Sec 2 G3 Maths Bukit Timah | Changing Formula Subject

Secondary 2 G3 Mathematics Tutor Bukit Timah | Changing the Subject of a Formula — Did you know? Rearranging a formula is not about magically moving letters across an equals sign. It is about keeping the same relationship true while making a different letter stand alone.

Quick answer: how do I change the subject of a formula?

The subject is the letter isolated on one side of an equation. To change it, undo the original operations with inverse operations applied to both sides: addition versus subtraction, multiplication versus division, then powers versus roots as needed. Check the rearranged formula by putting known values back into the original.

I find it useful to ask students: ‘What operation is being done to the letter right now?’ Once they can say that, the inverse step stops feeling like an arbitrary rule.

What is a formula subject?

Consider A = bh, where A represents area, b represents base and h represents height. In this equation, A is the subject because it stands alone. If the question says make h the subject, divide both sides by b to obtain h = A/b when b ≠ 0.

Nothing physical has changed. The area, base and height still describe the same rectangle. We have simply rearranged the equation to calculate another unknown.

Original formula	Required subject	Correct arrangement
A = bh	h	h = A/b, b ≠ 0
P = 2l + 2w	l	l = (P − 2w)/2
y = 3x − 4	x	x = (y + 4)/3
v = u + at	a	a = (v − u)/t, t ≠ 0

Worked example 1: make the triangle’s height the subject

Question: A = ½bh. Make h the subject.

Multiply both sides by 2, giving 2A = bh.
Divide both sides by b, giving h = 2A/b, where b is not zero.
Try A = 24 cm² and b = 8 cm: h = 48/8 = 6 cm.
Check in the original equation: ½ × 8 × 6 = 24 cm².

Did you know? Testing a formula using a simple number pair is one of the fastest ways to catch a missed fraction. That check also teaches the student the meaning of each variable.

Worked example 2: rearrange a formula containing a fraction

Question: Given y = (3x − 4)/5, make x the subject.

Multiply by 5: 5y = 3x − 4.
Add 4: 5y + 4 = 3x.
Divide by 3: x = (5y + 4)/3.
Check with y = 1: x = (5 + 4)/3 = 3. In the original, (3 × 3 − 4)/5 = 1.

The brackets around (5y + 4) matter. The entire expression is divided by 3. Writing 5y + 4/3 describes a different relationship.

Worked example 3: a squared variable

Question: Volume of a cylinder is V = πr²h. Make the radius r the subject, for positive height h and non-negative radius r.

Divide both sides by πh to isolate r²: r² = V/(πh).
Take the non-negative square root: r = √(V/(πh)).
For a check, take r = 3 cm, h = 2 cm and V = 18π cm³.
The new expression gives √(18π/(2π)) = √9 = 3 cm.

Mathematically, if x² = 9 then x could be 3 or −3. In this real-life formula, the radius is a non-negative length. The situation determines which mathematical result is physically meaningful.

Worked example 4: temperature conversion

The relationship between Fahrenheit F and Celsius C is F = (9/5)C + 32. To make C the subject, first subtract 32 from both sides and then multiply by 5/9.

The result is C = 5(F − 32)/9. For 68°F, this gives C = 5(68 − 32)/9 = 20°C. Check the original: (9/5) × 20 + 32 = 68.

Five mistakes students should catch

Changing only one side of the equation: the operation must preserve equality.
Dividing one term of a sum: place the entire sum in brackets if required.
Losing a minus sign: test with friendly values to detect the error.
Ignoring zero denominators: state restrictions where division by a variable is involved.
Taking a square root without thinking: identify whether the quantity is a physical length or an abstract number.

Try these four quick questions

A. Make x the subject of y = 4x + 7. Answer: x = (y − 7)/4.

B. Make w the subject of P = 2l + 2w. Answer: w = P/2 − l.

C. Make x the subject of k = (x + 2)/3. Answer: x = 3k − 2.

D. Make h the subject of V = πr²h. Answer: h = V/(πr²), where r ≠ 0.

The 12-minute revision routine

Three minutes: name the subject in four formulas.
Three minutes: rearrange two equations requiring one inverse operation.
Three minutes: rearrange one fraction and one expression containing brackets.
Three minutes: independently check both answers by substitution.

For exam questions, the heading may not tell the student that this is ‘changing the subject’. Ask the learner to identify the required quantity first. The goal is recognising the mathematical task rather than recalling a particular line from notes.

How can a Secondary 2 G3 Mathematics tutor help?

In a three-student tutorial, I would first give each learner a new formula with no hints. One may struggle with signed numbers, another with brackets, and a third with square roots. A good tutor finds the first unsupported move rather than giving all three the same extra worksheet.

The unchanged eduKateSG small-group Mathematics teaching reference describes premium three-pupil tutorials of about 1.5 hours weekly, with guided corrections and first-principles explanations. The published address is 8 Fourth Avenue, Singapore 268674, near Sixth Avenue MRT. Bukit Timah identifies families this guide serves, not a newly claimed branch. Please verify current Secondary 2 G3 class placement and vacancies.

How does this fit Singapore G3 Mathematics?

Under Full Subject-Based Banding, G3 refers to a subject level. A Secondary 2 student should follow the chapters and weighted assessment dates set by their school. The MOE G2/G3 Mathematics syllabus provides broader context; the school-based Secondary 2 Mathematics chapter guide shows one example of topic ordering.

The 2027 SEC G3 syllabus index is useful for later progression, but the full upper-secondary national examination topics are not all expected in a Secondary 2 school test.

What happens during a small-group lesson?

An illustrative 90-minute approach uses ten minutes of retrieval, fifteen minutes reviewing an unassisted mistake, twenty minutes learning the principle, twenty-five minutes practising changed formulas, fifteen minutes comparing explanations and five minutes setting a follow-up check. The timing is an illustration, not a fixed lesson promise.

Parent FAQ: Why does my child keep saying ‘move it to the other side’?

That phrase can conceal uncertainty about inverse operations. Ask ‘Which operation are you undoing?’ and ‘What happens to both sides?’ If the answer is unclear, the child may need another foundation example before a harder question.

Parent FAQ: Can rearranging a formula improve word problems?

Yes. Identifying what a quantity represents and isolating it is useful in geometry, rates, science and finance. The student should also check any units and restrictions rather than treating algebra as disconnected letter manipulation.

Programme details and references

The unchanged original is eduKateSG Secondary 1 Mathematics small-group tutorials. For subject context, see MOE’s G2/G3 Mathematics syllabus and a Secondary 2 school Mathematics chapter guide.

To enquire about Secondary 2 G3 Mathematics classes convenient to Bukit Timah, contact eduKate Singapore or ask about a parent–student consultation on WhatsApp.

Editorial review: 24 October 2026. All worked Mathematics examples are original educational illustrations; school topic sequencing and current centre arrangements should be confirmed.