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Essential Revision

Essential revision from Standard Grade

Completing the square

Factorising

Fractions

Indices and Surds

Trigonometry

Mathematics 1
LO1:-Use the properties of the Straight Line	y - b = m(x-a) gradient = tan theta distance formula midpoint formula perpendicular lines collinearity general equation of a straight line Triangles Altitudes Centroid Circumcentre Circumcircle Concurrency Median Orthocentre Perpendicular bisector
LO2:-Associate functions and graphs and solve related equations.	Functions Set notation Domain, codomain & range One to one correspondence Inverse function Inverse function - algebraic method Inverse function - graphical method composite functions Simple graphs of functions Reflections, translations, etc Graphs of functions an Excel reminder. (161 kb)
	Exponentials Logarithms Exponential / log functions - graphs Logarithmic scales on graphs Exponential / log functions - graphs An Excel reminder. (86 kb)
	Amplitude and Period definition Graphs of trig functions Excel (1737 KB) Algebra - Solving Trig equations
	Radians Converting degrees to Radians Exact values Radians & Degrees Using exact values : Radians & Degrees Conversion table
LO3:- Use basic differentiation
LO3:- Use basic differentiation	Differentiation Gradients Notation xⁿ axⁿ Derivatives of sums Applications Sketching functions and tangents Tangents- gradients Tangents- equations Increasing / decreasing functions Stationary points finding stationary points maxima and minima closed intervals curve sketching graphing derived functions Differential equations
LO4:-Design and interpret mathematical models of situations involving recurrence relations.	nth term of sequence Recurrence relations Divergence / convergence Linear recurrence relations Formula for linear recurrence relations Solving recurrence relations Special sequences Finding limits an Excel document reminder.

Mathematics 2
LO1:- Use the factor/remainder theorem and apply quadratic theory.	Coefficients etc. Nested form. Dividing polynomials The factor theorem The remainder theorem Synthetic division Dividing by ax+b Solving polynomial equations Sketching polynomial equations
	Quadratics Factorizing quadratics Finding roots of quadratics Finding roots of quadratics which don't factorise easily Quadratic formula Finding roots of quadratics - derivation Quadratic graphs Sketching quadratic functions Discriminant Quadratic equations Quadratic graphs - tangency Finding roots of quadratics an Excel document reminder. (50 kb)
LO2:- Use basic integration	Integral calculus indefinite integrals basic rules of integration indefinite integral of (ax+b)^n infinite integrals (discontinuities) indefinite integrals - trig functions indefinite integrals - exponentials & logarithmic functions Integration by substitution Integration and graphs Areas of graphs Newton's equations of motion areas under curves lower bound upper bound area function integration and the area function definite integrals fundamental theorem of calculus areas enclosed by graph and x-axis area between curve and the y-axis area between two graphs Formula for area between two graphs
LO3:- Apply trigonometric formulae	Deriving compound angle Trig refresher sec, cosec & cot Compound formulae Double Angle Half Angle Product formulae Multiple Angle Algebra - Solving Trig equations Compound angle formulae - Examples
LO4:-Use the equation of the circle.	The circle - higher course examples equation of circle : x² + y² = r² Equation of circle : given centre, radius Equation of circle : line joining diameter General equation of circle Intersection of line & circle Tangents to a circle Equation of a circle from chords

Mathematics 3
LO1:- UseVectors in three dimensions	Scalar and vector quantities Components Magnitude Position vectors Unit vector Zero vector Equal vectors Adding vectors Subtracting vectors Collinearity Perpendicular vectors Angle between vectors Scalar product example Section formula
LO2:- Use further differentiation and integration	Differentiating Sin and Cos functions Integrating trig functions Differentiating (x + a)ⁿ Differentiating (ax + b)ⁿ The chain rule Indefinite integral of (ax+b)^n Rectilinear motion
LO3:- Logarithmic and exponential functions	Exponentials Growth functions Decay functions Logarithms Logarithms - converting bases Logarithmic equations logarithm laws Log and Ln Exponential / log functions - graphs Logarithmic scales on graphs Exponential / log functions - graphs An Excel reminder. (86 kb)
LO4:-Apply further trigonometric relationships	Adding two waves Subtracting two waves Express in the form cos(x+a) Express in the form sin(x-a) Express in the form sin(x+a) Multiple Angles Maximum / Miminum Value Sketching graphs Solving equations

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