Project Maths  Ordinary Level
Revise for your leaving cert on the project maths ordinary level syllabus.
Description
This course is for students interested in studying the Project Maths Ordinary Level Course in its entirety. This course provides students with videos on all the Ordinary Level topics in one location listed by module and topic. In addition, a comprehensive assessment is provided which tests learners on the entire content of the Project Maths Ordinary Level Syllabus. These topics include Probability and Statistics, Geometry and Trigonometry, Numbers and Shapes, Algebra, Functions and Calculus.
Start Course NowModules
Module 1: Counting and Probability

Arrangements

Expected Value

Probability of simple events

Probability of compound events

Independent events

Probability using tree diagrams

Probability trees with and without replacement

Simple Bernoulli Trials

Bernoulli Trials  Part 2
Module 2: Statistics

Cumulative frequency and the Ogive

Cumulative frequency, quartiles and the interquartile range

Mean of grouped frequency tables

Constructing a stem and leaf diagram

Comparative stem and leaf diagram

Histograms  Understanding that area gives frequency

Statistical correlation

Measuring correlation  Pearson's Correlation Coefficient

Using Excel to calculate Pearson's Correlation Coefficient

Using Excel to find Pearson's Correlation Coefficient, using the inbuilt function
Module 3: Synthetic Geometry

Properties of Shapes

Geometric reasoning  Part 1

Geometric reasoning  Part 2

Geometric reasoning  Part 3
Module 4: Coordinate Geometry

Geometry with coordinates

Equation of a straight line

Parallel lines

Perpendicular lines

The graphs of y=kx^n

Translation of functions

Reflection of functions

Stretching functions

General transformation of functions

Equation of a circle 1  Centre (0,0)

Equation of a circle 1  Centre not (0,0)

Diameter of a circle

Tangent and normal to a circle
Module 5: Trigonometry

Finding angles with sine ratio

Finding sides with the sine ratio

Finding angles with the cosine ratio

Finding sides with the cosine ratio

Finding angles with the tangent ratio

Finding sides with the tangent ratio

Finding a missing side with the Sine Rule

Finding a missing angle with the Sine Rule

Problem solving with the Cosine Rule

Finding areas with trigonometry

Area of a segment
Module 6: Number Systems

Large numbers in standard form

Changing decimals to standard fom

Changing large numbers from standard form

Changing small numbers from standard form

Adding and multiplying simple powers

Working with indices

Negative indices

Fractional indices, numerator of 1

Index power equal to 0

Positive fractional indices all types

Negative fractional indices

Writing index numbers as a power of 2

Quadratic number patterns

Arithmetic series

Geometric series

Rational or irrational

Manipulating complex numbers and the complex conjugate

The Argand Diagram and Modulus

The meaning of i

Patterns with imaginary numbers
Module 7: Arithmetic  Financial Maths

Profit, markup and margin

Calculating profit with special offers

Percentage loss  Part 1

Percentage loss  Part 2

Simple interest – Calculating the interest

Simple interest – Calculating the rate

Simple interest – Calculating the principal

Simple interest – Calculating the period

Percentage changes using multipliers

Reverse percentages and VAT

Introducing compound interest

Compound interest and Annual Equivalent Rate

Compound interest APR with credit cards

Depreciation

Calculating APR

Calculating monthly interest from APR – 2 methods

Income tax, USC and PRSI

Net pay/Take home pay
Module 8: Length, Area and Volume

Circumference of a circle

Area of a circle

Finding radius and diameter of a circle from its perimeter

Finding radius and diameter from area of circle

Area of trapezium

Area of acute angled triangles

Area of obtuse angled triangles

Area of parallelogram

Area of rectangles

Area Compound Shapes (rectangles)

Area of compound shapes

Area of Compound shapes (Triangles)

Volume and surface area

Sectors and arcs

Area of a segment

Volume of compound solid
Module 9: Complex Numbers

Manipulating complex numbers and the complex conjugate

The Argand Diagram and Modulus

The meaning of i

Patterns with imaginary numbers
Module 10: Expressions and Formulae

Factorising quadratics

Factorising – Difference of two squares

Expanding brackets (grid method)

Expanding brackets (FOIL method)

Expanding any two brackets

Rearranging simple formulae

Rearranging simple formulae  2 steps

Rearranging formulae with squares and square roots

Rearranging formulae new subject appearing twice
Module 11: Solving Equations

Equations with linear functions in the denominator

Quadratic equations using the formula

Quadratic equations non unitary x squared

Quadratic equations both brackets the same sign

Quadratic equations brackets with different signs

Quadratic equations that have to be rearranged

From roots to functions

Solving simultaneous equations graphically

Simultaneous equations both negative signs

Simultaneous equations negative and positive signs

Simultaneous equations both positive

Equations with indices

Nonlinear simultaneous equations
Module 12: Inequalities
Module 13: Functions

Plotting quadratic graphs from table of values

Plotting cubic graphs from table of values

Plotting reciprocal graphs from table of values

Plotting exponential graphs from table of values

Matching equations and sketches

Matching functions and graphs – quadratic / exponential

Translation of functions using f(xa)

Translating of functions using f(x)+a

Sketching functions in x direction

Sketching functions in the y direction

The Discriminant
Module 14: Calculus  Differentiation

Basic differentiation of y = x^n

Differentiation of polynomials

Equation of a tangent

Equation of a normal

General differentiation of x^n

Second derivative

Differentiation of tangents

Differentiating products and quotients

Differentiation and rates of change

The Chain Rule

The Product Rule

The Quotient Rule

Applications of differentiation 1 (displacement / velocity / acceleration)

Applications of differentiation 2 (voltage / current)

Differentiation and turning points

Maximum volume of box

Differentiation and matching graphs
Module 15: Project Maths  Ordinary Level Assessment
Learning Outcomes
Having completed this course, students will be able to:  Describe the concepts of probability;  Understand outcomes of random processes;  Describe statistical reasoning with an aim to becoming a statistically aware consumer;  Find, collect and organise data;  Represent data graphically and numerically;  Analyse, interpret and draw inferences from data;  Develop synthesis and problemsolving skills;  Determine the slope of a line passing through two given points;  Find the equation of a line passing through two given points;  Find the equation of a line perpendicular to a given line and passing through a given point;  Determine the equation of a circle having a given centre and radius;  Find the equation of a tangent to a given circle at a specified point;  Find distance and angle using Sine and Cosine Rules;  Find length of an arc and area of a sector using circular measure;  Determine the area of a triangle given the lengths of two sides and the included angle;  Determine the sum of an arithmetic series;  Determine the sum of a geometric series;  Work out the profit made on a sale;  Work out the income tax paid on the gross pay;  Multiply and divide complex numbers;  Work out the areas and volumes of well known shapes and solids;  Solve linear simultaneous equations with 2 unknowns;  Factorise expressions of order 2;  Form quadratic equations with given roots;  Solve one linear equation and one equation of order 2 with two unknowns;  Solve basic inequalities;  Interpret the solutions of simple simultaneous equations;  Basic Differentiation of functions;  The rules of differentiation (product rule, quotient rule, chain rule);  Determine the local maxima and local minima turning points of a curve;  Understand rate of change of distance;  Use slope to determine the nature of a function;  How to use the Trapezoidal Rule to find area.
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