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:one::zero: AUS Y10 Patterns and Algebra (:file_folder:2. Expanding and…
:one::zero: AUS Y10
Patterns and Algebra
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Curriculum
Factorise algebraic expressions by taking out a common algebraic factor (ACMNA230)
(NSW Stage 5.2 Algebraic Techniques)
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using the distributive law and the index laws to factorise algebraic expressions :left_right_arrow:
understanding the relationship between factorisation and expansion :left_right_arrow:
NSW
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factorise algebraic expressions, including those involving indices, by determining common factors, eg factorise 3x^2−6x, 14ab+12a^2, 21xy−3x+9x^2, 15p^2q^3−12pq^4 :left_right_arrow:
recognise that expressions such as 24x2y+16xy^2=4xy(6x+4y) may represent 'partial factorisation' and that further factorisation is necessary to 'factorise fully' :left_right_arrow:
Simplify algebraic products and quotients using index laws (ACMNA231) :straight_ruler:
applying knowledge of index laws to algebraic terms, and simplifying algebraic expressions using both positive and negative integral indices :straight_ruler:
Apply the four operations to simple algebraic fractions with numerical denominators (ACMNA232)
(NSW Stage 5.2 Algebraic Techniques)
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expressing the sum and difference of algebraic fractions with a common denominator :straight_ruler:
using the index laws to simplify products and quotients of algebraic fractions :straight_ruler:
NSW
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simplify expressions that involve algebraic fractions with numerical denominators,
eg a/2+a/3, 2x/5−x/3, 3x/4×2x/9, 3x/4÷9x/2 :straight_ruler:
connect the processes for simplifying expressions involving algebraic fractions with the corresponding processes involving numerical fractions :straight_ruler:
Expand binomial products and factorise monic quadratic expressions using a variety of strategies (ACMNA233)
(NSW Stage 5.2 Algebraic Techniques)
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exploring the method of completing the square to factorise quadratic expressions and solve quadratic equations :left_right_arrow: :unlock:
identifying and using common factors, including binomial expressions, to factorise algebraic expressions using the technique of grouping in pairs :left_right_arrow:
using the identities for perfect squares and the difference of squares to factorise quadratic expressions :left_right_arrow:
NSW
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expand binomial products by finding the areas of rectangles :left_right_arrow:
use algebraic methods to expand binomial products, eg (x+2)(x−3), (4a−1)(3a+2) :left_right_arrow:- factorise monic quadratic trinomial expressions, eg x^2+5x+6, x2+2x−8 :left_right_arrow:
connect binomial products with the commutative property of arithmetic, such that (a+b)(c+d)=(c+d)(a+b) :left_right_arrow:
explain why a particular algebraic expansion or factorisation is incorrect, eg 'Why is the factorisation x^2−6x−8=(x−4)(x−2) incorrect?' :left_right_arrow:
Substitute values into formulas to determine an unknown (ACMNA234) :unlock:
solving simple equations arising from formulas :unlock:
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2. Expanding and Factorising
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Expanding Binomial Products
Factorising with Index Laws
Factorising by Completing the Square
Identifying Common Factors
Factorisation by Grouping
Factorising Perfect Squares
Factorising Differences of Two Squares
Factorising Quadratic Trinomials
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3. Algebraic Fractions
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Simplifying Algebraic Products with Index Laws
Adding Algebraic Fractions
Subtracting Algebraic Fractions
Multiplying Algebraic Fractions
Dividing Algebraic Fractions
Sinplifying Algebraic Quotients with Index Laws
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4. Using Formulas and Solving Equations
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Using Formulas
Solving Equations
Solving Quadratic Equations
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1. Review
Index Laws: Multiplying and Dividing Powers
Expanding
Factorising
Index Laws: The Zero Index and Stacked Powers
Evaluating Expressions and Using Formulas