Rearranging formulae and checking the subject · Foundation
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| subject/ˈsʌbdʒekt/ | biến thể chính của công thức |
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?
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
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 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.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
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.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
a=(19-4)/5=3.
To rearrange a formula, an operation may be applied to one side only.
Độ khó 1/5 · 100 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
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.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
x=(17-2)/3=5.
Match each formula to its rearranged subject.
Độ khó 2/5 · 140 xu + một phần thưởng nhỏ cho lần hoàn thành đầu tiên trong ngày
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), Foundation 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.