Algebraic notation, substitution and vocabulary · Higher
| English | 中文 | Pinyin |
|---|---|---|
| coefficient/ˌkəʊɪˈfɪʃənt/ | 系数 | xì shù |
What does each symbol do?
- A delivery charge is 4 yuan plus 3 yuan for each kilometre. What do the separate terms in 4+3d describe?
- This lesson studies coefficient 系数: The numerical factor multiplying a variable term.
Choose the mathematical structure
- A term is a part joined by addition or subtraction. In 4+3d, 4 is a constant and 3 is the coefficient of d. The expression has no equality sign; 4+3d=19 is an equation. A formula connects named quantities. In ab, multiplication is understood; a²b means a×a×b, not a×b×b.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines coefficient?
The numerical factor multiplying a variable term.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
For d=5, the charge is 4+3×5=19 yuan. For a=-2,b=3, a²b=(-2)²×3=12. The fraction coefficient in (3/4)x gives 6 when x=8. An inequality 4+3d≤19 describes all permitted distances, while an identity such as 2(x+3)=2x+6 is true for every x.
Algebraic notation, substitution and vocabulary
A term is a part joined by addition or subtraction
Compare the model with the worked case and explain one change.
Find 4+3d when d=5.
Substitute: 4+15=19.
Test a tempting shortcut
- Put a negative substituted number in brackets before squaring. A coefficient is not an exponent. An expression can be evaluated but cannot be solved unless a condition or equation is supplied.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
In the expression 3x², the coefficient of x² is 2. This claim is false. Explain which definition or assumption it violates.
Find a²b for a=-2,b=3.
Square -2 in brackets to get 4; multiply by 3.
In the expression 3x², the coefficient of x² is 2.
Put a negative substituted number in brackets before squaring. A coefficient is not an exponent. An expression can be evaluated but cannot be solved unless a condition or equation is supplied.
Interpret a new situation
- AQA A1–A3 require precise notation and vocabulary, including formulae from other subjects. Identify the inputs and units before substitution; keep fraction coefficients exact.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find (3/4)x for x=8.
8/4×3=6.
Match each part of a complete solution to its purpose.
An assumption justifies the model; a check tests the result; interpretation connects it to the question.
Use this in your course
- 8300 · Higher · 3.2. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
The numerical factor multiplying a variable term. Choose the relationship, show the method, check its assumptions and interpret the result.