akar, pangkat dan logaritma

LYDIA VALENSIA Email : lydia.valensia@yahoo.com SMA NEGERI 2 SEKAYU

INDICES, SURD AND LOGARITHM

INTRODUCTION

COMPETENCES

MATERIAL

EVALUATION

LET’S EXPLORE “INDICES, SURDS AND LOGARITHM”

INDICATOR

Are you smarter than 9th grader?

DO YOU KNOW ?

INTRODUCTION

COMPETENCES

MATERIAL

EVALUATION

INDICATOR

Math Aptitude TestWhich of the following sentences is correct?Nine and five are thirteen.orNine and five is thirteen.

Solution:Neither is correct ,9 + 5 = 14

Are you smarter than 9th grader?INTRODUCTION

COMPETENCES

MATERIAL

EVALUATION

INDICATOR

DO YOU KNOW?

History

How did we get the word "Surd" ?

Well around 820 AD al-Khwarizmi (the Persian guy who we get the name "Algorithm" from) called irrational numbers "'inaudible" ... this was later translated to the Latin surdus ("deaf" or "mute")

INTRODUCTION

COMPETENCES

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STANDARD COMPETENCE:1. Solving problems related to indices, surds and logarithms

BASIC COMPETENCE:

Using laws of indices, surds and logarithms.Doing the algebraic manipulation in computation related to indices, surds and logarithms.(Integrated with E- SETS )

COMPETENCES

MATERIAL

EVALUATION

INDICATOR

INTRODUCTION

INDICATORS:All of students should be able to:1.Change indices to surds or vice versa.2.Change indices or surds to logarithms form 3.Finish the computation related to indices, surds and logarithms.

MATERIAL

EVALUATION

INDICATOR

INTRODUCTION

COMPETENCES

MATERIAL

Indices or powers are also called exponent

The exponent of a number say how many times to use the number in multiplication.

In example 82 = 8 x 8 = 64In words: 82 could be called “8 to the second power”, “8 to the power 2” or simply “8 squared”.

Example :116 is easier to write and read than 11 x 11 x 11x 11 x 11x 11

INDICES

MATERIAL

Let b be a real number or a variable representing a real number. Let n be a positive integer. bn = b·b·b·b···b where there are n b’s

example: 85 = 8·8·8·8·8Example: x4 = x·x·x·x

In general:

INDICES

MATERIAL

INDICESLaw Example

x1 = x 61 = 6x0 = 1 70 = 1x-1 = 1/x 4-1 = ¼

xmxn = xm+n x2x3 = x2+3 = x5

xm/xn = xm-n x4/x2 = x4-2 = x2

(xm)n = xmn (x2)3 = x2×3 = x6

(xy)n = xnyn (xy)3 = x3y3

(x/y)n = xn/yn (x/y)2 = x2 / y2

x-n = 1/xn x-3 = 1/x3

MATERIAL

If it is a root and irrational, it is a surd. But not all roots are surds.

f a, b, (a ≠ 0 and b ≠ 0 are positive) and (m and n are real numbers) then 1. Multiplication of Surds :

SURDS

abbxabxabxa 21

21

21

2. Division of Surds

ba

ba

b

ababa

21

21

21

:.2

MATERIAL

If it is a root and irrational, it is a surd. But not all roots are surds.

f a, b, (a ≠ 0 and b ≠ 0 are positive) and (m and n are real numbers) then 1. Multiplication of Surds :

SURDS

abbxabxabxa 21

21

21

2. Division of Surds

ba

ba

b

ababa

21

21

21

:.2

MATERIAL

SURDS 636182.1 x

33333

323

21.3

55354.2

EVALUATION

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