In this course, students will develop the mathematical understanding and skills to solve problems relating to:

- Bivariate Graphs
- Probability and Relative Frequencies
- Loans and Compound Interest

The subject matter of the topics in this unit should be applied in a meaningful context and of interest to students. Two possible contexts in this unit are ‘Mathematics of health’ and ‘Mathematics of home loans’. However, these contexts may not be relevant to all students. Suitable contexts relevant to the particular student cohort should be chosen.

*Source – QCAA Applied Senior Syllabus 2019*

Lessons

#### Introduction to Probability

- Video - Basic Probability (11:40)
- Video - Standard Pack of 52 Cards (11:18)
- Topic - Basic Properties of Probability
- Topic - Informal Description of Chance: Drag
- Topic - Informal Description of Chance: Multiple Choice
- Topic - Informal Description of Chance: True or False
- Topic - Informal Description of Chance: Likely

#### Experimental Probability

- Video - Estimating Probabilities from Data (5:13)
- Video - Understanding Regular Pack of 52 Cards (2:52)
- Video - Solving Regular Pack of 52 Cards Problems involving Probability (4:57)
- Video - Probability of Choosing All Different Suits from Regular Pack of 52 Cards (3:31)
- Video - Probability involving Dice (7:22)
- Video - Probability involving Sum of Faces of Dice (2:20)
- Video - Probability involving Product of Faces of Dice (6:01)
- Topic - Counting Number of Cards
- Topic - Probability using Regular Pack of 52 Cards
- Topic - Two Digit Numbers by Dice
- Topic - Sum of Two Dice

#### Tree Diagrams

- Video - Basic Tree Diagrams (5:03)
- Video - Tree Diagrams involving Percentages (7:45)
- Video - Tree Diagrams involving Independent Events (3:44)
- Video - Tree Diagrams involving Compound Events (7:15)
- Video - Tree Diagrams involving Twice as Likely (6:31)
- Video - Asymmetrical Tree Diagrams (2:10)
- Video - Probability involving Probability Tree 1 (2:34)
- Video - Probability involving Probability Tree 2 (2:35)
- Video - Probability involving Probability Tree 3 (2:39)
- Topic - Play with Tree Diagrams

#### Compound Interest Applications

- Video - Investments by Compound Interest (4:32)
- Video - Amount of Interest Earned by Compound Interest (2:17)
- Topic - Compound Interest Applications: Compounded Annually
- Topic - Compound Interest Applications: Compounded Monthly
- Topic - Compound Interest Applications: Interest Earned
- Topic - Compound Interest Applications: Principal Amount

#### Personal Loans in Compound Interest

- Topic - Monthly Repayments of Reducing Balance Personal Loans
- Topic - Weekly Repayments of Reducing Balance Personal Loans
- Topic - Total Interest Charged on Personal Loans in Monthly Repayments
- Topic - Total Interest Charged on Personal Loans in Weekly Repayments
- Topic - Outstanding Balance on Personal Loans in Monthly Repayments
- Topic - Outstanding Balance on Personal Loans in Weekly Repayments

#### Home Loans in Compound Interest

- Topic - Monthly Repayments of Reducing Balance Home Loans
- Topic - Weekly Repayments of Reducing Balance Home Loans
- Topic - Total Interest Charged on Home Loans in Monthly Repayments
- Topic - Total Interest Charged on Home Loans in Weekly Repayments
- Topic - Outstanding Balance on Home Loans in Monthly Repayments
- Topic - Outstanding Balance on Home Loans in Weekly Repayments

#### Loan Repayments in Borrowing Money

- Video - Understanding Loan Repayments using Loan Balance Due (4:28)
- Video - Calculating the Values of Loan Repayments (4:27)
- Video - Loan Balance Sheet (4:33)
- Video - Understanding of Calculating Repayments in a Table (3:30)
- Video - Calculating Monthly Repayments in a Table (4:13)
- Video - Calculating Fortnightly Repayments in a Table (3:21)
- Topic - Understanding Loan Repayments using Loan Balance Due
- Topic - Calculating the Values of Loan Repayments
- Topic - Loan Balance Sheet
- Topic - Understanding of Calculating Repayments in a Table
- Topic - Calculating Monthly Repayments in a Table

#### Reducing Balance Loans

- Video - Reading a Table Reducing Balance Loan (2:56)
- Video - Reducible Balance Loan using Period-Loan Table (1:04)
- Video - Reducible Balance Loan using Interest-Loan Table (3:33)
- Video - Table for Reducing Balance Loan based on the Loan Amount (5:16)
- Video - Table for Reducing Balance Loan based on Interest Rates (3:45)
- Video - Graphs of Reducing Balance Loan (6:33)
- Video - Comparisons Monthly and Fortnightly Repayments using Graphs (2:53)
- Video - Monthly Instalments by Borrowing Table (8:47)

#### Loan Repayments using Present Value

- Video - Understanding Loan Repayments (6:20)
- Video - Annual Loan Repayments (1:03)
- Video - Monthly Loan Repayments (1:00)
- Video - Fortnightly Loan Repayments (3:32)
- Topic - Finding Annual Repayments using Present Value Formula
- Topic - Finding Quarterly Repayments using Present Value Formula
- Topic - Finding Monthly Repayments using Present Value Formula
- Topic - Finding Present Value by Annual Repayments
- Topic - Finding Present Value by Quarterly Repayments
- Topic - Finding Present Value by Monthly Repayments
- Topic - Finding Total Interest Paid

#### Annuities Formula

- Topic - Amount Owing in Monthly Repayments at Monthly Interest Rate
- Topic - Amount Owing in Quarterly Repayments at Quarterly Interest Rate
- Topic - Amount Owing in Weekly Repayments at Weekly Interest Rate
- Topic - Amount Owing in Fortnightly Repayments at Fortnightly Interest Rate
- Topic - Amount Owing in Monthly Repayments at Annual Interest Rate
- Topic - Amount Owing in Quarterly Repayments at Annual Interest Rate
- Topic - Amount Owing in Weekly Repayments at Annual Interest Rate
- Topic - Amount Owing in Fortnightly Repayments at Annual Interest Rate
- Topic - Amount of Monthly Repayment by Annuity Formula
- Topic - Amount of Quarterly Repayment by Annuity Formula
- Topic - Amount of Weekly Repayment by Annuity Formula
- Topic - Amount of Fortnightly Repayment by Annuity Formula
- Topic - Total Interest of Monthly Repayments by Annuity Formula
- Topic - Total Interest of Quarterly Repayments by Annuity Formula
- Topic - Total Interest of Weekly Repayments by Annuity Formula
- Topic - Total Interest of Fortnightly Repayments by Annuity Formula

#### Loan Repayments using Reducible Interest and Balance

- Video - Reducible Interest using Tables (4:34)
- Video - Reducible Interest Monthly (3:49)
- Video - Repayment Table of Reducible Interest Loans (4:38)
- Video - Repayment Table of Reducible Interest Loans: Interest Paid (4:38)
- Video - Completing Repayment Table of Reducible Interest Loans (5:24)
- Video - Repayment Table of Reducible Interest Loans: P + I - R (3:30)
- Video - Payout of Reducible Interest Loans (4:23)
- Video - Loan Statement of Reducible Interest Loans (5:01)
- Video - Hire Purchase or Buy Outright (3:11)
- Video - Flat Rate Loans and Reducing Balance Loans (6:23)