I85PREP
⌘ K
CCSLC Mathematics study materials
CCSLC Mathematics study resources

CCSLC Mathematics: Problem Solving

CCSLC Mathematics · Work through your exam, one topic at a time.

All guide sections

Problem Solving

Problem Solving in CCSLC Mathematics is tested through questions that describe a situation rather than an equation. The arithmetic is familiar; the difficulty is deciding what to do first, keeping several quantities straight, and knowing when the answer is actually finished. Marks are awarded for clear method as well as for the final value, so set out each stage on its own line with its unit attached.

A routine that works under pressure

  1. Understand: restate the task in your own words - "find the greatest number of kilometres that keeps the total under EC$1,500".
  2. Plan: list the quantities, mark which are fixed and which repeat, and decide the order of operations.
  3. Do: one calculation per line, carrying units through.
  4. Look back: estimate the size of the answer and substitute it back into the situation.

Strategies worth practising

  • Work backwards when the end result is given: undo each operation in reverse order.
  • Draw a diagram for routes, shared quantities, angles and mixtures.
  • Build a table when the same calculation repeats - instalments, hours, rates.
  • Try a simpler case with smaller numbers to expose the structure, then scale up.
  • Write an equation when a value is unknown and solve it rather than guessing.

Worked example

A van costs EC$150 per day plus EC$2.40 per kilometre. A group rents it for 3 days and has EC$1,500. How far can they travel? Fixed cost: 3 × 150 = EC$450. Money left for distance: 1,500 − 450 = EC$1,050. Kilometres: 1,050 ÷ 2.40 = 437.5. Each whole kilometre costs EC$2.40 and the budget cannot be exceeded, so they can travel 437 km; 438 km would cost 450 + 1,051.20 = EC$1,501.20. Check: 450 + 437 × 2.40 = 450 + 1,048.80 = EC$1,498.80, which is inside the budget.

Traps that cost marks

  • Charging a daily or one-off fee more than once.
  • Mixing units: minutes with hours, metres with kilometres, cents with dollars.
  • Rounding up when the context demands rounding down - complete packs, affordable kilometres, whole people.
  • Solving only the first part of a two-part question.
  • Giving a bare answer with no working, so method marks cannot be earned.