Trigonometric Functions & Graphs is one of the most under-appreciated topics on the Leaving Cert paper.
It is rarely mentioned amongst the heavy hitters like Calculus or Inferential Statistics.
But if you look at Tip #6 below, it appears in some shape of form, at least once every, in both Paper 1 AND Paper 2!
This post goes through some of the highlights of the Tacit Maths worksheet on Trigonometric Functions & Graphs, and some tips on how to approach it.
FREE Sample: In Tip #7, two "perfect" sample LCHL questions are highlighted. Students can try them out, and for teachers, the Powerpoint solutions are available for free.
The Worksheet (Click to Download)
How To Revise
The Tacit Maths revision worksheet on Tacit Maths is over 20 pages long.
Here are a few things you should be focusing on:
1. Geometry V Calculus
Worksheet: n/a
Powerpoint: Pg 2
Any time I survey students on the topic they are most concerned about they almost always mention "Trigonometry".
However, they nearly always are fine with the Triangles/Geometry aspect of Trig.
It's almost always Trigonometric Functions & Graphs that they are referring to.
I think it's important to distinguish the difference between the two.
You can treat them as two completely separate chapters!
2. Trig Equations: Full Example
Worksheet: Pg 2
Powerpoint: Pg 4-5
Very often, when revising this topic, students only need to be reminded of a full example of how to solve a Trigonometric Equation.
The first page of the worksheet contains such an example.
Tip: If you are overwhelmed by this example, don't panic! Each step will be covered in more detail in the following pages.
3. Radians: Working with Fractions
Worksheet: Pg 9
Powerpoint: Pg 43-46
Students are almost always turned off by Radians. Interestingly however, the main problem here is students ability to work with FRACTIONS.
Top Tip: Start your revision of Radians with this fractions exercise (without using calculators!). All the techniques used here are what is needed to tackling radians.
4. Radians: Working with Decimals
Worksheet: Pg 11 - 12
Powerpoint: Pg 54 - 70
If you analyse the LCHL exam questions, most questions involve the "special angles" (i.e. 30, 45 and 60).
However, a huge amount of the harder Part B questions involve decimals (like in the examples shown here).
I used to skip through this section before, but in recent years I've found that it's one of the most important exercises on the worksheet.
Warning: Before you tackle this exercise with decimals, you need to know the steps/method of solving "regular" Trig Equations inside out.
5. Trig Functions & Graph Intro
Worksheet: Pg 14
Powerpoint: Pg 54 - 70
The first page of the Functions & Graphs section (Section 3) is quite intense.
However, this is only an overall recap.
The details of the 4 Key Features are elaborated on in more detail in the following sections.
Use this page as revision tool when practicing exam questions.
6. Recent Appearances
As mentioned in the intro, Trig Functions and Graphs can come up in many shapes or forms.
It most often comes up as a Calculus questions. But it can also come up as a a question on it's own, or with Trigonometric Identities.
A question on Trigonometric Functions & Graphs has appeared in the following years:
Feel FREE to download a PDF of this Checklist here:
7. Two Perfect Exam Questions
What follows are two recent exam Questions (25 Mark and 50 Mark question).
For students: Feel free to download the free worksheet attached below. You can then look at the worked solution on our Youtube channel linked below,.
For Teachers: The Powerpoint solutions to these questions are attached below. Feel free to use this with your students.
(Click to view Powerpoint solutions and PDF of worksheet)
(Part A)
Leaving Cert 2014 Paper 2 - Question 5
Worksheet: Pg 27
Powerpoint: Pg 165 -166
This is a great little question that assesses:
1. Your ability to plot Trig Functions on graphs.
2. Your understanding of how functions in general work.
3. Your ability to solve Trigonometric equations.
Note: I have made a Youtube video going through this exam question (click button).
The Perfect Exam Question (Part B)
Leaving Cert 2017 Paper 2 Question 9
Worksheet: Pg 20 - 21
Powerpoint: Pg 140 -144
This would be one of the more difficult questions on this topic in recent years.
It assesses:
- Your ability to draw Trig Functions,
- Your understanding of the Key Features of a Trig Function (i.e. midline/range/period).
- Your understanding of the a, b and c variables in the Trig function. Note: The solution to this module is available to students in the 3rd eLearning Module in this page.
If you have any other comments/feedback on the Trigonometric Functions & Graphs module, or wish to gain access to the modules, by all means send me an email!
Diarmuid