Quadratic equations – Year 10 maths lesson
Lesson 30 of 37 in the Year 10 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 10 (ages 14–15) 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 10 (ages 14–15)
- 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 10 maths lessons
- Systematic listing and counting
- Standard form
- Laws of indices
- Surds
- Fractions, decimals and recurring decimals
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Vectors
- Circle theorems
- Bearings
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Histograms
- Pie charts and time series graphs
- Scatter graphs and correlation
- Sampling
- Combined events and tree diagrams
- Simplifying expressions
- Expanding brackets
- Factorising
- Solving linear equations
- Inequalities
- Sequences and the nth term
- Straight-line graphs
- Simultaneous equations
- Functions
- Graphs of functions
- Algebraic proof and identities
- Growth and decay
- Direct and inverse proportion
- Scale drawings and maps
- Rates of change from graphs
Curriculum
National Curriculum for England, Year 10: “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 10: “identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square}”
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Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.