A-Level Maths - Core/Pure 1

- A-Level Maths PURE/CORE 1
- 1.1 Rational Indices Law
- 1.2 Surds
- 1.3 Four rules with Polynomials
- 1.4 Factorising Polynomials
- 1.5 Identities
- 1.6 Algebraic Division
- 1.7 Factor Theorem
- 1.8 Complete Square Quad. Functs. & graphs
- 1.9 Square form of quadratic equation
- 1.10 Solve quad. equ FACTORISE, SQUARE or FORMULA
- 1.11 Solving 2 simult. equ. Linear and quad
- 1.12 Inequals. Linear and quad solving
- 2.1 Radian measures
- 2.2 Radian Arc Lengths
- 2.3 Radian Area of Sector
- 2.4 Trig in 4 quadrants
- 2.5 Drawing graphs of Sinx Cosx Tanx
- 2.6 Trig Identities SIN^2 COS^2=1 solving trig equ
- 2.7 Gradients, straight & parallel lines
- 3.1 nth term sequences
- 3.2 Arithmetic Sequences and Series
- 3.3 Geometric Series

ax^2 + bx +c = 0 Divide all terms by a so as to reduce the coefficient of x^2 to 1 x^2 +b/a x + c/a=0 Subtract the constant term from both sides of the equation x^2+b/a x = - c/a To have a square on the left side the third term (constant) should be (b/(2a))^2 So add that amount to both sides x^2 +b/a x +(b/(2a))^2 = (b/(2a))^2 - c/a Re-write the left-side as a square (x+(b/(2a)))^2 = (b/(2a))^2 -c/a Take the square root of both sides (remembering that the result could be plus or minus) x+(b/(2a)) = +-sqrt((b/(2a))^2 -c/a) Subtract the constant term on the left side from both sides x = +-sqrt((b/(2a))^2 -c/a) - (b/(2a)) or, with some simplification x= (-b+-sqrt(b^2-4ac))/(2a) (the standard form for solving a quadratic)

Completing the square is a useful technique for solving quadratic equations. It is a more powerful technique than factorisation because it can be applied to equations that do not factorise.

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