1. Copyright © Ed2Net Learning Inc.1 Graphing in four Quadrants

2. Copyright © Ed2Net Learning Inc.2 Warm Up 1.The sum of the probabilities of all the outcomes in the sample space is _____. 2. Relationship between permutation and combination is____________ 3. A walk in which each parent node is traversed before its children is called ___________. 4. Each node in a tree has zero or more child nodes, which are ______ it in the tree. 5. Define Counting principle.

3. Copyright © Ed2Net Learning Inc.3 There are two basic types of trees Unordered Tree Ordered Tree Lets review what we have learned in the last lesson A Sub tree is a portion of a tree data structure that can be viewed as a complete tree in itself A Forest is an ordered set of ordered trees In graph theory, a tree is a connected acyclic graph.

4. Copyright © Ed2Net Learning Inc.4 Event : An Event is an experiment. Outcome: Possible outcomes of an event are the results which may occur from any event. Counting principle: Counting principles describe the total number of possibilities or choices for certain selections.

5. Copyright © Ed2Net Learning Inc.5 Event : An Event is an experiment. Outcome: Possible outcomes of an event are the results which may occur from any event. Counting principle: Counting principles describe the total number of possibilities or choices for certain selections.

6. Copyright © Ed2Net Learning Inc.6 Dependent events Two events, A and B, are dependent if the fact that A occurs does not affects the probability of B occurring. P(A and B) = P(A) x P(B, once A has occurred ) Independent events Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. P(A and B) = P(A) x P(B).

7. Copyright © Ed2Net Learning Inc.7 5. The number of ways (or combinations) in which r objects can be selected from a set of n objects, where repetition is not allowed, is denoted by, or C(n, r) n C r n! n C r = (n-r)! r! 6. Pascal’s Triangle illustrates the symmetric nature of a combination. i,e C(n,r) = C(n,n-r) 4. A combination focuses on the selection of objects without regard to the order in which they are selected

8. Copyright © Ed2Net Learning Inc.8 The symbol n P r is used to indicate the number of permutations n objects taken r at a time. n P r = n!/ (n - r)! The numbers of n objects is n!. If a set of n elements has n 1 elements of one kind, n 2 of another kind alike and so on, then the number of permutations, P, of the n elements taken n at a time is given by: P = n! n 1 !.n 2 !.......

9. Copyright © Ed2Net Learning Inc.9 Experimental Probability or Estimated Probability is the ratio of the number of times an event occurred to the number of times tested. P = fr (E)/N If all the outcomes in a sample space are equally likely, and E is an event within that sample space, then the theoretical probability of the event E is the ratio of number of favorable outcomes to the total number of outcomes. The probability that an event E will occur is one minus the probability that it will not occur.

10. Copyright © Ed2Net Learning Inc.10 Definition Grid – A pattern of horizontal and vertical lines, usually forming squares. Lets get Started

11. Copyright © Ed2Net Learning Inc.11 Definition Coordinate System – Made up of horizontal and vertical number line that intersect at zero point. The point of intersection is called the origin. 5 4 3 2 1 1234 5 = Origin 0

12. Copyright © Ed2Net Learning Inc.12 Definition The Horizontal Line of the coordinate system is called the x axis 1234506 x

13. Copyright © Ed2Net Learning Inc.13 The Vertical Line of the coordinate system is called the y axis. 1 2 3 4 5 0 6 y Definition

14. Copyright © Ed2Net Learning Inc.14 Coordinates – an ordered pair of numbers that give the location of a point on a grid. (3, 4) 1 2 3 4 5 0 6 1234506 (3,4) Definition

15. Copyright © Ed2Net Learning Inc.15 Remember The first number always represents the x coordinate. The second number always represents the y coordinate. 1 3 2 4 5 0 6 1234506 (3,4)

16. Copyright © Ed2Net Learning Inc.16 How to Plot Ordered Pairs Step 1 – Start from the Origin. Always find the x value first, then move horizontally either right (positive) or left (negative). 1 3 2 4 5 0 6 1234506 (2, 3) y x

17. Copyright © Ed2Net Learning Inc.17 Step 2 – Starting from your new position find the y value by moving vertically either up (positive) or down (negative). 1 3 2 4 5 0 6 1234506 (2, 3) y x

18. Copyright © Ed2Net Learning Inc.18 What is the ordered pair at the point? 1 3 2 4 5 0 6 1234506 y x

19. Copyright © Ed2Net Learning Inc.19 The ordered pair is 1 3 2 4 5 0 6 1234506 (3,5) y x

20. Copyright © Ed2Net Learning Inc.20 1 3 2 4 5 0 6 1234506 y x What is the ordered pair at the point?

21. Copyright © Ed2Net Learning Inc.21 1 3 2 4 5 0 6 1234506 (2,0) y x The ordered pair is

22. Copyright © Ed2Net Learning Inc.22 Four Quadrants of Coordinate System When the number lines are extended into the negative number lines you add 3 more quadrants to the coordinate grid. -2 0 1 2 -3 3 -2 012-33 y x Quadrant 1 Quadrant 2 Quadrant 3Quadrant 4

23. Copyright © Ed2Net Learning Inc.23 Four Quadrants of Coordinate System -2 0 1 2 -3 3 -2012-33 y x Quadrant 1 X = Positive Y = Positive Quadrant 2 X = Negative Y = Positive Quadrant 3 X = Negative Y = Negative Quadrant 4 X = Positive Y = Negative The Values of X and Y in each Quadrant

24. Copyright © Ed2Net Learning Inc.24 Four Quadrants of Coordinate Grid If the x is negative you move to the left of the 0. -2 0 1 2 -3 3 -2 0 12 -3 3 x = -2 y x

25. Copyright © Ed2Net Learning Inc.25 Four Quadrants of Coordinate Grid If the y is negative you move down below the zero. -2 0 1 2 -3 3 -2012-33 y = - 3 y x

26. Copyright © Ed2Net Learning Inc.26 How to Plot in 4 Quadrants Step 1 - Plot the x number first moving to the left if the number is negative. -2 0 1 2 -3 3 -20 12 -3 3 (-3, -2) y x

27. Copyright © Ed2Net Learning Inc.27 How to Plot in 4 Quadrants Step 2 - Plot the y number moving from your new position down 2 when the number is negative. -2 0 1 2 -3 3 -2 012-33 (-3, -2) y x

28. Copyright © Ed2Net Learning Inc.28 Lets see another Example When x is positive and y is negative, plot the ordered pair in this manner. -2 0 1 2 -3 3 -2 012-33 (2, -2) y x

29. Copyright © Ed2Net Learning Inc.29 How will we plot the Ordered Pair -2 0 1 2 -3 3 -2 012 -3 3 (-3, -3) y x

30. Copyright © Ed2Net Learning Inc.30 -2 0 1 2 -3 3 -2 012-33 (-3, -3) y x

31. Copyright © Ed2Net Learning Inc.31 Your Turn -2 0 1 2 -3 3 -2 012-33 y x A B C D E F Write the ordered pairs represented by the alphabets A to F

32. Copyright © Ed2Net Learning Inc.32 Your Turn In Quadrant 2 the sign of X is always_______. In Quadrant 3 the sign of X and Y is_______. The ordered pair (0,0) represent the_______. The Horizontal axis is called the__ axis Fill in the Blanks:

33. Copyright © Ed2Net Learning Inc.33

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35. Copyright © Ed2Net Learning Inc.35 1) The two forwards of the football team are standing on the positions (-3,2) and (2,2). Plot these and find out the distance between the two forwards

36. Copyright © Ed2Net Learning Inc.36 2) Plot three ordered pairs who when joined should make a straight line passing through three quadrants

37. Copyright © Ed2Net Learning Inc.37 3) Plot a Square crossing all four Quadrants

38. Copyright © Ed2Net Learning Inc.38 Grid – A pattern of horizontal and vertical lines, usually forming squares. Coordinate System – Made up of horizontal and vertical number line that intersect at zero point. The point of intersection is called the origin. The first number always represents the x coordinate. The second number always represents the y coordinate. Lets review what we have learned in this lesson

39. Copyright © Ed2Net Learning Inc.39 Definition Coordinates – An ordered pair of numbers that give the location of a point on a grid. (3, 4) 1 2 3 4 5 0 6 1234506 (3,4)

40. Copyright © Ed2Net Learning Inc.40 Four Quadrants of Coordinate System When the number lines are extended into the negative number lines you add 3 more quadrants to the coordinate grid. -2 0 1 2 -3 3 -2012-33 y x Quadrant 1Quadrant 2 Quadrant 3 Quadrant 4

41. Copyright © Ed2Net Learning Inc.41 Keep up the good work