Quadratic equations – Year 11 maths lesson
Lesson 11 of 17 in the Year 11 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 11 (ages 15–16) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 11 (ages 15–16)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “What does the discriminant tell you before you solve?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Only giving one solution. Set each factor to zero: there are usually two.
- Getting the signs wrong in the formula. Write a, b and c down with their signs first.
Tip for home: Talk about the path of a thrown ball as a quadratic curve.
What your child will learn
We are learning to solve quadratic equations by factorising, the formula and completing the square.
Success looks like
- I can solve by factorising.
- I can use the quadratic formula.
- I can complete the square.
Key words
- quadratic
- with x² as the highest power
- root
- a solution of the equation
- discriminant
- b² − 4ac, which tells how many solutions
- turning point
- the highest or lowest point of the curve
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use a graph-plotting app or table of values to see where y = x² − 4 crosses the x-axis.
The big ideas (for the adult)
A quadratic equation has an x² term. Rearrange to = 0, factorise, then set each bracket to zero: (x − 2)(x + 5) = 0 gives x = 2 or x = −5.
When it will not factorise, use the quadratic formula: x = (−b ± √(b² − 4ac)) / 2a.
Completing the square writes x² + bx + c as (x + b/2)² + k, which also shows the turning point of the graph.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 11 maths lessons
- Volume and surface area
- Trigonometry: SOH CAH TOA
- Sine rule, cosine rule and area of a triangle
- Transformations
- Similarity and congruence
- Vectors
- Circle theorems
- Factorising
- Inequalities
- Sequences and the nth term
- Iteration
- Functions
- Algebraic fractions
- Graphs of functions
- Algebraic proof and identities
- Growth and decay
Curriculum
National Curriculum for England, Year 11: “solve quadratic equations {including those that require rearrangement} algebraically by factorising, {by completing the square and by using the quadratic formula}; find approximate solutions using a graph”
National Curriculum for England, Year 11: “identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square}”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.