Rearranging formulae and checking the subject · Higher
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| subject/ˈsʌbdʒekt/ | 公式主项 | gōng shì zhǔ xiàng |
Can we work backwards from the area?
- A triangle has known area and height, but its base is missing. How can the area formula be reversed?
- This lesson studies subject 公式主项: The quantity written alone on one side of a formula.
Choose the mathematical structure
- Undo operations on both sides in reverse order. In A=bh/2, multiply both sides by 2 then divide by nonzero h to obtain b=2A/h. When the desired variable occurs twice, collect it before dividing. State restrictions introduced by division.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines subject?
The quantity written alone on one side of a formula.
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 A=24,h=6, b=2×24/6=8. From v=u+at, a=(v-u)/t; for v=19,u=4,t=5 this gives a=3. From y=3x+2, x=(y-2)/3. From p=qx+r, x=(p-r)/q for q≠0. Higher may factor repeated subjects: y=3x+px gives x=y/(3+p) when p≠-3.
Rearranging formulae and checking the subject
Undo operations on both sides in reverse order
Compare the model with the worked case and explain one change.
Find b when A=24,h=6 in A=bh/2.
b=2A/h=48/6.
Test a tempting shortcut
- Doing an operation to only one side breaks the equality. The subject is a variable, not a numerical answer. Check the rearranged result by putting the found value into the original formula.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
To rearrange a formula, an operation may be applied to one side only. This claim is false. Explain which definition or assumption it violates.
Find a for v=19,u=4,t=5 in v=u+at.
a=(19-4)/5=3.
To rearrange a formula, an operation may be applied to one side only.
Doing an operation to only one side breaks the equality. The subject is a variable, not a numerical answer. Check the rearranged result by putting the found value into the original formula.
Interpret a new situation
- AQA A5 includes standard and given formulae from other subjects, in words and symbols. Choose a valid unit conversion before substituting; a rearrangement does not itself change units.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find x for y=17 in y=3x+2.
x=(17-2)/3=5.
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 quantity written alone on one side of a formula. Choose the relationship, show the method, check its assumptions and interpret the result.