1. IB Math Studies Year 1
I. Sets of Numbers

2. Natural #s: N
Set of positive integers including zero.
{0, 1, 2, 3, 4, …}

3. Integers: Z
Positive and negative whole numbers and zero.
No fractions or decimals
{…-5, -4, -3, -2, -1, 0, 1, 2, 3, …}
Positive integers: Z+ ={1,2, 3, …}

4. Rational #s: Q
Can be written as the ratio p/q of 2 integers where q ≠ 0.
In other words: any number that can be written as a fraction!
Includes integers, natural numbers, repeating decimals, terminating decimals
Ex: ½, -4.13, …, √144

5. Positive Rational #s: Q+
Written in set notation form
{x|xєQ, x>0}
Read: x such that x is an element of the rational #s and x is greater than 0

6. Irrational #s: I
These numbers CANNOT be written as the ratio of 2 integers (can’t be written as a fraction)
Ex: √2, π, e

7. Real #s: R
All of the above sets of #s are real numbers
For IB, we’re not going to be studying the Complex Number System 

8. Represent Real #s Graphically
On a number line, remember 0 is the origin. To the left are negative numbers and to the right are positive #s.

9. II. Absolute Value and Distance
Absolute value: the distance between the origin and the point
|a| = {a, if a≥0; -a, if a<0}
The distance between 2 points on the real number line
d(a,b) = |b – a| = |a – b|
Ex: d(-4, 2)= |-4 – 2| = |2 – -4| = 6

10. III. Algebraic Expressions
Constants (just a number)
Variables (a letter that stands for a #)
Algebraic expression (combine constants and variables with operations +, -, x, ÷ and exponentiation)
Terms: 3x2 – 5x + 8 has 3 terms: 3x2, -5x, and 8.

11. Breakdown of Terms
3x2
The 3 is the coefficient, x is the base, and 2 is the exponent or power.

12. Evaluate
Just substitute (plug in)
Ex: Evaluate the algebraic expression -3x + 5 if x = 3
Solution: -3(3) + 5 = = -4

13. IV: Inequalities
a < b: a is less than b if b – a is positive ≡ (logically equivalent)
b > a: b is great than a
≤ less than or equal to (at most)
≥ greater than or equal to (at least)
< > OPEN ( )
≤ ≥ CLOSED [ ]

14. Continue notes on your own paper

15. 1. Use inequality notation to describe:
Examples:
1. Use inequality notation to describe:
d is at least 4
j is at most -2
all m in the interval [-4, 6)

16. 2. Give a verbal description of each interval:
Examples:
2. Give a verbal description of each interval:
(-2, 1)
[2, ∞)
(-∞, 5)
(-4, 6]

17. Law of Trichotomy
For any 2 real #s a and b, one of the 3 relationships is possible:
a = b
a < b
a > b

18. HW:
Set #2 #1-6 AND #19-28