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717896
Indices and Surds
Description
Indices and Surds | AS OCR Maths
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a levels
c1
maths
maths
c1
a levels
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james_hobson
, updated more than 1 year ago
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Created by
james_hobson
over 10 years ago
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Resource summary
Indices and Surds
Indices
Multiplication Rule
x^a * x^b = x^a+b
e.g. 2^2 * 2^3 = 2^5 = 32
Division Rule
x^a / x^b = x^a-b
e.g. 2^3 / 2^2 = 2^1 = 2
Power on Power Rule
(x^a)^b = x^a*b
e.g. (2^3)^2 = 2^3*2 = 2^6 = 64
Power of Zero
x^0 = 1
e.g. 2^0 = 1
Negative Powers
x^-a = 1/x^a
e.g. 2^-2 = 1/2^2 = ¼
Fractional Indices
x^a/b = (b√(x))^a
e.g. 8^2/3 = (cube √(8))^2 = 2^2 = 4
Surds
Addition
a*√(b) + c*√(b) = (a+c)*√(b)
e.g. 4*√(7) + 3*√(7) = 7*√(7)
Subtraction
a*√(b) - c*√(b) = (a-c)*√(b)
e.g. 4*√(7) - 2*√(7) = 2*√(7)
Multiplication Rule
√ab = √a * √b
e.g. √2*4 = √2*√4 = 2√2
Division Rule
√a/b = √a / √b
e.g. √2/3 = √2 / √3
Rationalising the Denominator
a / √b * √b / √b = a√b / b
e.g. 1 / √2 * √2 / √2 = √2 / 2
a / b+√c * b-√c / b-√c = a(b-√c) / (b+√c)(b-√c)
e.g. 1 / 2+√2 * 2-√2 / 2-√2 = 2-√2 / 4-2 = 2-√2 / 2
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