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Ruslan
- Rate L251
- Response 1h
L251/hr
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- Maths
Maths Grinds for Leaving Certificate and Junior Cycle students of all levels
- Maths
Lesson location
About Ruslan
Hi there, I’m Ruslan Murphy, a graduate of Confey College, Co. Kildare, in 2022.
I enjoy learning and helping others with maths and taught myself each topic from the book and through regular practice.
I achieved a H1 (honours) grade in the 2022 Leaving Cert, scoring 98.4%, as well as an A in both the Junior Cert and mock paper.
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About the lesson
- Primary
- Lower Secondary
- Senior Secondary
- +5
levels :
Primary
Lower Secondary
Senior Secondary
Adult Education
Bachelor's Degree
Master's Degree
Doctorate
Other
- English
All languages in which the lesson is available :
English
What I offer :
- Affordable tutoring of a multitude of topics ie. Algebra, Trigonometry, Geometry, Statistics & Probability
- Relevant self-made notes on what one needs to know for the exam.
- Appropriate practise questions for said exams & tips on what frequently appears on papers and patterns to be seen over the years.
Major Topics Covered :
- Algebra (polynomials and graphs, factorising, binomials, manipulation of formulae, simultaneous equations, quadratics & roots, indices & surds, the factor theorem, modulus, algebraic identities, inequalities, exponential & logarithmic functions)
- Trigonometry (radian measure, trigonometric ratios, Sine & Cosine rules, graphing trigonometric functions, compound angles, inverse trigonometric functions, trigonometric identities, all relevant formulae)
- Probability (permutations vs. combinations, experimental & elementary probability, addition rule, mutiplication law, conditional probability, tree diagrams, probability distributions, the Bernoulli trials, independency & mutualism, simulations)
- Differential Calculus (tangents : increasing vs. decreasing, limits & continuity, differentiation by first principles, product rule, quotient rule, chain rule, second derivatives, deriving trigonometric functions, deriving exponential & logarithmic functions, stationary points, finding the maximum & minimum, related rates of change)
- Statistics (types of data, collecting data, measures of location & variability, sampling, stem & leafs, histograms, shape of distributions, scatter diagrams, correlation & the line of best fit, the normal distribution)
- Coordinate Geometry (the area of a triangle, the equation of a line, dividing a line segment, finding the slope, concurrencies of a triangle, perpendicular distance & the modulus, the angle between two lines, the equation of a circle, tangents to a circle, the common chord, touching circles, axes and circles)
Geometry (triangles & parallelograms, the types of angles, ratio theorems, circle theorems, enlargements, all relevant constructions)
Minor Topics Covered :
- Sequences, Series & Patterns (arithmetic vs. geometric sequences, arithmetic vs. geometric series, limits of sequences, number patterns and formulae)
- Complex Numbers (irrational numbers, form of complex numbers, adding & subtracting complex numbers, dividing & multiplying complex numbers, transformations, conjugate roots theorem, polar form of complex numbers, De Moivre’s theorem & proof, applications of De Moivre’s theorem)
- Integration (Antidifferentiation, integrating exponential & trigonometric functions, definite integrals, finding areas by integration, average value of a function)
- Financial Maths (compound interest, depreciation, instalment savings / annuities, loans & mortgages, the mortgage formula & proof)
- Length, Area & Volume (sectors of circles, 3-dimensional objects, trapezoidal rule)
- Functions & Graphs (inputs & outputs, composite functions, types of functions [injective, surjective, bijective], inverse functions, graphing functions, exponential & logarithmic functions)
- Inferential Statistics (confidence intervals for population proportions, hypothesis testing for population proportions, sampling distribution of the mean & the centrallimit theorem, confidence intervals for a population mean, hypothesis testing for a population mean)
- Proofs by induction (introduction to proving by induction, series proofs, factor proofs, inequality proofs, relevant notation & statements)
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Rates
Rate
- L251
Pack prices
- 5h: L1255
- 10h: L2510
online
- L251/h
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