• Year 11

# Basic Arithmetic and Algebra

approx. 27 hrs

11 topics

65 concepts

Enhance your skills and application of Basic Arithmetic and Algebra to set you up for success in Year 12.

Available in
NSW

### Overview

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.

### Topics & Concepts We Cover

This learning program is made up of the following 11 topics, broken down into 65 concepts.

• #### Basic Arithmetic 6 concepts

1. Enter and read scientific notation on a calculator

2. Determination of powers and roots

3. Convert numbers expressed in scientific notation to decimal form

4. Express numbers in scientific notation

5. Classification of rational and irrational numbers

6. Converting recurring decimals into simple fractions

• #### Expansion 5 concepts

1. Expand the Difference of Two Squares

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

3. Expand perfect squares

4. Expand algebraic expressions including indices and/or negative coefficients

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. Factorise the sum or difference of two cubes

2. Mixed factorisations involving quadratic and/or cubic expressions

3. Factorise the Difference of Two Squares

4. Factorise by grouping in pairs

5. Factorise non-monic quadratic trinomial expressions

6. Factorise perfect squares

7. Factorise monic quadratic trinomial expressions

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

• #### 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. Dividing surds

6. Multiplying surds

7. Subtracting surds

8. Simplifying surds

9. Expand and simplify binomial products with 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 single algebraic term denominator

5. Simplifying algebraic fractions addition/ subtraction with a numerical 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

• #### 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

• #### Quadratic Equations 6 concepts

1. Solve non-monic quadratic equations

2. Solve monic quadratic equations

3. Complete the square to solve quadratic equations

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

5. Use the quadratic formula to solve quadratic equations

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

• #### Linear Inequations 7 concepts

1. Proving inequalities using induction

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

3. Solve quadratic inequations and graph the solution

4. Double inequalities

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

6. Represent linear inequalities on the number line

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

• #### Absolute Values 8 concepts

1. Solve linear absolute value inequalities (variable RHS)

2. Evaluate absolute values using the geometric interpretation

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

4. Solve linear absolute value inequalities (constant RHS)

5. Solve linear absolute value equations

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

### 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

### Ready to start this program?

Simply pick a time that works for you

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime