Leaving Cert Higher Level Maths for Dummies, or how to just get those extra 25 points
Leaving Cert Higher Level Maths giving you headaches? Get those extra 25 points with this concise guide in its seventh edition. It is a printable 55,000 word, 168 page PDF download.
€39
This is a deviation from our usual approach of striving for the absolute top grade. This is aimed at people who aren’t naturally brilliant at Maths, do not like to casually use “hence or otherwise” at the end of every sentence, and generally did HL Maths because of those 25 points. (There is nothing wrong with that!)
Our motto was, “If you can’t explain it simply, you don’t understand it well enough.” It is written by a group of students who got H1s in Maths and 625 points, but the tone is light and the explanations are kept simple.
Start by getting our free sample chapter on Statistics!
Contents of the seventh edition
- HL Maths: Understanding what the question is asking you to do – how you can practice at home
- Key Maths question terms
- Algebra
- The basics
- Factorising
- Roots and the nature of roots, the discriminant, forming equations from roots and the integer method
- Maximum and minimum points and graphs
- Cubic graphs, other graph rules and the integer method recap
- Inequalities
- Functions
- The basics
- Finding roots
- Types of functions
- Limits of functions
- Trigonometry
- The basics
- Trigonometric ratios and equations
- Graphing trigonometric functions
- Using formulae in the log tables
- 3D trigonometry problems
- Differentiation
- The basics
- Differentiation from first principles
- Differentiation by rule
- Differentiation of specific functions
- How differentiation relates to graphs
- Rates of change
- Integration
- The basics
- Integration of specific functions
- Area calculations
- Using integration to find the average value
- Complex numbers
- The basics
- De Moivre’s theorem
- Roots of complex numbers
- Rotations, dilations and further complex numbers
- Patterns, sequence and series
- The basics
- Arithmetic sequences and series
- Geometric sequences and series, sum to infinity
- Number patterns
- Shapes and their properties
- Length, area and volume
- 3D shapes and trapezoidal rule
- The circle: length, area and volume
- The Circle
- The basics
- Equations of circles and tangents
- The Line
- The basics
- Concurrencies of a triangle
- Points in relation to a line, distances and transformations
- Financial Maths
- The basics
- Bonds and rounding, amortisation and sequences and series
- Present values and depreciation
- Amortisation Formula
- Proof by induction
- Divisibility
- Series
- Inequalities
- Proving De Moivre’s Theorem by Induction
- Probability
- Operations, permutations and combinations
- The basics
- Conditional probability
- Probability distributions
- Other – sample space, tree diagrams, Bernoulli trials etc.
- Statistics
- Proofs
- De Moivre’s theorem for n𝜖N using induction
- The square root of two is not rational .
- Amortisation formula/ mortgage formula derivation using future values
- Theorem 11: Prove that if 3 parallel lines cut off equal segments on some transversal line, then they will cut off equal segments on any other transversal line
- Theorem 12: Let ABC be a triangle. If a line L is parallel to BC and cuts |AB| in the ratio s:t then it also cuts |AC| in the same ratio
- Theorem 13: Prove that if two triangles 𝛥 ABC and 𝛥 DEF are similar, then their sides are proportional in order:
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