• Mathematics General
• Year 12

# Algebra and Modelling

approx. 19 hrs

5 topics

52 concepts

Develop an aptitude for Algebra and Modelling and select and apply algebraic techniques with confidence.

Available in
VIC

### Overview

The Year 12 Algebra and Modelling program is aligned with the content outlined in the Australian curriculum for General Mathematics. Students studying Algebra and Modelling apply algebraic skills and techniques to enhance their ability to interpret and use linear and non-linear mathematical models in a range of contexts.

### Topics & Concepts We Cover

This learning program is made up of the following 5 topics, broken down into 52 concepts.

• #### Modelling Linear Relationships 15 concepts

1. Classify the nature of a gradient from a linear function

2. Sketch a linear relationship from a table of values on a cartesian plane

3. Determine the gradient and y-intercept using the gradient-intercept form of a linear relationship

4. Find the gradient of a line between two points using rise over run

5. Reading the x and y intercept from a graph

6. Finding the y - intercept at x=0

7. Use the gradient and y-intercept to graph a linear equation

8. identify independent and dependent variables in a practical context

9. solving practical problems with linear relationships

10. Graph two intersecting lines on the same set of axes and read off the point of intersection

11. Interpolation and Extrapolation

12. Analyse step graphs

13. Use a piecewise linear function to model and solve practical situations

14. establish meaning for the gradient and intercepts in a practical context

15. apply break-even analysis to linear models

• #### Inequations 10 concepts

1. Determine the maximum value of an objective function for a given feasible region

2. Determine the minimum value of an objective function for a given feasible region

3. Set up a basic linear programming problem

4. Solve basic linear programming problems

5. Sketch a region defined by a linear inequality

6. Solve a linear inequation using graphs

7. Double inequalities

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

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

10. Represent linear inequalities on the number line

• #### Algebraic Expressions 9 concepts

1. Apply index laws for multiplying

2. Apply index laws for dividing

3. The zero index

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

5. Expanding algebraic expressions involving terms with indices and/or negative coefficients

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

7. Simplify algebraic expressions by adding or subtracting like terms

8. Identify like terms

9. Substitute positive or negative values into an algebraic expression and evaluate the result

• #### Equations 9 concepts

1. Solve linear equations involving more than three steps

2. Solve one-step equations

3. Solve two-step equations

4. Solve three-step equations

5. Rearrange a formula to change the subject of the equation

6. Substitute positive or negative integers into a given formula

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

8. Solve linear simultaneous equations using substitution method

9. Solve linear simultaneous equations using elimination method

• #### Modelling Non-Linear Relationships 9 concepts

1. Sketch parabolic graphs - positive quadrant

2. Sketch cubic graphs - positive quadrant

3. Sketch hyperbola graphs - positive quadrant

4. Sketch exponential graphs - positive quadrant

5. solve contextual problems - including determining minimum and maximum values

6. develop non-linear equations where one variable varies directly as a power of another

7. recognise the limitations of non-linear modelling - interpolating and extrapolating

8. develop linear equations from practical contexts where one variable directly varies with another

9. Solve inverse variation problems

### 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 Algebra and Modelling

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 book in your first session and match you to an expert tutor

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime