Prepared by Muhammad Tayyab, Subject Specialist Mathematics, Govt Christian High School Daska
📌 Based on National Curriculum 2023 / PECTAA 2026 Syllabus
📖 What's Inside: This exercise covers making a variable the subject of a formula – rearranging linear, quadratic, and geometric formulas to solve for a specific variable. Perfect for Punjab Boards exam preparation.
📚 Related Resources – Unit 2: Quadratic Equations & Inequalities
Class 10 Math Unit 2 Exercise 2.6 – Changing the Subject: Complete Guide
Exercise 2.6 of Unit 2 introduces the important skill of changing the subject of a formula. Students learn to rearrange formulas to make a specific variable the subject. This skill is essential for solving problems in physics, chemistry, economics, and other fields where formulas need to be rearranged.
What You Will Learn
By working through Exercise 2.6, students master: making a variable the subject of a formula using inverse operations, rearranging linear formulas (e.g., \( y = mx + c \)), rearranging geometric formulas (e.g., volume of cylinder, area of trapezoid), and rearranging formulas with powers and fractions.
Topics Covered in This Exercise
- Temperature Conversion – making \( F^\circ \) the subject
- Simple Interest – making \( P \) and \( T \) the subject
- Arithmetic Sequences – making \( a \) the subject
- Cylinder Volume – making \( h \) the subject
- Trapezoid Area – making \( h \) the subject
- Linear Equations – making \( x \) the subject
- Rectangle Perimeter – making \( l \) the subject
- Parabola Equation – making \( x \) the subject
- Profit Formula – making \( S \) the subject
- Cone Volume – making \( h \) the subject
Why Exercise 2.6 Is Important
Exercise 2.6 builds essential algebraic manipulation skills. Board exam papers frequently feature questions on rearranging formulas. This exercise helps students understand the relationship between variables in formulas.
Punjab Board Preparation
Students preparing for board exams under any of the 10 BISE Punjab boards should prioritise this exercise. Changing the subject of a formula is a frequently tested topic. Practising every question by hand is highly recommended.
Exam Tips for Changing the Subject
- Identify the variable you want to make the subject.
- Use inverse operations to isolate the variable.
- Work from the outside in – undo addition/subtraction first, then multiplication/division.
- Check your answer by substituting values into the original and rearranged formulas.
Common Mistakes Students Make
- Not applying inverse operations correctly.
- Forgetting to perform the same operation on both sides.
- Making sign errors when moving terms.
- Not simplifying the final answer.
📖 Exercise 2.6 – Solved Problems
1 Make \(F\) the subject of the formula, \(C^\circ = \frac{5}{9}(F^\circ - 32)\).
\[
\begin{aligned}
C^\circ &= \frac{5}{9}(F^\circ - 32) \\
C^\circ \cdot \frac{9}{5} &= F^\circ - 32 \\
\frac{9C^\circ}{5} + 32 &= F^\circ \\
\boldsymbol{F^\circ} &= \boldsymbol{\frac{9C^\circ}{5} + 32}
\end{aligned}
\]
✅ \(F^\circ = \frac{9C^\circ}{5} + 32\)
2 The formula for finding simple interest is \(I = PRT\).
(a) Make \(P\) the subject of the formula.
\[
\begin{aligned}
I &= PRT \\
\frac{I}{RT} &= P \\
\boldsymbol{P} &= \boldsymbol{\frac{I}{RT}}
\end{aligned}
\]
(b) Make \(T\) the subject of the formula.
\[
\begin{aligned}
I &= PRT \\
\frac{I}{PR} &= T \\
\boldsymbol{T} &= \boldsymbol{\frac{I}{PR}}
\end{aligned}
\]
3 Make \(a\) the subject of the formula \(S = 2a + (n-1)d\).
\[
\begin{aligned}
S &= 2a + (n-1)d \\
S - (n-1)d &= 2a \\
\frac{S-(n-1)d}{2} &= a \\
\boldsymbol{a} &= \boldsymbol{\frac{S-(n-1)d}{2}}
\end{aligned}
\]
4 The volume of a cylinder is given by the formula \(V = \pi r^2 h\). Make \(h\) the subject of the formula.
\[
\begin{aligned}
V &= \pi r^2 h \\
\frac{V}{\pi r^2} &= h \\
\boldsymbol{h} &= \boldsymbol{\frac{V}{\pi r^2}}
\end{aligned}
\]
5 The area of a trapezoid is \(A = \frac{1}{2}h(b_1 + b_2)\), make \(h\) the subject of the formula.
\[
\begin{aligned}
A &= \frac{1}{2}h(b_1+b_2) \\
2A &= h(b_1+b_2) \\
\frac{2A}{b_1+b_2} &= h \\
\boldsymbol{h} &= \boldsymbol{\frac{2A}{b_1+b_2}}
\end{aligned}
\]
6 If \(y = mx + c\), then make \(x\) the subject of this equation.
\[
\begin{aligned}
y &= mx + c \\
y - c &= mx \\
\frac{y-c}{m} &= x \\
\boldsymbol{x} &= \boldsymbol{\frac{y-c}{m}}
\end{aligned}
\]
7 Perimeter \((P)\) of a rectangle is \(P = 2(l + w)\), make \(l\) as the subject of this formula.
\[
\begin{aligned}
P &= 2(l+w) \\
P &= 2l+2w \\
P+2w &= 2l \\
\frac{P+2w}{2} &= l \\
\boldsymbol{l} &= \boldsymbol{\frac{P+2w}{2}}
\end{aligned}
\]
8 The equation of a parabola is \(y^2 = 4ax\), make \(x\) as a subject of this equation.
\[
\begin{aligned}
y^2 &= 4ax \\
\frac{y^2}{4a} &= x \\
\boldsymbol{x} &= \boldsymbol{\frac{y^2}{4a}}
\end{aligned}
\]
9 If \(P = S - C\), where \(S\) is selling price and \(C\) is cost price. Make \(S\) as subject of the equation.
\[
\begin{aligned}
P &= S - C \\
P+C &= S \\
\boldsymbol{S} &= \boldsymbol{P+C}
\end{aligned}
\]
10 Volume of the cone is \(V = \frac{1}{3}\pi r^2 h\), make \(h\) as subject of this formula.
\[
\begin{aligned}
V &= \frac{1}{3}\pi r^2 h \\
3V &= \pi r^2 h \\
\frac{3V}{\pi r^2} &= h \\
\boldsymbol{h} &= \boldsymbol{\frac{3V}{\pi r^2}}
\end{aligned}
\]
📝 Multiple Choice Questions (Unit 2 Review)
1. If \(C^\circ = \frac{5}{9}(F^\circ - 32)\), then \(F^\circ =\)
✅ Correct Answer: (A) \(\frac{9C^\circ}{5} + 32\)
\(C = \frac{5}{9}(F-32) \implies F = \frac{9C}{5} + 32\).
\(C = \frac{5}{9}(F-32) \implies F = \frac{9C}{5} + 32\).
2. In \(I = PRT\), making \(T\) the subject gives:
✅ Correct Answer: (A) \(T = \frac{I}{PR}\)
\(I = PRT \implies T = \frac{I}{PR}\).
\(I = PRT \implies T = \frac{I}{PR}\).
3. From \(V = \pi r^2 h\), making \(h\) the subject gives:
✅ Correct Answer: (A) \(h = \frac{V}{\pi r^2}\)
\(V = \pi r^2 h \implies h = \frac{V}{\pi r^2}\).
\(V = \pi r^2 h \implies h = \frac{V}{\pi r^2}\).
4. In \(A = \frac{1}{2}h(b_1+b_2)\), making \(h\) the subject gives:
✅ Correct Answer: (A) \(h = \frac{2A}{b_1+b_2}\)
\(A = \frac{1}{2}h(b_1+b_2) \implies h = \frac{2A}{b_1+b_2}\).
\(A = \frac{1}{2}h(b_1+b_2) \implies h = \frac{2A}{b_1+b_2}\).
5. From \(V = \frac{1}{3}\pi r^2 h\), making \(h\) the subject gives:
✅ Correct Answer: (A) \(h = \frac{3V}{\pi r^2}\)
\(V = \frac{1}{3}\pi r^2 h \implies h = \frac{3V}{\pi r^2}\).
\(V = \frac{1}{3}\pi r^2 h \implies h = \frac{3V}{\pi r^2}\).
📈 Key Concepts – Changing the Subject
- Goal: Isolate the required variable on one side of the equation.
- Inverse Operations: Use addition/subtraction, multiplication/division, and powers/roots to rearrange.
- Order of Operations: Work from the outside in – undo addition/subtraction first, then multiplication/division.
- Check: Verify by substituting a simple value into the original and rearranged formulas.
- Common Formulas: Temperature conversion, simple interest, cylinder volume, trapezoid area, linear equations, rectangle perimeter, parabola, profit, cone volume.
❓ Frequently Asked Questions
What is taught in Exercise 2.6 of Class 10 Math Unit 2?
Exercise 2.6 covers making a variable the subject of a formula – rearranging linear, quadratic, and geometric formulas to solve for a specific variable. It includes formulas from temperature conversion, simple interest, arithmetic sequences, cylinder volume, trapezoid area, linear equations, rectangle perimeter, parabola, profit, and cone volume.
How many questions are there in Unit 2 Exercise 2.6?
Exercise 2.6 has 10 questions covering making different variables the subject of various formulas including temperature conversion, simple interest, arithmetic sequences, cylinder volume, trapezoid area, linear equations, rectangle perimeter, parabola, profit, and cone volume.
What does 'making a variable the subject' mean?
Making a variable the subject means rearranging a formula so that the variable appears on its own on one side of the equation. This is done using inverse operations to isolate the required variable.
What are the steps to change the subject of a formula?
The steps are: 1) Identify the variable to make the subject, 2) Use inverse operations to isolate it, 3) Work from the outside in – undo addition/subtraction first, then multiplication/division, 4) Check the result by substituting values.
Is this solution according to the PECTAA 2026 syllabus?
Yes, these solutions are prepared according to the PECTAA 2026 / National Curriculum 2023 syllabus for Class 10 Mathematics.
Is this Exercise 2.6 solution valid for all Punjab Boards?
Yes, the content follows the unified Punjab textbook and is applicable to students of all 10 BISE Punjab boards.
Are solved PDF notes available for Exercise 2.6?
Yes, a complete solved PDF for Exercise 2.6 is embedded on this page and available to download for free.
Can I download the Unit 2 Exercise 2.6 solution as a PDF?
Yes, use the Download PDF button on this page to save the complete solved Exercise 2.6 notes to your device.
Is Exercise 2.6 important for Class 10 board exams?
Yes, changing the subject of a formula is frequently tested in board exams. Exercise 2.6 builds essential skills in algebraic manipulation and rearranging formulas.
Who prepared these Class 10 Math Unit 2 notes?
These notes were prepared by Muhammad Tayyab, Subject Specialist Mathematics at Govt Christian High School Daska, for Hira Science Academy.