Please enable JavaScript.
Coggle requires JavaScript to display documents.
Year 10A Real Numbers (Surds (Introduction to Surds (Equivalent index form…
Year 10A Real Numbers
Surds
Introduction to Surds
Equivalent index form
sqrt(x) undefined for x<0
sqrt(x) is positive root
Index Laws and Fractional Powers
Rationalising Denominators
Rationalise binomial denominators
Simplifying Surds
Adding and Subtracting Surds
explain why 3√+5√≠√8
Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264)
Multiplying and Dividing Surds
Binomial Surds
Expanding (FOIL)
Add and subtract (separate parts)
Logarithms
Introduction to Logarithms
Convert between exponential and logarithmic forms.
Algorithmic definition
Log Laws 1
Multiplication→addition
Division→subtraction
Derive from index laws
Log Laws 2
Logs of exponents
log(1)=0, log_a(a)=1
Use the definition of a logarithm to establish and apply the laws of logarithms (ACMNA265)
Solving Exponential Equations with Logarithms
NSW Only. Appears under Linear and Non-Linear for AUS/VIC
Review
Fractional Indicies
Square Roots
Index Laws
Index notation
Extension
The number e
The Natural Logarithm
Pre-Learning: Roots and Powers
Cube Roots and Beyond
Square Numbers, Cube Numbers and More
Small square and cube numbers to memorise/recognise
Squares: 2,3,4,5,6,7,8,9,10,11,12
Cubes: 2,3,4,5
Quartics: 2,3
Quintic: 2
Problem Solving
Applications of Surds
Solve problems where a decimal answer is insufficient - height of equilateral triangle
Activities
Showing Numbers on Number lines
Use Compass and straight edge to construct simple rational numbers and surds on number line
Cover in activity lesson?
Rational and Irrational Numbers
Real Numbers
Define Rational and Irrational
Rational Numbers
Terminating and Recurring decimals
0.9999...=1
https://www.basic-mathematics.com/converting-repeating-decimals-to-fractions.html
Decimal form
Both are real numbers
Not all reals are rational
Distinguish between rational and irrational number