Mathematics • Year 10 • Unit 2 • Lesson 10

Formulas and Rearrangement — Skill Drill

Build fluency with the three tools from Lesson 10: changing the subject of a linear formula, applying reverse BIDMAS to multi-step formulas, and isolating variables that are squared (powers and roots). One worked example, one guided trace, then eight problems.

Build · I Do / We Do / You Do

1. I do — fully worked example

Changing the subject of a two-step formula using reverse BIDMAS. Read each reason.

Problem. Make h the subject of V = (1/3)Bh.

Step 1 — Identify the operation chain on h.

h → × B → Bh → ÷ 3 → V

Reason: h is multiplied by B, then divided by 3 to get V. Reverse BIDMAS: undo ÷ 3 first, then undo × B.

Step 2 — Multiply both sides by 3 (undo ÷ 3).

3V = 3 × (1/3)Bh = Bh

Step 3 — Divide both sides by B (undo × B).

3V/B = Bh/B = h

Step 4 — Write h alone on the left.

h = 3V/B

Answer: h = 3V/B (restriction: B ≠ 0).

Stuck? Revisit lesson § "Reverse BIDMAS for Formulas" — Worked Example 2.

2. We do — fill in the missing steps

Making r the subject of A = πr². Fill in each blank. 5 marks

Problem. Make r the subject of A = πr².

Step 1 — Operation chain on r: r → squared → ____ → × π → A.

Step 2 — Reverse BIDMAS says undo × π first. Divide both sides by ____:

A / ____ = πr² / ____ = ____

Step 3 — Now undo the square. Take the ____ of both sides:

√(A/π) = r

Step 4 — Write r alone on the left:

r = ________________

Step 5 — Quick check: if A = 9π, then r = √(9π/π) = √9 = ____. And π(3)² = ____ ✓.

Stuck? Revisit lesson § "Powers and Roots" — Worked Example 3.

3. You do — independent practice

Show every step. State any restrictions (variable dividing must not be zero).

Foundation — single skill

3.1 Make x the subject of y = x + 5. 1 mark

3.2 Make x the subject of y = 4x. 1 mark

3.3 Make r the subject of C = 2πr. 1 mark

3.4 Make a the subject of v = u + at. 1 mark

Standard — two-step

3.5 Make x the subject of y = 3x + 5. 2 marks

3.6 Make b the subject of P = 2a + 2b. 2 marks

Extension — powers, roots, multi-step

3.7 Make r the subject of A = πr². State the restriction. Then evaluate r when A = 100π. 3 marks

3.8 Make C the subject of F = (9C/5) + 32 (Celsius-to-Fahrenheit). Use it to convert F = 68 °F to °C. 3 marks

Stuck on 3.8? Subtract 32 first, then multiply by 5, then divide by 9.

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Section 2 — We do (A = πr²)

Step 1: chain is r → squared → r² → × π → A. Step 2: divide both sides by π: A/π = πr²/π = r². Step 3: take the square root of both sides. Step 4: r = √(A/π). Step 5: r = 3; π(3)² = 9π ✓.

3.1 — y = x + 5

Subtract 5: x = y − 5.

3.2 — y = 4x

Divide by 4: x = y/4.

3.3 — C = 2πr

Divide by 2π: r = C/(2π).

3.4 — v = u + at

Subtract u: v − u = at. Divide by t: a = (v − u)/t (t ≠ 0).

3.5 — y = 3x + 5

Subtract 5: y − 5 = 3x. Divide by 3: x = (y − 5)/3.

3.6 — P = 2a + 2b

Subtract 2a: P − 2a = 2b. Divide by 2: b = (P − 2a)/2.

3.7 — A = πr²

Divide by π: A/π = r². Take √: r = √(A/π) (r ≥ 0 for a real radius). At A = 100π: r = √(100π/π) = √100 = 10.

3.8 — F = (9C/5) + 32

Subtract 32: F − 32 = 9C/5. Multiply by 5: 5(F − 32) = 9C. Divide by 9: C = 5(F − 32)/9. At F = 68: C = 5(36)/9 = 180/9 = 20 °C.