Grade 10 Formulae: Short Notes

10 ශ්‍රේණිය · 22 පරිච්ඡේදය · සූත්‍ර

52%

of Grade 10 term tests include it (28 of 54)

171

marks in past papers (31 questions)

10 min

full lesson with quick checks

🎯 What you'll learn

Substitute values into a formula correctly
Change the subject of a formula by undoing operations in reverse order
Change the subject when it is squared, under a root or in a denominator
Change the subject first, then substitute to solve a problem

How far can Rs 740 take you?

A three-wheeler in Kurunegala charges Rs 100 to start plus Rs 80 per kilometre, so the fare is C = 100 + 80d. You have Rs 740 in your pocket. How far can you go? Turning the formula around answers it straight away.

Formula, subject, substitution

A formula links quantities with letters. In C = 100 + 80d, C stands alone on one side, so C is the subject.To substitute, put numbers in place of letters:d = 5 gives C = 100 + 80 × 5 = Rs 500.To find d from C, we make d the subject instead.

Undo in reverse order

To make d the subject, notice what was done to d: first × 80, then + 100.Undo them in reverse order with the inverse operations: first − 100, then ÷ 80.Whatever you do, do it to both sides, just like solving an equation.

Forwards and backwards

Top: build C from d. Red path: undo the steps in reverse to get back to d.

✏️ Back to the three-wheeler

Make d the subject of C = 100 + 80d, and find d when C = 740.

1Subtract 100 from both sides: C − 100 = 80d.
2Divide both sides by 80: d = (C − 100)/80.
3Substitute: d = (740 − 100)/80 = 640/80 = 8.

✅ d = (C − 100)/80; 8 km

🧮 A formula from physics

s is multiplied by 2a, then u² is added. Undo: subtract u², then divide by 2a. Example: v = 10, u = 4, a = 3 gives s = (100 − 16)/6 = 14.

v² = u² + 2as ⇒ s = (v² − u²) / 2a

✏️ Making n the subject

The nth term of an arithmetic progression is Tₙ = a + (n − 1)d. Make n the subject, then find n when a = 5, d = 3 and Tₙ = 62.

1Done to n: − 1, then × d, then + a.
2Undo + a: Tₙ − a = (n − 1)d.
3Undo × d: (Tₙ − a)/d = n − 1.
4Undo − 1: n = (Tₙ − a)/d + 1.
5n = (62 − 5)/3 + 1 = 19 + 1 = 20.

✅ n = (Tₙ − a)/d + 1; n = 20

⚠️ Undoing in the wrong order

Examiners report this every few years. With Tₙ = a + (n − 1)d, some students divide by d first and write n − 1 = Tₙ/d − a. Wrong: a was added last, so it must be removed first.Before you move anything, write the order of operations on the new subject, then reverse it.

Squares and square roots

Squaring and square-rooting undo each other.• A = πr² → divide by π, then take the root: r = √(A/π)• y = √(2x − 1) → square both sides first: y² = 2x − 1, so x = (y² + 1)/2When the subject is under a root, get the root alone, then square both sides.

⚠️ A root does not split over + or −

From v² = u² + 2as, writing v = u + √(2as) is wrong. √(u² + 2as) is not √u² + √(2as). Check: √(9 + 16) = √25 = 5, but 3 + 4 = 7.Correct: v = √(u² + 2as). Keep the whole side under one root.

📌 Remember

• The subject is the letter standing alone on one side.• Substitute by replacing letters with numbers; follow BODMAS.• To change the subject, list what was done to it, then undo in reverse order on both sides.• Square both sides to remove a root; take the root of the whole side to remove a square.• Make the subject first, then substitute.

🧾 Quick revision sheet

What is the subject of a formula?	The letter on its own on one side, e.g. C in C = 100 + 80d.
Inverse of + 5? Of × 3? Of squaring?	− 5, ÷ 3, square root.
Order for undoing operations	Reverse order: the last thing done is undone first.
A = πr²: r = ?	r = √(A/π)
v² = u² + 2as: s = ?	s = (v² − u²)/2a
V = ⅓πr²h: h = ?	h = 3V/(πr²)
Is √(a² + b²) equal to a + b?	No. A root never splits over + or −.