Leaving Cert Course Basics of each Chapter

Arithmetic  Percentages - Getting x% of something - Expressing x as a % of y  Interest/Depreciation – AER etc.  Household Tax - Income Tax - USC - PRSI/PAYE

Complex Number  Conjugate – how to find it?  Modulus – How to get it? - What does it mean??  Multiplying complex Numbers?  Dividing Complex Numbers?  Getting rid of a complex number below the line?

Numbers  Scientific notation  Rules of indices - Multiplying/dividing indices? - What does 3x -2 or x ½ mean?  Rules of surds

Sequences & Series  What is an arithmetic SEQUENCE?  How do you use the formula?  What is an arithmetic SERIES?  How do you use the formula?

Functions and Graphs What do the following functions look like?  f(x) = 3x + 5  f(x) = 2x 2 – 12x + 14  f(x) = x 3 + 4x 2 + 2x – 14 

Algebra  Quadratics – Guide Number method?  Algebraic Fractions - Express as a single fraction - Solving algebraic fractions - Difference between the two?  N.B. - Simultaneous Equations – One linear, one non-linear  Algebra and Surds (see Numbers section)

Differentiation  1 st principles – ALL THE STEPS  Basic differentiation – eg. Differentiate:  Differentiating functions How do you find: - Slope? - Minimum/Maximum Points? - Turning Points?  Distance/Speed V Time graphs - How do you find distance? - How do you find speed? - How do you find acceleration? - What does it mean if or

Paper 2

Area and Volume  Area/Perimeter/Volume Formulae – how to use all of them  Given the area/volume, looking for the radius/height?  Volume of a prism?  Trapezoidal Rule - How to use it? - What is it used for? - Using it with graphs?

Probablilty  Under Construction

Statistics Collecting Data  Numerical, Categorical, Ordinal, Nominal, Discrete, Continuous?  Problems with collecting data- population, bias etc. Measures of Location & Spread  Mean, Mode, Mean  Standard Deviation  Calculating the above for Frequency Distribution tables  Range/Interquartile Range Representing Data  Distribution – Normal, positive/negative skew  Stem and Leaf graphs – Calculating mean, mode and median  Correlation

Coordinate Geometry  Formulae – Distance, Slope, Midpoint, equation of a line  What comes to mind when parallel/perpendicular is mentioned?  What happens when crossing the x/y-axis?  How do you show a point is on the line?  Point of Intersection?  Area of triangle

The Circle  What does this equation mean? x 2 + y 2 = 16  Finding the centre/radius when centre isn’t (0,0)?  Points of Intersection – Line and a circle  Circle crossing x and y axis

Trigonometry  Sin, Cos, Tan, Pythagoras – When can/can’t you use them?  Finding the length of a side/angle?  Formulae - Sin Rule - Cosine Rule - Area Formula - Area/Length of a sector/arc When/how would you use these?

Geometry  Straight Line rule/Triangle Rule/Exterior Angle  Isosceles/equilateral/right angled triangle?  Parallel Lines/Equal angles?  Congruent Triangles - What does it mean? - How do you prove it?  Parallelogram – ALL the charateristics/getting area?  Similar triangles – how to use them? How to prove them?  Transversals? (Parallel Lines with a line going through)  Circle theorems – Tangents, chords, angle on the diameter  Enlargements – Scale factor - How to calculate it? How to use it? - Difference when area/volume is involved?  Circumcentre/Incentre/Centroid – What do each of them mean

Constructions  Circumcentre and circumcircle  Incentre and incircle  Angle of 60degrees (without using protractor or setsquare)  Tangent to a circle  Parallelogram with sides of a given length  Centroid of Circle