Solving quadratics and completing the square
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 2 worked examples, 5 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Three ways in
- Factorising
Read the transcript of the teaching part
Last time
Before we start: last time, in Composite and inverse functions, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Three ways in
A ball is thrown, a field is fenced, a profit is optimised. All of them lead to a quadratic equation. You have three tools: factorising, the formula, and completing the square. Today you will see when each one wins.
Factorising
First, get everything on one side so it equals zero. Find two numbers that multiply to six and add to minus five. They are minus two and minus three. If a product is zero, one factor is zero. So x is two or x is three. Never divide through by x. You lose a root.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Completing the square.
The whole chapter: Quadratic Functions.
Chapter 2: Quadratic functions
- Solving quadratics and completing the square 5 min
- The discriminant, a line and a curve 6 min
- Quadratic inequalities 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.