Rearrange and evaluate simple formulas
Make a singly occurring variable the subject · Substitute signed values with parentheses · Identify division conditions
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Linear equation operations
- Order of calculation
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Make a singly occurring variable the subject
- Substitute signed values with parentheses
- Identify division conditions
Undo operations around the subject
To make a variable the subject, perform inverse operations on both sides. In p = rt−q, add q then divide by t: r = (p+q)/t, provided t ≠ 0. Use parentheses to show that the entire sum is divided.
For w = (r−t)/y with y ≠ 0, multiply by y then add t: r = wy+t. If a rearrangement requires division by a quantity that could be zero, check that case separately.
Substitute before calculating
For xy² at x = −3 and y = 4, the value is (−3)×4² = −48. For (xy)² it would be 144: parentheses specify different expressions. Match the requested units and state any needed non-zero dimensions.
Sources for this lesson
Pause and explain
In p = rt−q, what is r when t ≠ 0?
Worked example
For V = lwh, make w the subject; evaluate at V = 60, l = 5 and h = 3.
Show the worked solution
- Divide both sides by lh, assumed non-zero: w = V/(lh).
- w = 60/(5×3) = 4.
Answer w = V/(lh), lh ≠ 0; numerical value 4.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Make x the subject of y = 4x+3.
Give me a hint
Subtract 3 before dividing.
Compare my reasoning
- y−3 = 4x.
- x = (y−3)/4.
x = (y−3)/4.
Look for these in your work
- Operate on both sides
- Use brackets
Evaluate ab² when a = −2 and b = −3.
Give me a hint
Only b is squared.
Compare my reasoning
- (−3)² = 9.
- (−2)×9 = −18.
−18.
Look for these in your work
- Substitute with parentheses
- Respect exponent placement
The perimeter of a rectangle is P = 2l+2w. Make w the subject; find w when P = 34 cm and l = 10 cm.
Give me a hint
Isolate the entire 2w term.
Compare my reasoning
- w = (P−2l)/2.
- w = (34−20)/2 = 7 cm, a positive feasible length.
w = (P−2l)/2; 7 cm.
Look for these in your work
- Rearrange before substitution
- Check physical feasibility
Common mistakes
- Divide the whole numerator, not its last term.
- Do not silently divide by zero.
What can you explain now?
In p = rt−q, what is r when t ≠ 0?
Compare with the explanation
(p+q)/t.
Add q before dividing the full result by t.
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Make it stick
In p = rt−q, what is r when t ≠ 0?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.