• Mathematical Methods
  • Year 11

Basic Arithmetic and Algebra

approx. 27 hrs

11 topics

66 concepts

Deepen your understanding of Basic Arithmetic and Algebra to set you up for success in Year 12 enhance your examination results.

Available in
ACT NT QLD SA TAS VIC WA

Overview

Basic Arithmetic and Algebra are essential components of Year 11 Mathematical Methods, as outlined in the Australian curriculum. This program gives students the skills to perform arithmetic and algebraic procedures across a range of fluency-based questions and problem-solving tasks up to a complex level.

Topics & Concepts We Cover

This learning program is made up of the following 11 topics, broken down into 66 concepts.

  • Absolute Values 8 concepts

    1. Evaluate absolute values using the geometric interpretation

    2. Expressing absolute functions as the sum of piecewise defined functions

    3. Solve linear absolute value equations

    4. Solve linear absolute value inequalities (constant RHS)

    5. Solve linear absolute value inequalities (variable RHS)

    6. Sketching the absolute value of a linear function on the number line

    7. Application of identities involving absolute value including the triangle inequality

    8. Sketching the absolute value of a linear function on the number plane

  • Quadratic Equations 6 concepts

    1. Solve non-monic quadratic equations

    2. Solve monic quadratic equations

    3. Substitute a pronumeral to simplify higher-order equations to solve the equation

    4. Use the quadratic formula to solve quadratic equations

    5. Complete the square to solve quadratic equations

    6. Select the appropriate factorising method to solve a given quadratic equation

  • Linear Inequations 8 concepts

    1. Solve logarithmic and exponential equations

    2. Proving inequalities using induction

    3. Solve quadratic inequations and graph the solution

    4. Solve inequations with a variable in the denominator and graph the solution

    5. Double inequalities

    6. Solve linear inequalities, recognising that there are infinite solutions

    7. Solve linear inequalities by reversing the direction of the inequality sign when multiplying or dividing by a negative number

    8. Represent linear inequalities on the number line

  • Simultaneous Equations 6 concepts

    1. Systems of Three Equations in Three Variables

    2. Solve simultaneous equations, where one or more equations are non-linear and interpret results

    3. Generate and solve linear equations from word problems and interpret the results

    4. Solve linear simultaneous equations using elimination method where one or both of the equations need to be modified

    5. Solve linear simultaneous equations using substitution method

    6. Solve linear simultaneous equations using elimination method

  • Surds 9 concepts

    1. Expand and simplify the square of a binomial with surds

    2. Rationalising the denominator

    3. Expand and simplify sum by difference with surds

    4. Expand and simplify binomial products with surds

    5. Simplifying surds

    6. Adding surds

    7. Subtracting surds

    8. Multiplying surds

    9. Dividing surds

  • Algebraic Fractions 7 concepts

    1. Factorise and simplify algebraic expressions involving multiplying and/or dividing algebraic fractions with a quadratic expression on the numerator and/or denominator

    2. Factorise and simplify algebraic expressions involving a quadratic expression on the numerator and/or denominator

    3. Factorise and simplify algebraic expressions involving adding and/or subtracting algebraic fractions with a quadratic expression on the numerator and/or denominator

    4. Simplifying algebraic fractions addition/ subtraction with a numerical denominator

    5. Simplifying algebraic fractions addition/ subtraction with a single algebraic term denominator

    6. Add or subtract algebraic fractions with binomial numerators or denominators

    7. Simplifying algebraic fractions multiplication/ division with a numerical denominator or single algebraic term

  • Linear Equations 2 concepts

    1. Solve linear equations involving more than one algebraic fraction

    2. Solve linear equations involving more than three steps

  • Expansion 5 concepts

    1. Expand perfect squares

    2. Expand the Difference of Two Squares

    3. Expand and simplify a variety of expressions involving binomial products

    4. Expand algebraic expressions by removing grouping symbols and collecting like terms

    5. Expand binomial products using FOIL method or distributive method

  • Substitution 1 concept

    1. Substitute integers, fractions, decimals or surds into expressions or formula involving the four operations, powers and roots

  • Factorisation 8 concepts

    1. Mixed factorisations involving quadratic and/or cubic expressions

    2. Factorise the sum or difference of two cubes

    3. Factorise by grouping in pairs

    4. Factorise non-monic quadratic trinomial expressions

    5. Factorise the Difference of Two Squares

    6. Factorise perfect squares

    7. Factorise monic quadratic trinomial expressions

    8. Factorising algebraic expressions involving terms with indices and/or negative coefficients

  • Basic Arithmetic 6 concepts

    1. Determination of powers and roots

    2. Enter and read scientific notation on a calculator

    3. Express numbers in scientific notation

    4. Convert numbers expressed in scientific notation to decimal form

    5. Classification of rational and irrational numbers

    6. Converting recurring decimals into simple fractions

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Basic Arithmetic and Algebra

Reporting

  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

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Starting at

$49(inc. GST)

per session

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