VICGeneral Mathematics

Unit 3 Recursion and financial modelling

14 dot points across 14 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do annuity investments and savings plans grow when regular payments are added to a compounding balance, and how is the finance solver set up for them?

Model an annuity investment or savings plan where a regular payment is added to a compounding balance using the recurrence relation, analyse it on a finance solver, and find the final balance, total interest and required payment
A focused answer to the VCE General Mathematics Unit 3 Recursion and financial modelling key-knowledge point on annuity investments. Regular additions to a compounding balance, the growth recurrence, finance solver sign conventions, final balance, total interest, and solving for the required payment.
7 min answer →

How do you investigate the association between two categorical variables, or between a numerical and a categorical variable, using tables and grouped displays?

Construct and interpret a two-way frequency table, convert it to percentages to investigate association between two categorical variables, use a segmented or side-by-side bar chart, and compare a numerical variable across categories with parallel boxplots
A focused answer to the VCE General Mathematics Unit 3 Data analysis key-knowledge point on categorical association. Two-way frequency tables, column percentages, segmented bar charts, judging association, and comparing a numerical variable across groups with parallel boxplots.
6 min answer →

How do you build a boxplot from a five-number summary, test for outliers, and compare two groups using parallel boxplots?

The five-number summary, construction and interpretation of boxplots, the use of the lower and upper fences to identify outliers, and comparison of distributions using parallel boxplots
A focused answer to the VCE General Mathematics Unit 3 data analysis key knowledge on the five-number summary, constructing and reading boxplots, applying the 1.5 IQR fence rule for outliers, and comparing groups with parallel boxplots.
6 min answer →

How do you measure the association between two numerical variables and fit a least-squares line to model and predict?

Investigate the association between two numerical variables using a scatterplot, the correlation coefficient and the coefficient of determination, fit a least-squares regression line, and interpret its slope, intercept and residuals
A focused answer to the VCE General Mathematics Unit 3 Data analysis key-knowledge point on bivariate data. Reading scatterplots, the correlation coefficient r, the coefficient of determination, fitting and interpreting a least-squares line, residual plots and the dangers of extrapolation.
6 min answer →

When a scatterplot is curved, how do the squared, log and reciprocal transformations straighten the data so a least-squares line can be fitted?

Recognise non-linear association from a scatterplot and residual plot, apply the squared, logarithmic or reciprocal transformation to the explanatory or response variable to linearise the data, fit a least-squares line to the transformed data, and use it to predict
A focused answer to the VCE General Mathematics Unit 3 Data analysis key-knowledge point on data transformation. Spotting curvature, the circle-of-transformations idea, applying the squared, log and reciprocal transformations, fitting a line to transformed data, and predicting back.
7 min answer →

How do you classify data, choose the right display, and describe the shape, centre and spread of a distribution?

Types of data (categorical and numerical), appropriate graphical displays, and describing a numerical distribution in terms of shape, centre and spread using the mean, median, range, interquartile range and standard deviation
A focused answer to the VCE General Mathematics Unit 3 data analysis key knowledge on classifying data, choosing graphical displays, and describing numerical distributions by shape, centre and spread with the mean, median, range, IQR and standard deviation.
6 min answer →

How do you summarise, display and describe the distribution of a single numerical or categorical variable in VCE General Mathematics?

Display and describe the distribution of a numerical variable using a histogram, dot plot, stem plot or boxplot, summarise it with measures of centre and spread, and identify outliers using the lower and upper fences
A focused answer to the VCE General Mathematics Unit 3 Data analysis key-knowledge point on univariate data. Choosing displays, describing shape, centre and spread, computing the five-number summary, and finding outliers with the 1.5 IQR fence rule.
6 min answer →

How does the normal distribution describe data, and how do the 68-95-99.7 rule and standardised z-scores let you compare and find percentages?

Use the normal distribution and the 68-95-99.7 rule to estimate the percentage of values within a number of standard deviations of the mean, and standardise a value to a z-score to compare values from different distributions
A focused answer to the VCE General Mathematics Unit 3 Data analysis key-knowledge point on the normal distribution. The bell shape, the 68-95-99.7 rule for finding percentages, standardising a value to a z-score, and comparing values from different normal distributions.
6 min answer →

What is a perpetuity, how does the balance stay constant when the payment exactly equals the interest, and how do you find the payment or the principal?

Model a perpetuity as a special annuity in which the regular payment equals the interest earned each period so the balance never changes, and find the perpetual payment, the required principal or the interest rate
A focused answer to the VCE General Mathematics Unit 3 Recursion and financial modelling key-knowledge point on perpetuities. The condition that payment equals interest, the constant-balance recurrence, the formula linking payment, principal and rate, and finding each unknown.
6 min answer →

How are compound interest investments, reducing-balance loans and annuities modelled with recurrence relations and analysed on a financial solver?

Model and analyse compound interest investments, reducing-balance loans, annuities and perpetuities using a first-order recurrence relation and a finance solver, and interpret balance, repayment, interest and the effect of changing parameters
A focused answer to the VCE General Mathematics Unit 3 Recursion and financial modelling key-knowledge point on financial modelling. Compound interest, reducing-balance loans, annuities and perpetuities, the mixed recurrence relation, the finance solver, and interpreting interest, balance and repayment.
6 min answer →

How do seasonal indices quantify a repeating pattern, and how do you deseasonalise and reseasonalise time series data?

Calculate seasonal indices from time series data, interpret an index as a percentage above or below the seasonal average, deseasonalise data by dividing by the index, and reseasonalise a forecast by multiplying by the index
A focused answer to the VCE General Mathematics Unit 3 Data analysis key-knowledge point on seasonal indices. Calculating seasonal indices that sum to the number of seasons, interpreting them as percentages, deseasonalising by dividing, and reseasonalising a forecast by multiplying.
7 min answer →

How do first-order recurrence relations generate arithmetic and geometric sequences, and how are their terms and sums found?

Use a first-order linear recurrence relation to generate a sequence, recognise arithmetic and geometric sequences, find the nth term with an explicit rule, and compute the sum of an arithmetic or geometric series
A focused answer to the VCE General Mathematics Unit 3 Recursion and financial modelling key-knowledge point on sequences. First-order recurrence relations, arithmetic and geometric rules, explicit nth-term formulas, and the sums of arithmetic and geometric series.
6 min answer →

How do simple and compound interest differ, how does each follow a recurrence relation, and how do you compare them with effective rates?

Model simple interest with a linear recurrence and compound interest with a geometric recurrence, find balances and interest earned, convert between nominal and effective annual rates, and compare simple and compound growth
A focused answer to the VCE General Mathematics Unit 3 Recursion and financial modelling key-knowledge point on interest. Simple interest as a linear recurrence, compound interest as a geometric recurrence, the rule for the nth balance, compounding periods, and effective annual rate.
7 min answer →

How do you display and describe a time series, and how do moving-mean and moving-median smoothing reveal the underlying trend?

Construct and interpret a time series plot, describe its features (trend, seasonality, cycles, irregular fluctuations), smooth it using moving-mean and moving-median smoothing, and fit a least-squares trend line for forecasting
A focused answer to the VCE General Mathematics Unit 3 Data analysis key-knowledge point on time series. Reading a time series plot, describing trend, seasonality and irregular variation, moving-mean and moving-median smoothing, centred smoothing, and a least-squares trend line for forecasting.
7 min answer →