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MATHEMATICAL SCIENCE CENTRE
Go down deep enough into anything and you will find mathematics
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)
· 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.
· 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.
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)
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
· Logs and Indices
· Financial Mathematics
Algebra (Strand 4)
· Multiplication and division of Polynomials
· Factor Theorem
· Solving linear equations with 3 unknowns
· 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
· 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
· Integrate functions of the form
· Determine areas of plane regions
bounded by polynomial and exponential curves