Module 3 of 6 · MA4-EQU-C-01
Formulas & substitution
Solve equations arising from substitution into formulas
01
Substitute, then solve
A formula is just an equation waiting for numbers. Put in every value you were given, and what's left is an ordinary equation in one pronumeral — solve it exactly the way you solved the ones in Module 1.
02
Substitute carefully with negatives
Always write brackets around a value you substitute, especially a negative one. In v = u + at with a = −3 and t = 4, write u + (−3)(4), not u − 34.
03
Squares give two answers
If x² = 25 then x = 5 or x = −5, because both squares give 25. Write x = ±5. In area and length problems you then reject the negative one, because a length can't be negative — but say so.
04
Exact form and decimals
If x² = 5 the exact answer is x = ±√5. Your calculator gives ≈ ±2.24. The syllabus wants both, so give the exact form first and the rounded decimal after.
The rules to know by heart
- A = l × warea of a rectangle
- A = ½bharea of a triangle
- A = πr²area of a circle
- P = 2(l + w)perimeter of a rectangle
- v = u + atfinal speed from starting speed, acceleration and time
- C = (5/9)(F − 32)Fahrenheit to Celsius
See it work
Try it — change the numbers and watch the equation change
the formula
v = u + atsubstitute what you know
29 = 5 + (4)tsolve, step 1
29 − 5 = (4)tsolve, step 2
24 = 4tanswer
t = 6
A worked example
Use the formula v = u + at. If v = -22, u = 18 and a = -5, find t.
v = u + atWorked solution
- v = u + at
Every line has its reason in brackets. In the test, that bracket is worth marks on its own — write it even when the number feels obvious.
Words for this module
Formula
A rule written as an equation connecting quantities, such as A = l × w.
Watch out: Substitute values in brackets, especially negatives: v = u + (−3)(4).
Substitution
Replacing a pronumeral with a given number, then evaluating.
Watch out: Also how you *check* an answer: put it back in and see if LHS = RHS.
ready?
Practise until you get five in a row.