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Presentation on theme: "Click to start Higher Mathematics Indices www.maths4scotland.co.uk Next."— Presentation transcript:

1

2 Click to start

3 Higher Mathematics Indices Next

4 Indices Higher Mathematics What are Indices Indices are a mathematical shorthand If, we have: We can say that this is: 3 multiplied by itself 5 times We write this as: pronounced 3 to the power 5 3 is the BASE 5 is the POWER or INDEX

5 Indices Higher Mathematics What are Indices The plural of INDEX is is written in INDEX form also known as power form or power notation INDICES So,

6 Indices Higher Mathematics Rules of Indices

7 Indices Higher Mathematics Rules of Indices Consider the following What can we make of it ? Can we generalise to make a rule ?

8 Indices Higher Mathematics 3 times 4 times 7 times

9 Indices Higher Mathematics m times n times m + n times Generalising

10 Indices Higher Mathematics When multiplying We ADD the indices Generalising

11 Indices Higher Mathematics Examples Remember – to MULTIPLY you ADD the indices

12 Indices Higher Mathematics Rules of Indices Consider the following What can we make of it ? Can we generalise to make a rule ?

13 Indices Higher Mathematics 5 times 2 times 2 terms on the bottom will cancel out 2 terms on the top

14 Indices Higher Mathematics 5 times 2 times terms 2 terms on the bottom will cancel out 2 terms on the top

15 Indices Higher Mathematics m times n times m - n terms n terms on the bottom will cancel out n terms on the top Generalising

16 Indices Higher Mathematics When dividing We SUBTRACT the indices Generalising

17 Indices Higher Mathematics Examples Remember – to DIVIDE you SUBTRACT the indices

18 Indices Higher Mathematics Rules of Indices Consider the following What can we make of it ? Can we generalise to make a rule ?

19 Indices Higher Mathematics 3 times 4 times 4  3 terms

20 Indices Higher Mathematics m times n times m  n terms

21 Indices Higher Mathematics Examples Remember – for POWERS you MULTIPLY the indices

22 Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

23 Indices Higher Mathematics 3 times Recall division

24 Indices Higher Mathematics Examples Remember – anything to the power of 0 is 1

25 Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

26 Indices Higher Mathematics 3 times 2 times Recall division

27 Indices Higher Mathematics Examples Remember – anything to the power of 1 is itself

28 Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

29 Indices Higher Mathematics 3 times 4 times Recall division

30 Indices Higher Mathematics Rules of Indices a ‘minus’ index means ‘1 over’ A useful way of remembering this

31 Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

32 Indices Higher Mathematics 2 times 5 times Recall division

33 Indices Higher Mathematics m times m +n times Generalising

34 Indices Higher Mathematics Examples Remember – minus means 1 over Express in positive index form

35 Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

36 Indices Higher Mathematics Recall multiplication ButSo, Hence Thus

37 Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

38 Indices Higher Mathematics Recall multiplication and, Hence Thus n times

39 Indices Higher Mathematics Examples Remember – fraction denominator gives the root Express in root form

40 Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

41 Indices Higher Mathematics Recall powers Thus So,But,

42 Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? Finally, what meaning can we give to

43 Indices Higher Mathematics Examples Remember – fraction denominator gives the root Express in root form Remember – fraction numerator gives the power

44 Indices Higher Mathematics Recall Then and,

45 Indices Higher Mathematics Examples Express in root form Remember – minus means 1 over

46 Indices Higher Mathematics Rules of Indices Multiplying Dividing Powers

47 Indices Higher Mathematics Special Indices Power of 0 Power of 1

48 Indices Higher Mathematics Negative and Fractional Indices Negative Fraction Negative fraction minus means ‘1 over’

49 Indices Higher Mathematics More Examples - 1 Simplify

50 Indices Higher Mathematics More Examples - 2 Simplify

51 Indices Higher Mathematics More Examples - 3 Multiply out the brackets

52 Indices Higher Mathematics More Examples - 4 Simplify

53 Indices Higher Mathematics More Examples - 5 Solve the equation:

54 Indices Higher Mathematics More Examples - 6 Simplify and express in positive index form

55 Indices Higher Mathematics More Examples - 7 Write in root form

56 Indices Higher Mathematics More Examples - 8 Write in index form

57 Indices Higher Mathematics More Examples - 9 Evaluate

58 Indices Higher Mathematics More Examples - 10 Simplify

59 Indices Higher Mathematics More Examples - 11 Simplify

60 Quit C P D © CPD 2004

61 THE END


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