MathsPoints.ie

*** Permuations and Combinations ***

A series of Permutations (Arrangements) and Combinations (Selections) questions created by the Project Maths Development Team for the launch of the new Syllabus in the early 2010s.
The accompanying solutions to this pack contain varying methods of solution showing the difference between the counting method and sequential probability method for questions about selecting cards, lotto balls etc.

This pack so important to go over in case of a dreaded 'Lotto' type question.

A lottery consists of drawing 6 balls and a bonus ball from a total of 45 balls. The balls are numbered from 1 to 45. If a person buys just one ticket:

What is the probability of getting 3 of the winning numbers plus the bonus ball?

Very difficult to do by sequential probability (multiplying fractions) so very important to know the 'choosing' method!

Navigate to:

📁 LCHL Resources by Topic
📁 Probability LCHL
📁 Probability LCHL Subtopics

Link in bio to sign up.

*** LCHL Learned Off Material ***

Clear and colourful versions of all the LCHL learned off material can be found on the website under:

📁 Resources by Topic
📁 Learned Off Content

What do you need to know??

👉 3 Geometry Proofs
👉 8 Trigonometry Proofs
👉 Constructions 16 - 22
👉 De Moivre’s Theorem by Induction
👉 Sum of Geometric Series by Induction
👉 Sum to Infinity of Geometric Series (Limits)
👉 Derive Amortisation Formula
👉 Proof By Contradiction – √2 is not Rational
👉 Construction of √2 and √3

Link in the bio to sign up!

*** JCHL Sets Revision ***

This guided revision pack has 30 questions across 3 levels of difficulty.

Essential
1. Definition of a Set
2. Set Notation
3. Subsets
4. Subsets and Primes
5. Shading 2 Set Venn Diagram
6. Shading 3 Set Venn Diagram
7. Complete 3 Set Venn Diagram
8. Complete 2 Set Venn Diagram (Real World)
9. 3 Set Venn Diagram (Factors, Multiples and Primes)
10. 3 Set Venn Diagram (Real World)

There are another 20 questions in the Intermediate and Advanced sections progressing the difficulty level.

The pack of questions, worked solutions and animated PowerPoint can be found in the Resources by Topic section under Guided Revision!

Link in the bio to sign up!

*** LCOL Number and Arithmetic ***

This is one of the major topics to look over if dropping last minute from Higher to Ordinary Level...

This pack has 30 questions across 3 levels of difficulty with worked solutions and an animated PowerPoint.

Topics include:

👉 Distance, Speed and Time
👉 Percentages
👉 Scientific Notation
👉 Rules of Indices
👉 Ratio and Proportion
👉 Comparing Types of Number

and lots more...

*** Probability - Key Questions ***

Struggling to know where to start revising Probability. Our LCHL Probability - Key Questions pack has 30 questions across 3 levels of diffiiculty.
Hours have been spent selecting and arranging the questions into levels so that students can see all types of probability questions and at varying difficulties.

Essential
1. Definitions
2. Two Way Table
3. Tree Diagram
4. Venn Diagram (Independence)
5. Mutually Exclusive
6. Arrangements (Permuations)
7. Selections (Combinations)
8. Sequential Probability and Bernoulli
9. z-scores and Normal Distrubution
10. Expected Value

Intermediate
11. z-score (Real World)
12. Bernoulli Trials and Expected Value
13. Conditional Probability'
14. 3 Set Venn Diagram
15. Algebra in Probability
16. Contingency Table
17. Binomial Distribution
18. Expected Value with Negative Value
19. Selection without Replacement
20. Combinations (Selecting Teams)

Advanced
21. Arrangements (Codes)
22. Probability Two People Born on the Same Date
23. Bernoulli with Unknown n
24. Independent Events (Algebra)
25. Real World - Diabetes
26. Real World - Hotel Stay
27. Real World - Eggs
28. Real World - Running
29. Sequenctial Events and Combinations
30. Long Term Probability

These can be found in the Resources by Topic section under Guided Revision!

Link in the bio to sign up!

💻New JCHL Resource 💻

Just added a JCHL Algebra - Manipulation of Formula pack of questions and worked solutions to the website.

You can find them by navigating to:

📁 JCHL Resources by Topic
📁 Algebra JCHL
📁 Algebra JCHL Subtopics

Link in bio to sign up.

✏️ Don't Neglect Enlargements ✏️

Enlargements is a very poorly revised topic at Leaving Cert Higher Level due to the fact it rarely appears!

After a very tricky question in 2011 it took 14 years for the topic to make a reappearance on the paper.

This pack of guided revision questions is broken down by difficulty level with 5 Essential, 5 Intermediate and 5 Advanced questions.

The 5 advanced questions include the appearances on the aforementioned 2011 and 2025 LCHL papers along with 2 great LCOL questions and a rarely seen enlargements question from a Project Maths development pack.

My class did these questions over the last few days and found the 2012 LCOL Paper 2 - Q8 (Q12 on this pack) quite challenging.

One brilliant student had a very novel method to solve part (iv) which I will post here tomorrow.

The final question is a cracker asking students to work out the scale factor that enlarges an A4 sheet to an A3 given that an A3 is twice the area of an A4!

One final thing worth thinking about.

If an image area is k² times the object area, where k is the scale factor....what would a formula be for image volume of a shape?

This pack with, worksheets, worked solutions and animated powerpoint can be found under the Guided Revision section of the LCHL Resources by Topic on the website (link in bio to sign up).

💻New JCHL Resource 💻

Just added a JCHL 3 Set (Real World) pack of questions and worked solutions to the website.

You can find them by navigating to:

📁 JCHL Resources by Topic
📁 Sets JCHL
📁 Sets JCHL Subtopics

Link in bio to sign up.