Algebra: Formulas, Equations and Linear Relationships
What you must understand
Algebra in Standard 2 is about using formulas and linear models rather than symbolic manipulation. You need to substitute values into formulas, rearrange a formula to make a variable the subject, solve linear equations, and read and build linear relationships of the form y = mx + b, where m is the gradient and b the y-intercept. You should also be able to work with simultaneous linear equations by substitution or elimination, and interpret the point of intersection as the solution satisfying both conditions.
Traps to watch
- Order of operations and negatives: substituting a negative value into a formula requires brackets, e.g. x² when x = −3 is 9, not −9.
- Rearranging: whatever you do to one side you must do to the other; undo operations in reverse order. A common error is dividing only one term of a sum.
- Gradient sign and meaning: a negative gradient means the quantity is decreasing, not that the calculation is wrong.
- Units: if a formula uses time in hours, convert minutes before substituting.
- Rounding too early: keep full calculator values until the final answer.
Worked example
The cost C of hiring a machine is C = 45h + 80, where h is hours. Find the time when C = 350. Solve 45h + 80 = 350, so 45h = 270 and h = 6 hours. Check: 45(6) + 80 = 350. ✓
Rule of thumb
Always substitute, then solve, then check by putting your answer back into the original formula. If the question asks for a variable to be the subject, isolate it step by step and test with simple numbers.