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###### MATHEMATICAL SCIENCE CENTRE

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 Go down deep enough into anything and you will find mathematics
 Paper 2   Geometry and Trigonometry (Strand 2)   · Perform constructions 1-15 and 22. · Prove theorems 11, 12, 13 concerning ratios. · Co-ordinate geometry of the line · Co-ordinate geometry of the circle · Solve problems using the sine and cosine rules · Use trigonometry to solve 3D problems. · Graph trigonometric functions. · Solve trigonometric equations · Derive trigonometric formulae   Probability and Statistics (Strand 1)   Probability ·  Addition Rule:            P(A U B) = P(A) + P(B) − P(A n B) · Mutually Exclusive Events:            P(A U B) = P(A) + P(B) · Multiplication Law            P(A n B) = P(A|B) × P(B) ·  Independent Events:            P(A n B) = P(A) × P(B) · Arrangements and Permutations. · Calculate Expected Values. · Calculate Probabilities using the Normal Distribution tables and the Binomial Distribution.   Statistics · Finding, collecting and organising data. · Representing data graphically and numerically. · Draw the line of best and make predictions. · Calculate the correlation coefficient using a calculator.   Correlation Coefficient r = 0………………....None 0 < r ≤ 0.3……….Weak 0.3 < r ≤ 0.7.….Moderate 0.7 < r < 1……….Strong r = 1………………....Perfect   · Calculate the margin of error · Conduct a hypothesis test · Make decisions based on the Empirical Rule.   68% of the data will fall within 1 standard deviation of the mean. 95% of the data will fall within 2 standard deviations of the mean. 99.7% of the data will fall within 3 standard deviations of the mean.
 LEAVING CERT PROJECT MATHS (HIGHER LEVEL)
 Paper 1   Number (Strand 3)   · Number Systems N, Z ,Q, R, C · Complex numbers (z = a + ib) · Arithmetic Sequences and Series · Geometric Sequences and Series · Proof by Induction · Limits · Logs and Indices · Financial Mathematics               Algebra (Strand 4)   · Multiplication and division of Polynomials · Factor Theorem · Solving linear equations with 3 unknowns · Inequalities · Complex numbers in rectangular and polar form · De Moivre’s Theorem   Functions and Calculus (Strand 5)               · Finding the period and range. If   y = asinbx  or  y = acosbx  Period = 2π/b     Range = [-a,a]   · Recognise surjective, injective  and bijective functions  and finding the inverse of a bijective function     · Given a graph of a function sketch the graph of its inverse ·  Express quadratic functions in complete square form ·  Graph functions of the form ax2+bx + c, abx , logarithmic, exponential and trigonometric · Informally explore limits and continuity of functions     Differential Calculus · Differentiate linear and quadratic functions from first principles ·  Differentiate the following functions polynomial, exponential, trigonometric, rational powers , inverse functions and logarithms · Find the derivatives of sums, differences, products, quotients and compositions of functions · Apply the differentiation of the above functions to solve problems   Integral calculus: ·  Integrate functions of the form xa ax Sin ax,     cos ax ·  Determine areas of plane regions bounded by polynomial and exponential curves