Algebraic notation and manipulation
Cambridge IGCSE Mathematics (0580) · Unit 2: Algebra and graphs · 9 flashcards
Algebraic notation and manipulation is topic 2.1 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 2 — Algebra and graphs , alongside Equations, Inequalities and Sequences. In one line: The coefficient is the numerical part of the term, which is 7. The variable is the letter representing an unknown value, which is 'x'.
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 — 4 definitions and 1 key concept — covering the precise wording mark schemes reward. Use the 4 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.
Identify the coefficient and variable in the term '7x'
The coefficient is the numerical part of the term, which is 7. The variable is the letter representing an unknown value, which is 'x'.
Questions this Algebraic notation and manipulation deck will help you answer
- › Explain the purpose of brackets in an algebraic expression.
Identify the coefficient and variable in the term '7x'.
The coefficient is the numerical part of the term, which is 7. The variable is the letter representing an unknown value, which is 'x'.
Simplify the following expression by collecting like terms: 3a + 2b - a + 5b.
Combine the 'a' terms (3a - a = 2a) and the 'b' terms (2b + 5b = 7b). The simplified expression is 2a + 7b.
What is the difference between a term and an expression in algebra?
A term is a single number, variable, or product of numbers and variables (
Expand the following expression: 4(2x - 3).
Multiply each term inside the brackets by 4: 4 * 2x = 8x and 4 * -3 = -12. The expanded expression is 8x - 12.
Factorise the following expression: 6x + 9.
Find the highest common factor (HCF) of 6 and 9, which is 3. Divide each term by 3 and write it outside the brackets: 3(2x + 3).
Explain what 'like terms' are and give an example.
Like terms are terms that have the same variable raised to the same power.
What is a constant term in an algebraic expression? Give an example.
A constant term is a term that does not contain any variables; it's a fixed number.
Simplify the algebraic fraction: 10x / 5.
Divide the coefficient of the numerator by the denominator: 10 / 5 = 2. Therefore, the simplified fraction is 2x.
Explain the purpose of brackets in an algebraic expression.
Brackets indicate the order of operations. Operations inside the brackets are performed before operations outside the brackets (following the order of operations - PEMDAS/BODMAS).
Key Questions: Algebraic notation and manipulation
Identify the coefficient and variable in the term '7x'.
The coefficient is the numerical part of the term, which is 7. The variable is the letter representing an unknown value, which is 'x'.
What is the difference between a term and an expression in algebra?
A term is a single number, variable, or product of numbers and variables (
Explain what 'like terms' are and give an example.
Like terms are terms that have the same variable raised to the same power.
What is a constant term in an algebraic expression? Give an example.
A constant term is a term that does not contain any variables; it's a fixed number.
Tips to avoid common mistakes in Algebraic notation and manipulation
- ● Double-check the operation that the question is asking you to perform.
- ● Strengthen your algebra skills by routinely checking each manipulation as you proceed.
- ● When expanding (a + b)(c + d), use FOIL (First, Outer, Inner, Last) carefully, and put brackets around everything until the last step.
More topics in Unit 2 — Algebra and graphs
Algebraic notation and manipulation 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 Algebraic notation and manipulation 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.
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