1. SLEs Investigate some of the approximations to π which have been used.

2. 11 Mathematics C Topics - Semester 1 Real and Complex Number Systems I Vectors and Applications I Matrices and Applications I Introduction to Groups Structures and Patterns I Real and Complex Number Systems II Topics - Semester 2 Vectors and Applications II Structures and Patterns II Matrices and Applications II Dynamics I Periodic and Exponential Functions I

3. TOPIC 1 Real and Complex Number Systems I (4 weeks)

4. Structure of the Real Number System including: rational numbers irrational numbers Simple manipulation of surds Subject Matter

5. Unit 1 Real and Complex Number Systems I

6. Real Rational (a/b)Irrational (  a/b) IntegersNon-integersSurdsTranscendental (…-2,-1,0,1,2,…) (¼,-3.453,43/17,…) (  5,  5.17,-  17…) (π,e)

7. Real numbers are any numbers which can be placed on the real number line. Rational numbers are any numbers which can be expressed as a ratio p where p and q are integers q All integers, terminating decimals or recurring decimals are rational

9.  i Get real !

10.  i Get rational!

11. Model Express each of the following as fractions: (a) 0.454545…. (b) 0.14676767…..

12. (a)0.454545…. Let x = 0.454545….  100x = 45.454545…. 100x – x = 45 99x = 45 x = 45/99 = 5/11

13. (b) 0.14676767….. Let x = 0.14676767…..  10000x = 1467.676767….. 100x = 14.676767….. 9900x = 1453 x = 1453/9900

14. Page 16 Ex 1.3

15. Surds

21. Page 21 Ex 1.4

26. Page 26 Ex 1.5

27. Inequalities Model ModelSolve and graph

31. Page 34 Ex 1.6 1 (second column) 3(first column)

32. Graphing Inequalities Solve and graph x – 10 < 4x – 2 ≤ 2x + 8

33. x – 10 < 4x – 2 and 4x – 2 ≤ 2x + 8 -3x < 8 and 2x ≤ 10 x > -2 ⅔ and x ≤ 5

34. Page 34 Ex 1.6 2 c-j

35. Absolute Value  -3  = 3  2-8  =  -6  = 6  4-2  -  5-9  = 2 – 4 = -2

36. Page 34 Ex 1.6 4

37. Graphing Absolutes Solve and graph: (a)  2x+4  = 10 (b)  x-3  ≥ 4 (c)  3-x  < 4 (d)  3x-2  ≤ 1

38. (a)  2x+4  = 10  2x+4 = -10 or 2x+4 = 10 2x = -14 or 2x = 6 x = -7 or x = 3

39. (b)  x-3  ≥ 4  x-3 ≤ -4 or x-3 ≥ 4 x ≤ -1 or x ≥ 7

40. (c)  3-x  < 4  3-x > -4 and 3-x < 4 -x > -7 and -x < 1 x -1

41. (d)  3x-2   1  3x-2  -1 and 3x-2  1 3x  1 and 3x  3 x  and x  1

42. Page 34 Ex 1.6 5a-c,7,8

43. Solve and graph | 16+4x | ≤ 5-7x (P35 No 9h) If the question said: | 16+4x | ≤ 3 then you would say: i.e. 16 + 4x ≥ -3 and 16 + 4x ≤ 3

44. Solve and graph | 16+4x | ≤ 5-7x (P35 No 9h) | 16+4x | ≤ 5-7x i.e. 16 + 4x ≥ -(5-7x) and 16 + 4x ≤ 5 - 7x 16 + 4x ≥ -5 + 7x and 16 + 4x ≤ 5 - 7x 21 ≥ 3x and 11x ≤ -11 x ≤ 7 and x ≤ -1

45. Page 34 Ex 1.6 9

46. Page 3 Ex 1.1

47. Symbol Meaning  is an element of b  M means that b is an element of the set M where M = {a,b,c,…}  for all 2x is even  x where x is a positive integer : such that {x: x is even} means the set of all x such that x is even  there exists  A : b  A means there exists a set A such that b is an element of A * A defined binary operation e.g. x*y = 2x+y – 3  4*5 = 2x4 + 5 – 3 = 10

48. Laws of Addition on the set of integers (J) Closure Law The sum of any two integers results in another number which is also an integer.  a,b ∈ J, a + b = c where c ∈ J

49. Commutative Law The order in which numbers are added does not alter their sum.  a,b ∈ J, a + b = b + a

50. Associative Law No matter how numbers are associated in addition, it does not alter their sum.  a,b,c ∈ J, ( a + b) + c = a + (b + c)

51. Identity Law of Addition 0 is the identity element for addition. When 0 is added to any number, the sum is the same as that number.  a ∈ J, a + 0 = 0 + a = a

52. Additive Inverse Law For every integer, a, there exists another unique number, -a, such that they add to give 0 (the identity element)  a ∈ J,  -a ∈ J a + -a = 0

53. Page 7 Ex 1.2