Rearranging formulae and checking the subject · Higher
도입됨| English | 의미 |
|---|---|
| subject/ˈsʌbdʒekt/ | 주변변수(공식 주체) |
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.
The method
- 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.
To make b the subject of A=bh/2, which sequence is valid?
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
Undo the operations in reverse order, applying each to BOTH sides: 2A=bh, then b=2A/h. A one-sided operation destroys the equality.
A worked case
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.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
b=2A/h=48/6.
Where it goes wrong
- 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.
Not true: To rearrange a formula, an operation may be applied to one side only. The same operation must be applied to both sides to keep the equation balanced.
Find a for v=19,u=4,t=5 in v=u+at.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
a=(19-4)/5=3.
To rearrange a formula, an operation may be applied to one side only.
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
The same operation must be applied to both sides to keep the equation balanced.
Applying it
- 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.
Find x for y=17 in y=3x+2.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
x=(17-2)/3=5.
Match each formula to its rearranged subject.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
Each rearrangement undoes the outermost operation first and finishes by dividing by the variable’s coefficient, with any restrictions stated.
In your course
- AQA GCSE Mathematics (8300), Higher tier, specification section 3.2.
- Paper 1 is non-calculator: keep fractions, surds and π exact and show each step. On calculator papers, still write the expression before its value.
- Subject: The quantity written alone on one side of a formula.
- Undo operations on both sides in reverse order.
- Watch for: doing an operation to only one side breaks the equality.