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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
MATERIAL
EVALUATION
INDICATOR
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:3.Change indices to surds or vice versa.4.Change indices or surds to logarithms form 5.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 = 8·8·8·8·8
Example: x4 = x·x·x·x
In general:
INDICES
MATERIAL
INDICES Law Examplex1 = x 61 = 6x0 = 1 70 = 1x-1 = 1/x 4-1 = ¼xmxn = 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 === 2
12
1
2
1
2. Division of Surds
b
a
b
a
b
a
b
aba =
===
2
1
2
1
2
1
:.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 === 2
12
1
2
1
2. Division of Surds
b
a
b
a
b
a
b
aba =
===
2
1
2
1
2
1
:.2
MATERIAL
SURDS 636182.1 ==x
333
33
3
23
2
1.3 ==+
55354.2 =−
EVALUATION
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TERIMA KASIH
