Topic 4.1: Time series analysis (15 hours) §

Describing and interpreting patterns in time series data §

• construct time series plots (4.1.1)
• describe time series plots by identifying features such as trend (long term direction), seasonality (systematic, calendar-related movements), and irregular fluctuations (unsystematic, short term fluctuations), and recognise when there are outliers (4.1.2)

Analysing time series data §

• smooth time series data by using a simple moving average, including the use of spreadsheets to implement this process (4.1.3 )
• calculate seasonal indices by using the average percentage method (4.1.4)
• deseasonalise a time series by using a seasonal index, including the use of spreadsheets to implement this process (4.1.5)
• fit a least-squares line to model long-term trends in time series data (4.1.6)
• predict from regression lines, making seasonal adjustments for periodic data (4.1.7)

The data investigation process §

• implement the statistical investigation process to answer questions that involve the analysis of time series data (4.1.8)

Topic 4.2: Loans, investments and annuities (20 hours) §

Compound interest loans and investments §

• use a recurrence relation to model a compound interest loan or investment and investigate (numerically or graphically) the effect of the interest rate and the number of compounding periods on the future value of the loan or investment (4.2.1)
• calculate the effective annual rate of interest and use the results to compare investment returns and cost of loans when interest is paid or charged daily, monthly, quarterly or six-monthly (4.2.2)
• with the aid of a calculator or computer-based financial software, solve problems involving compound interest loans, investments and depreciating assets (4.2.3)

Reducing balance loans (compound interest loans with periodic repayments) §

• use a recurrence relation to model a reducing balance loan and investigate (numerically or graphically) the effect of the interest rate and repayment amount on the time taken to repay the loan (4.2.4)
• with the aid of a financial calculator or computer-based financial software, solve problems involving reducing balance loans (4.2.5)

Annuities and perpetuities (compound interest investments with periodic payments made from the investment) §

• use a recurrence relation to model an annuity, and investigate (numerically or graphically) the effect of the amount invested, the interest rate, and the payment amount on the duration of the annuity (4.2.6)
• with the aid of a financial calculator or computer-based financial software, solve problems involving annuities (including perpetuities as a special case) (4.2.7)

Topic 4.3: Networks and decision mathematics (20 hours) §

Trees and minimum connector problems §

• ntify practical examples that can be represented by trees and spanning trees (1. ide)
• identify a minimum spanning tree in a weighted connected graph, either by inspection or by using Prim’s algorithm (4.3.2)
• use minimal spanning trees to solve minimal connector problems (4.3.3)

Project planning and scheduling using critical path analysis (CPA) §

• construct a network to represent the durations and interdependencies of activities that must be completed during the project (4.3.4)
• use forward and backward scanning to determine the earliest starting time (EST) and latest starting times (LST) for each activity in the project (4.3.5)
• use ESTs and LSTs to locate the critical path(s) for the project (4.3.6)
• use the critical path to determine the minimum time for a project to be completed (4.3.7)
• calculate float times for non-critical activities (4.3.8)

Flow networks §

• solve small-scale network flow problems, including the use of the ‘maximum flow-minimum cut’ theorem (4.3.9)

Assignment problems §

• Use a bipartite graph and/or its tabular or matrix form to represent an assignment/ allocation problem (4.3.10)
• Determine the optimum assignment(s), by inspection for small-scale problems, or by use of the Hungarian algorithm for larger problems (4.3.11)