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MathidiaMathematics Academy
Year 12 synthesis
Lesson 71 of 75
Introduction

Pure mathematics synthesis

Objective. Select and connect algebra, functions, trigonometry and calculus.

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

Learn: the key idea

Pure mathematics synthesis means combining algebra, functions, trigonometry and calculus within a single multi-step problem, recognising which technique unlocks each stage. For example, finding a stationary point on a trigonometric function might require differentiating using the chain rule, setting the derivative to zero, then solving the resulting trigonometric equation over a given interval. Success depends on correctly identifying the structure of the problem first, then applying each relevant method in the right order, checking units and domains throughout.

Worked example

Find the x-coordinate of the stationary point of y=x²−6x+5 as a pure mathematics synthesis exercise combining algebra and calculus.

6 … 5
Coordinate grid with the line 6 … 5
  1. 1Differentiate: dy/dx=2x−6
  2. 2Set the derivative equal to zero for a stationary point
  3. 32x−6=0
  4. 4x=3

Answer: x=3

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 apply only the most recently learned technique to every synthesis problem, even when it does not fit. Always identify the mathematical structure of the problem before choosing which combined techniques to apply.

Your progress

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