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JCHL - Inequalities and The Number Line - Exam Solutions
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Representing inequalities on a Number Line is a very nice question to get on your Junior Cert paper (and easy to score marks on) if you can remember a couple of rules. In this video I give a recap on the different types of numbers (link to video below) that you will be asked about (both in Junior Cert and Leaving Cert), and walk through some Exam Questions to help explain what's happening, and how to get your full marks.
Exam Questions covered:
2019 Paper 1 Q 7
2018 Paper 1 Q 11
2016 Paper 1 Q 7(b)
Link to Video on Different Types of Numbers:
Key Points:
X ∈ means “x is an element of”. Whatever letter comes after the “∈” symbol indicates your answer should be in that form.
N= Natural Numbers (Positive, Whole Numbers)
Z= Integers (Positive or Negative Whole Numbers)
Q= Rational Numbers (Can be written as a Fraction)
R/Q (R without Q) = Irrational Numbers (Cannot be written as a Fraction)
R = Real Numbers (Positive, Negative, Decimals, Fractions, Zero, etc.)
Natural Numbers and Integers are represented on the Number Line by dots.
Real Numbers are represented on the Number Line by a continuous straight line.
If you are dealing with a “≤” or a “≥” sign, use a filled in dot.
For the "greater than" or "less than" signs, use an empty dot.
When rearranging an equation with an inequality sign in it, remember:
Isolate “x” on it’s own as you would if there was an “=“ sign in your equation.
Remember to change the direction of your inequalities signs if you are multiplying (or dividing) everything by a negative number.
All the best,
Mr. Ludden
Exam Questions covered:
2019 Paper 1 Q 7
2018 Paper 1 Q 11
2016 Paper 1 Q 7(b)
Link to Video on Different Types of Numbers:
Key Points:
X ∈ means “x is an element of”. Whatever letter comes after the “∈” symbol indicates your answer should be in that form.
N= Natural Numbers (Positive, Whole Numbers)
Z= Integers (Positive or Negative Whole Numbers)
Q= Rational Numbers (Can be written as a Fraction)
R/Q (R without Q) = Irrational Numbers (Cannot be written as a Fraction)
R = Real Numbers (Positive, Negative, Decimals, Fractions, Zero, etc.)
Natural Numbers and Integers are represented on the Number Line by dots.
Real Numbers are represented on the Number Line by a continuous straight line.
If you are dealing with a “≤” or a “≥” sign, use a filled in dot.
For the "greater than" or "less than" signs, use an empty dot.
When rearranging an equation with an inequality sign in it, remember:
Isolate “x” on it’s own as you would if there was an “=“ sign in your equation.
Remember to change the direction of your inequalities signs if you are multiplying (or dividing) everything by a negative number.
All the best,
Mr. Ludden
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