then be solved. Finally, substitute the solved variable's value back to get the other variable.
Tips to avoid common mistakes in Equations
- ● Scrutinize every single part of every question before you start your solution.
- ● Always write out the full equation, y = mx + c, then fill in the values for m and c.
- ● Double-check every sign when combining like terms to eliminate variables.
- ● When using the quadratic formula to solve simultaneous equations, show every step, including the values of a, b, and c that you subbed in.
More topics in Unit 2 — Algebra and graphs
Equations sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Equations deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
How to study this Equations deck
Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.
Study Mode
Space to flip • ←→ to navigate • Esc to close
You're on a roll!
You've viewed 10 topics today
Create a free account to unlock unlimited access to all revision notes, flashcards, and study materials.
You're all set!
Enjoy unlimited access to all study materials.
Something went wrong. Please try again.
What you'll get:
- Unlimited revision notes & flashcards
- Track your study progress
- No spam, just study updates