- Mathematics Advanced
- Year 11
Basic Arithmetic and Algebra
approx. 27 hrs
11 topics
66 concepts
Enhance your skills and application of Basic Arithmetic and Algebra to set you up for success in Year 12.
approx. 27 hrs
11 topics
66 concepts
Enhance your skills and application of Basic Arithmetic and Algebra to set you up for success in Year 12.
Basic Arithmetic and Algebra are essential components of Year 11 Mathematics Advanced, as outlined in the NSW Mathematics syllabus. In this program, students learn how to perform arithmetic and algebraic procedures across a range of fluency-based questions, and how to approach problem-solving tasks up to a complex level.
This learning program is made up of the following 11 topics, broken down into 66 concepts.
Evaluate absolute values using the geometric interpretation
Expressing absolute functions as the sum of piecewise defined functions
Solve linear absolute value equations
Solve linear absolute value inequalities (constant RHS)
Solve linear absolute value inequalities (variable RHS)
Sketching the absolute value of a linear function on the number line
Application of identities involving absolute value including the triangle inequality
Sketching the absolute value of a linear function on the number plane
Solve non-monic quadratic equations
Solve monic quadratic equations
Substitute a pronumeral to simplify higher-order equations to solve the equation
Use the quadratic formula to solve quadratic equations
Complete the square to solve quadratic equations
Select the appropriate factorising method to solve a given quadratic equation
Solve logarithmic and exponential equations
Proving inequalities using induction
Solve quadratic inequations and graph the solution
Solve inequations with a variable in the denominator and graph the solution
Double inequalities
Solve linear inequalities, recognising that there are infinite solutions
Solve linear inequalities by reversing the direction of the inequality sign when multiplying or dividing by a negative number
Represent linear inequalities on the number line
Systems of Three Equations in Three Variables
Solve simultaneous equations, where one or more equations are non-linear and interpret results
Generate and solve linear equations from word problems and interpret the results
Solve linear simultaneous equations using elimination method where one or both of the equations need to be modified
Solve linear simultaneous equations using substitution method
Solve linear simultaneous equations using elimination method
Expand and simplify the square of a binomial with surds
Rationalising the denominator
Expand and simplify sum by difference with surds
Expand and simplify binomial products with surds
Simplifying surds
Adding surds
Subtracting surds
Multiplying surds
Dividing surds
Factorise and simplify algebraic expressions involving multiplying and/or dividing algebraic fractions with a quadratic expression on the numerator and/or denominator
Factorise and simplify algebraic expressions involving a quadratic expression on the numerator and/or denominator
Factorise and simplify algebraic expressions involving adding and/or subtracting algebraic fractions with a quadratic expression on the numerator and/or denominator
Simplifying algebraic fractions addition/ subtraction with a numerical denominator
Simplifying algebraic fractions addition/ subtraction with a single algebraic term denominator
Add or subtract algebraic fractions with binomial numerators or denominators
Simplifying algebraic fractions multiplication/ division with a numerical denominator or single algebraic term
Solve linear equations involving more than one algebraic fraction
Solve linear equations involving more than three steps
Expand perfect squares
Expand the Difference of Two Squares
Expand and simplify a variety of expressions involving binomial products
Expand algebraic expressions by removing grouping symbols and collecting like terms
Expand binomial products using FOIL method or distributive method
Substitute integers, fractions, decimals or surds into expressions or formula involving the four operations, powers and roots
Mixed factorisations involving quadratic and/or cubic expressions
Factorise the sum or difference of two cubes
Factorise by grouping in pairs
Factorise non-monic quadratic trinomial expressions
Factorise the Difference of Two Squares
Factorise perfect squares
Factorise monic quadratic trinomial expressions
Factorising algebraic expressions involving terms with indices and/or negative coefficients
Determination of powers and roots
Enter and read scientific notation on a calculator
Express numbers in scientific notation
Convert numbers expressed in scientific notation to decimal form
Classification of rational and irrational numbers
Converting recurring decimals into simple fractions
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