Skip to main content
MathidiaMathematics Academy
GCSE synthesis and exam readiness
Lesson 73 of 75
Standard practice

Multi-topic problem solving

Objective. Connect algebra, geometry, proportion and data in unfamiliar settings.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Multi-topic problem solving connects algebra, geometry, proportion and data skills within a single unfamiliar question, requiring you to identify which techniques apply before starting any calculation. Read the whole problem first, underline given values and the actual question asked, then plan a sequence of smaller familiar steps that together reach the solution. Unfamiliar wording often hides a standard technique, such as similar triangles disguised as a shadow-and-height scenario, or ratio disguised as a mixing problem. For a problem mixing paint in ratio 3:2 then scaling for a larger area, first solve the ratio, then apply proportional reasoning to the new total. Breaking an unfamiliar problem into known sub-problems is the key strategy.

Worked example

A ladder 5 m long leans against a wall reaching a height of 4 m. A similar, larger ladder reaches a height of 12 m. Find the length of the larger ladder.

5 … 4
Illustrated card showing 5 … 4
  1. 1Scale factor = 12 ÷ 4 = 3
  2. 2Ladders are similar, so apply the same scale factor to length
  3. 3Larger ladder length = 5 × 3
  4. 4Larger ladder length = 15 m

Answer: 15 m

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Students often attempt an unfamiliar multi-topic problem by guessing a single formula immediately, rather than identifying the smaller known sub-problems hidden within it, leading to an incomplete or wrong approach.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard