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Students learn how to solve a range of quadratic equations using factorisation, applying the formula and completing the square. Learning progresses from solving equations to deriving and sketching quadratics as a graph.

This unit takes place in Year 11 Term 1 and follows on from solving linear and simultaneous equations.

- Simplify and manipulate algebraic expressions by:
- Expanding products of two or more binomials
- Factorising quadratic expressions of the form x
^{2}+ bx + c, including the difference of two squares - Simplifying expressions involving sums, products and powers, including the laws of indices
- Factorising quadratic expressions of the form ax
^{2}+ bx + c.

- Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs
- Simplify and manipulate algebraic expressions by factorising quadratic expressions of the form ax
^{2}+ bx + c. - Understand and use standard mathematical formulae; rearrange formulae to change the subject
- Identify and interpret roots, intercepts, turning points of quadratic functions graphically
- Deduce roots algebraically and turning points by completing the square
- Recognise, sketch and interpret graphs of quadratic functions
- 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
- Solve two simultaneous equations in two variables linear/quadratic algebraically; find approximate solutions using a graph

- Check brackets have been factorised correctly by multiplying them back out.
- To solve quadratics by factorising students need to identify two numbers that have a product of c and a sum of b. Roots are found when each bracket is made to equal zero and are solved for x.
- When a quadratic cannot be solved by factorising students should use completing the square or the quadratic formula.
- Students should be able to derive the quadratic formula from the method of completing the square.
- A sketched graph is drawn freehand and includes the roots, turning point and intercept values.
- Quadratic identities in the form (x + a)
^{2}+ b ≡ ax^{2}+ bx + c can be solved either through completing the square to RHS = LHS or by expanding the brackets to LHS = RHS and equating the unknowns. - Quadratic and linear simultaneous equations should be sketched before solved algebraically to ensure students know to find and the x and y values.

- The method of trial and improvement is often incorrectly used to try and solve quadratics.
- When solving quadratic and linear simultaneous equations students often forget to find the y values as well the x.
- When using the formula to solve quadratics students often forget to evaluate the negative solution. Some students also incorrectly apply the division by reducing the terms it covers.
- Students tend to struggle deriving quadratic equations from geometrical facts.

July 6, 2019

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

June 24, 2019

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out. This is presented to the class as they come into the lesson. Writing Equivalent Ratios A few students immediately go […]