A-Level Maths - Core/Pure 1

- A-Level Maths PURE/CORE 1
- 1.1 and 1.4 Rational Indices Law
- 1.2 Expanding Brackets
- 1.3 Factorising Polynomials
- 1.5 and 1.6 Surds
- 2.1 Solve quad. equ FACTORISE
- 2.2 Square form of quadratic equation
- 2.3 and 2.4 Complete Square Quad. Functs. & graphs
- 2.5 The discriminant
- 2.6 Modelling with Quadratics
- 3.1-3.3 Solving 2 simult. equ. Linear and quad
- 3.4-3.6 Inequals. Linear and quad solving
- 3.6 Inequalities on a graph
- 3.7 Regions bound by quadratics and straight lines
- 4.1 Cubic Graphs
- 4.2 Quartic Graphs
- 4.3 Reciprocal graphs
- 4.4 Points of intersection
- 4.5-4.7 Transformation of graphs
- REVIEW WEEK (1)
- 5.1-5.3 Gradients, straight & parallel lines
- 5.4 Line lengths and areas
- 5.5 Modelling with straight lines
- 6.1-6.2 Circle mid points and equation
- 6.1-6.4 Perpendicular, tangent and chord
- 6.3 Circle line intersections
- 7.1 Factor Theorem
- 7.2 Proof Methods
- Algebraic Division
- Radian measures
- Radian Arc Lengths
- Radian Area of Sector
- Trig in 4 quadrants
- Identities
- Drawing graphs of Sinx Cosx Tanx
- Trig Identities SIN^2 COS^2=1 solving trig equ
- nth term sequences
- Arithmetic Sequences and Series
- Geometric Series
- Differentiation
- Differentiation - 2nd derivative MIN MAX pts
- Integration
- Indefinite Integrals
- Boundary conditions and Definite Integrals
- Integration - Areas under a curve

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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