Algebra and Functions
Algebra and Functions tests whether you can use letters to stand for quantities, substitute into formulas, solve simple linear equations and read linear graphs in context. Expect practical formulas such as cost, pay, distance, temperature or mobile-phone plans.
Core rules
- Substitute carefully: replace each letter with its value and use brackets.
- Solve linear equations by doing the same operation to both sides; aim to isolate the unknown.
- A linear function y = mx + c has gradient m (rate of change) and intercept c (fixed starting value).
- Check by substituting your answer back into the original equation.
- Keep units with the answer and interpret what the numbers mean.
Worked example
A phone plan costs €20 per month plus €0.10 per minute. (a) Find the cost for 150 minutes. (b) Find the minutes used if the bill is €35. (a) Cost = 20 + 0.10 × 150 = 20 + 15 = €35. (b) Let m = minutes. 20 + 0.10m = 35. Subtract 20: 0.10m = 15. Divide by 0.10: m = 150 minutes. The fixed charge is the intercept (20); the cost per minute is the gradient (0.10).
Traps that cost marks
- Forgetting the fixed charge when working backwards from a total.
- Dividing by 0.10 incorrectly; 15 ÷ 0.10 = 150, not 1.5.
- Mixing cents and euro.
- Reading a graph's intercept as the gradient, or ignoring the scale on the axes.