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## Junior Certificate Project Maths - Ordinary Level Learning Path

The Irish Junior Certificate course is the predecessor of the leaving certificate and lays the fundamental building blocks needed for the Leaving Certificate course. Undertaking the ordinary level project maths at Junior Certificate level familiarise the student with the basic principles that govern more advanced mathematical equations. The Alsion learning path on Junior Certificate ordinary level project maths will familiarise the student with the kinds of problems which they can expect to see on the exam. The Alsion learning path in junior certificate ordinary level maths will be of interest to anyone hoping to undertake the exam, or those who wish to review what they had previously learned on the course. This course is also of interest to those hoping to undertake the leaving certificate ordinary paper in the future. This Alsion learning path will cover the basic principles of areas on the course, such as; probability, statistics, geometry, trigonometry, numbers and shapes, algebra, functions, and calculus.

### Courses in this Learning Path

1. #### Junior Certificate Strand 1 - Ordinary Level - Probability and Statistics

This course begins by teaching you how to compute for arrangements. You will study how to arrange and select objects as well as look at a group frequency table to compute for the estimated mean, median class, modal class, and range. You will also learn that a stem and leaf diagram can help you quickly summarize data while maintaining the individual data points. You will then study how to construct a stem and leaf diagram and get them in order.

Stem-and-leaf diagrams are a visual representation of grouped discrete data and are an excellent tool for organizing information. This course will teach you how to draw a comparative stem-and-leaf diagram for data. You will then look into a histogram which is a graphical display of data using bars of different heights to help you discover and visualise the underlying frequency distribution (shape) of a set of continuous data. You will also look into the probability of simple events.

Statistics looks at the data handling cycle and analysis of collected data. Upon the completion of this course, you will be able to understand the process involved in posing a question, collecting data on that question, presenting that data, analyzing the data using measures of spread and centre, and interpreting the results. So, check out the course and learn how to contextualize and justify your findings using probability and statistics to make informed decisions.

1-2 Hour
50 Points
2. #### Junior Certificate Strand 2 - Ordinary Level - Geometry and Trigonometry

A ratio is a relationship between two numbers. It tells how much of one thing there is compared to another thing. This course begins by teaching the steps in finding angles and sides using trigonometrical ratios such as sine, cosine, and tangent ratios. You will then learn about different applications of geometric reasoning, which is the use of critical thinking, logical arguments, and spatial reasoning to solve problems and find new relationships.

Coordinates are a set of values that show an exact position, and are usually a pair of numbers you can see on graphs. This course will teach you about geometry with coordinates. You will look into the equation of a straight line, parallel lines, and perpendicular lines. You will also study the Pythagorean theorem which is a mathematical formula that provides us with the relationship between the sides in a right-angled triangle.

Trigonometry is used to measure angles while geometry deals with angles only in terms of equality of angles and sums of angles. Upon the completion of this course, you will have a better understanding of synthetic geometry, right-angled triangles, coordinate geometry, and trigonometrical ratios. You will also be able to practice answering miscellaneous trigonometry questions. So, check out the course today and starting give your maths skills a solid boost.

2-3 Hours
50 Points
3. #### Junior Certificate Strand 3 - Ordinary Level - Numbers and Shapes

This course will first introduce you to the proper method of changing decimals, small numbers, and large numbers to standard form. You will study how to work with indices and all types of positive and negative fractional indices. You will learn how to compute for profit, markup, and margin, as well as study interest, rate, principal, and period. You will also touch on the topic of percentage loss, percentage changes using multipliers, reverse percentages, VAT, and compound interest.

You will then study the circumference of a triangle and the area of a circle. This course will also teach you how to find the radius and diameter of a circle from its perimeter as well as from its area. You will learn how to find the area of a trapezium, acute-angled triangle, obtuse-angled triangle, rectangle, and parallelogram. In addition, you will be taught how to find the area of a compound rectangle.

Numbers are so important in our everyday lives. Upon the completion of this course, you will have a much better understanding of complex numbers as well as understand how to add, subtract, multiply and divide them. You will also find it much easier to measure the perimeter and area of various shapes such as triangles, rectangles, hexagons, and circles. Check out the course and learn more about the concept of complex numbers today!

2-3 Hours
50 Points
4. #### Junior Certificate Strand 4 - Ordinary Level - Algebra

Algebra is one of the broad parts of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations. This course begins by teaching you how to rearrange a simple formula. You will learn how to expand any two brackets as well as factorize quadratics and the difference of two squares. You will also look into quadratic equations that have brackets of the same and different signs.

In a quadratic equation, the discriminant helps you find the number of solutions to solve the equation. This course will teach you how to use a discriminant. You will look into equations with indices and learn how to solve simultaneous equations with both negative signs, with both positive signs, and with a negative and a positive sign. You will also learn how to solve linear inequalities of fractions that have different denominators.

Knowing how to solve algebraic notation can help you analyze real-world problems. Upon the completion of this course, you will learn how to represent numbers with letters, convert problems into algebraic equations, and solve simultaneous, quadratic and cubic equations. You will also gain a deeper understanding of how to solve inequalities, search for roots by trial and error, and use synthetic division. Check out the course and start enhancing your skills in algebra today!

2-3 Hours
50 Points
5. #### Junior Certificate Strand 5 - Ordinary Level - Functions and Calculus

This course first teaches the rules of differentiation which includes product rule, quotient rule, and chain rule. You will learn the use of differentiation to find the slope of a tangent to a curve at a specified point. This is then extended to the study of increasing and decreasing functions. You will also learn how to determine the local maxima and local minima turning points of a curve.

You will then study average speed, which is the rate of change of distance. This course also teaches the use of slope to determine the nature of a function. You will learn the concept of numerical integration and how to use the Trapezoidal Rule to find the area under specific curves. With the help of video presentations, you will then be guided through the process of completing the square and sketching the full method.

Functions and calculus are used in real life to help us understand rates of increase and decrease. Upon the completion of this course, you will be able to solve problems involving the maximum speed reached by car and the highest point reached by a firework or rocket. You will also learn that a Trapezoidal Rule is a numerical approach to finding definite integrals where no other method is possible. So, check out the course and gain a better understanding of functions and calculus, today.

1-2 Hour
50 Points

### Complete!

Successfully complete all of these courses to receive a Junior Certificate Project Maths - Ordinary Level Learning Path Award.