Grade 9 Formulae: Short Notes

9 ශ්‍රේණිය · 17 පරිච්ඡේදය · සූත්‍ර

53%

of Grade 9 term tests include it (21 of 40)

marks in past papers (24 questions)

10 min

full lesson with quick checks

🎯 What you'll learn

Say which variable is the subject of a formula
Change the subject of a formula by undoing operations in reverse order
Change the subject when the formula has a square or a square root
Change the subject when it appears twice, by factorising
Substitute values to find an unknown after changing the subject

How far for Rs 640?

A three-wheeler in Kandy charges C = 60d + 40 rupees for d km. That formula tells you the fare from the distance. But you have Rs 640 in your pocket: how far can you go? Turning a formula round to answer the other question is what this lesson is about.

What is the subject?

A formula links variables, like A = lb or C = 60d + 40.The subject is the variable standing alone on one side, with no other copy of it on the other side.In C = 60d + 40, the subject is C.Changing the subject means rearranging so a different variable, say d, stands alone.

Undo in reverse order

To build C from d: × 60, then + 40. To get d back, undo in reverse: − 40 first, then ÷ 60. So d = (C − 40)/60.

The golden rule

A formula is a balance. Whatever you do to one side, do to the other side too.• + is undone by −, and − by +• × is undone by ÷, and ÷ by ×• a square is undone by a square root, and √ by squaringRemove the operation that was done last first.

✏️ Make a the subject

Make a the subject of v = u + at.

1a is multiplied by t, then u is added. Undo the + u first.
2Subtract u from both sides: v − u = at.
3Divide both sides by t: a = (v − u)/t.

✅ a = (v − u)/t

⚠️ Dividing only part of a side

From v − u = at, students often write a = v − u/t. That divides only u by t. The whole side is divided, so keep a bracket: a = (v − u)/t. Another slip is a = (v + u)/t: moving u across without changing + to −. Doing the same to both sides avoids both.

✏️ A formula with a fraction

The mean of two marks is m = (a + b)/2. Make b the subject, and find b when m = 70 and a = 64.

1Undo ÷ 2 first: multiply both sides by 2, so 2m = a + b.
2Subtract a: b = 2m − a.
3Substitute: b = 2 × 70 − 64 = 76.

✅ b = 2m − a; b = 76

Squares and square roots

A square is undone by a square root.A = πr² → divide by π: r² = A/π → square root: r = √(A/π)A square root is undone by squaring.v = √(2gh) → square both sides: v² = 2gh → divide by 2g: h = v²/(2g)

When the subject appears twice

1. Bring every term with the new subject to one side, the rest to the other.2. Factorise: take the subject out as a common factor.3. Divide by the bracket.Example: make x the subject of ax = b + cx.ax − cx = b → x(a − c) = b → x = b/(a − c)

⚠️ The subject is still on both sides

Answers like x = (m − kx)/l get no marks: x is still on the right, so it is not the subject. If the letter you want appears twice, collect those terms together and factorise. Check your final line: the subject must appear once, alone.

📌 Remember

• The subject stands alone on one side.• Undo operations in reverse order, doing the same to both sides.• Divide the whole side: keep brackets, like (v − u)/t.• Square ↔ square root undo each other.• Subject twice: collect, factorise, divide.

🧾 Quick revision sheet

What is the subject of a formula?	The variable standing alone on one side
v = u + at, make a the subject	a = (v − u)/t
A = πr², make r the subject	r = √(A/π)
What undoes a square root?	Squaring both sides
Subject appears twice: three steps	Collect the terms, factorise, divide by the bracket
m = (a + b)/2, make b the subject	b = 2m − a

Now test yourself: 5 quick checks and 2 more worked examples

The full lesson checks your answers as you go, and Gedara Sir tracks which parts you've got.

📖 Start the 10-minute lesson free ▶ Practise 5 past-paper questions