General, Injective, Surjective and Bijective Functions

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MATHEMATICAL SCIENCE CENTRE
 

Project Maths

MATHEMATICAL SCIENCE CENTRE         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.

 

 

 

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Leaving Cert
Project Maths 
Syllabus
2017/2018

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 = acosb

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