Rearranging formulae and checking the subject · Foundation
| English | Español |
|---|---|
| subject/ˈsʌbdʒekt/ | tema |
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 in A=bh/2, b=2×24/6=8. From v=u+at, a=(v-u)/t; v=19,u=4,t=5 gives a=3. From y=3x+2, x=(y-2)/3. From p=qx+r, x=(p-r)/q for q≠0. Substitute the result into the original equation to check it.
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 · Foundation · 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.