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**Scheme of work: GCSE Higher: Year 11: Term 1: Mathematical Proof**

- Know the difference between an equation and an identity;
- 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 apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

- Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagorasâ€™ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs.
- Argue mathematically to show algebraic expressions are equivalent and use algebra to support and construct arguments and proofs.
- Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results.
- Use vectors to construct geometric arguments and proofs.

- Know the difference between an equation and an identity;
- 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 apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment
- Parallel lines have vectors that are multiples of each other.

- A common incorrect approach is to attempt to prove an algebraic and geometrical property through numerical demonstrations.
- Students often struggle to generalise the rules of arithmetic to produce a reasoned mathematical argument.
- Some students expand brackets incorrectly when proving a quadratic identity.
- Students often lose marks when attempting to prove geometrical properties due to not connecting the various angle properties.
- Incorrect application of ratio notation leads to difficulty when proving geometrical properties.
- Students often fail to label vector diagrams sufficiently to identify known paths.
- Providing a proof of geometrical facts tends to separate the most able from the majority.

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