Level 4 · Mathematics M4.9
Quadratics
Expand, factorise and solve quadratic equations, and draw their curved graphs.
Planned. This book is not written yet. Below is its plan, which a teacher can already use.
You are ready for this book if
You can expand 3(x + 4) and factorise 6x + 9.
- One step up M5.1 Functions, polynomials and the binomial
- This book M4.9 Quadratics
- One step down M3.9 Coordinates and straight lines
The plan
- M4.9.1 Expanding two brackets
- Expand (x + 3)(x − 5)
- Expand (2x + 1)² without losing the middle term
- M4.9.2 Factorising quadratics
- Factorise x² + 7x + 12
- Factorise a difference of two squares, like x² − 49
- Factorise 2x² + 7x + 3
- M4.9.3 Using factorising
- Solve x² − 5x + 6 = 0 by factorising
- Explain why ab = 0 means a = 0 or b = 0
- Simplify (x² − 9)/(x + 3) by factorising
- M4.9.4 Completing the square
- Write x² + 6x + 2 as (x + 3)² − 7
- Solve a quadratic by completing the square
- M4.9.5 The quadratic formula
- Solve any quadratic equation with the formula
- Use b² − 4ac to say how many solutions there are
- Form and solve a quadratic from an area problem
- M4.9.6 Graphs of quadratics
- Draw y = x² − 2x − 3 from a table of values
- Find the roots, turning point and y axis crossing from a graph
- M4.9.7 Quadratic sequences
- Use second differences to spot a quadratic sequence
- Find the nth term of a sequence like 2, 6, 12, 20
- M4.9.8 A line and a curve
- Solve a linear and a quadratic equation together
- Solve a quadratic inequality like x² < 9
For parents and teachers
Level 4 fits learners who can already: follow a written argument. use letters for numbers. In many schools that is about 14 to 16, but start wherever the learner is.
Strand: Algebra. Written and drawn by attnom. Free to read, print and share.