Original post by thekidwhogamesYou can just Google it. I think this is everything: learning all of this will get you a 9 assuming practice, etc.
Topics include:
- sine/cosine rule, area of triangle as 1/2abSinC
- trig
- trig exact ratios
- solving linear, quadratic equations (include fractional, algebraic fractions, etc)
- completing the square for when the coefficient is an integer or not (both +ve/-ve) and using this to: solve quadratics, show how many roots, find maximum/minimum points (and hence sketch)
- sketch functions including: quadratics, linear functions, reciprocal graphs, 1/x^2 graphs, cubics etc
- direct/inverse proportion
- FDP
- recurring decimals as fractions and vice versa
- angles & geometrical properties of shapes
- nets/elevations
- counting combinations
- solve quadratics by factorization, completing the square, using the formula, iteration
- use graphs to solve stuff like: f(x) = c (where c is a constant) or f(x) = x+1 (intersection of 2 functions)
- composite/inverse functions (and the fact that the inverse is a reflection)
- transformations including reflections, rotations, enlargements, translations (and this is applied to functions e.g. sketching 2f(x), f(1/2x), f(-x), -f(x), f(x) + c, f(x+c))
- rearranging and using iterative formulas
- circle theorems (and proving them)
-understanding what are: natural numbers, irrational numbers, rational numbers, integers, etc.
- surds
- Pythagoras
- ratios (and ratios applied in graphs and straight lines)
- combining ratios
- rearranging equations
- indices (and solving incidial equations)
- equation of a circle
- understanding what a function is
- trig graphs (sine, cos, tan) & symmetry
- LCM, HCF, cubes, squares
- upper/lower bounds; error intervals
- mixed fractions, improper fractions (all about fractions)
- algebraic fractions
- algebraic proof
- rounding
- percentage, reverse percentage
- growth and decay; exponential functions and their graphs (and contextual problems)
- simple/compound interest and VAT
- BIDMAS
- standard form
- exchange rates
- direct and inverse proportion graphs
- simplifying expressions
- identities
- negative/fractional indices
- expanding/factorisation
- difference of squares
- inequalities (linear, quadratics)
- inequalities (graphical)
- simultaneous equations (linear/quadratic; graphical)
- midpoint/length of a line segment/perpendicular/parallel lines/equation of a line (also y-y1 = m(x-x1))
- applying gradient contextually
- recognising graphs (and graphs that have been transformed)
- 3D cosine rule, sine rule, Pythagoras, trig
- set notation for inequalities
- understanding asympotes (basic level)
- tangents to curves (estimating instaneous gradient and average gradient)
- area under curves and saying whether it's over/under estimate
- basic sequences
- arithmetic, geometric, quadratic progressions (finding terms, nth term, proof etc)
- Fibonnaci sequences (algebraic included)
- evaluating functions
Statistics:
- mean, mode, range, etc.
- mean from a table (estimaed and actual)
- median from a table
- pie charts, time series graphs, frequency polygons
- boxplots
- histograms
- cumultive frequency
- moving averages
- scatter graphs, line of best fit, coorelation
- outliers, interpolation, extrapolation
- pictograms, 2 way tables, stem and leaf (and back to back ones)
- sampling
- stratified sampling
- quartiles
- comparing graphs i.e. boxplots, cumultive frequency, histograms
Probability:
- theoritical probability
- listing outcomes
- basic notation e.g. P(a) is the prob of event a occuring
- mutually exclusive events; OR rule / AND rule
- relative frequency; expectd outcomes
- frequency trees
- independant evens; conditional probability
- set notation
- Venn Diagrams and shading e.g. (AUB)'
- venn diagrams problem solving
Geometry (some covered earlier):
- area/perimeter of: rectangle, square, paralleogram, triangle, kite, trapezium, compound shapes, triangular prism, pyramid, etc
- parts of circle e.g. sector
- area of sector, arc length
- volume of a shape (and capacity)
- surface area
- volume/surface area for cones, spheres, cylinders, compound shapes made up of them and problem solving
- frustums
- congruency/similarity and proof
- angles
- metric units
- circle theorems
- bearings (incl. trig)
- angle bisectors, line bisector
- loci/constuctions and regions
- combining transformations e.g. translating, rotating, reflecting, enlarging
- line/rotational symmetry
- plans/elevations
- speed/distance/time graphs
- velocity time graphs (area under curve, gradient)
- density, pressure, etc
- kinematics (for OCR) including SUVAT
- vectors, magnitute, vector notation, geometric proof, vector problem solving, proving parallel vectors and colinear points
- 3D pythagoras, trig, sine/cosine rule
- graphs of trig functions with basic equations; transforming trig graphs