SACE Stage 2 General Mathematics key terms

The original amount of money borrowed or invested, before any interest is added. Interest calculations are usually performed on this starting figure, though some loans recalculate it as repayments are made.

Interest calculated only on the original principal for each period, so the interest amount stays the same every period. The total grows in a straight line rather than accelerating.

Interest calculated on the principal plus any interest already earned, so each period's interest is added to the balance. The balance grows by a fixed percentage each period, producing exponential growth.

A percentage charged or paid for the use of money over a period, usually quoted per year. It must be converted to a decimal and matched to the compounding period before being used in a formula.

The stated yearly interest rate before any adjustment for how often interest is compounded. It does not by itself tell you the true yearly cost or return when compounding occurs more than once a year.

The true percentage increase in a balance over one full year once compounding within the year is taken into account. It allows fair comparison between offers that compound at different frequencies.

The length of time between one addition of interest and the next, such as monthly or quarterly. The rate per period equals the annual rate divided by the number of periods in a year.

A rule that defines each value in a sequence using one or more previous values, for example balance next month equals balance this month times a growth factor plus a deposit. It is well suited to spreadsheet modelling.

The multiplier applied to a quantity in one step of a recurrence, equal to one plus the rate as a decimal. A factor above one increases the value; below one it decreases it.

A series of equal payments made at regular intervals, such as a loan repayment or a superannuation contribution. Its future value depends on the payment size, the rate per period and the number of payments.

The process of paying off a loan through regular repayments, where each repayment covers the interest owing and reduces the outstanding balance. Early repayments are mostly interest; later ones are mostly principal.

A loan where interest each period is charged on the amount still owed rather than the original amount. Because the balance falls, interest charges fall too, so more of each repayment reduces the debt.

The amount of money today that is equivalent to a future sum or stream of payments, given a specified interest rate. It lets you compare amounts received at different times on a common basis.

The amount an investment or series of deposits will be worth at a stated future date, after interest has been applied for the whole term. It is found by applying the growth factor repeatedly.

A general rise in the prices of goods and services over time, which reduces what a fixed amount of money can buy. It is modelled as a percentage increase applied repeatedly to prices.

The quantity of goods and services a given sum of money can buy at a particular time. Rising prices erode it, so a nominal amount can grow while real purchasing power falls.

The complete set of individuals or items about which information is wanted in a statistical investigation. Its size is often unknown or impractical to measure in full.

A subset of a population selected for measurement, used to draw conclusions about the whole. Conclusions are uncertain, and their reliability depends on how the sample was chosen and how large it is.

A survey that attempts to collect data from every member of a population. It removes sampling error but is usually costly, slow and sometimes impossible to complete.

A systematic tendency for a sample to differ from the population in a way that distorts results, caused by the selection method rather than chance. Increasing the sample size does not remove it.

A selection method in which every member of the population has a known, usually equal, chance of being chosen. It supports valid inference because chance variation can be quantified.

The number of observations included in a sample. Larger samples generally give more precise estimates, with the standard error shrinking in proportion to the square root of the size.

A characteristic that is recorded for each individual in a data set and can take different values. Variables are classified as categorical or numerical, which determines the graphs and summaries that are appropriate.

A variable whose values are labels or groups rather than measured numbers, such as eye colour or suburb. Summaries use counts and percentages, and displays use bar charts or segmented charts.

A variable whose values are numbers on which arithmetic makes sense, such as height or income. It may be discrete, taking separated values, or continuous, taking any value in a range.

The sum of all values divided by the number of values. It uses every observation but is strongly affected by unusually large or small values, unlike the median.

The middle value when observations are arranged in order, or the average of the two middle values when the count is even. It is resistant to extreme values.

A measure of the typical distance of observations from the mean, found from the square root of the variance. Larger values indicate greater spread about the mean.

The difference between the upper and lower quartiles, covering the middle half of the data. It describes spread while ignoring the most extreme quarter at each end.

A display showing the minimum, lower quartile, median, upper quartile and maximum of a numerical data set. It highlights the centre, spread and possible outliers, and allows side-by-side comparison of groups.

An observation lying unusually far from the rest of the data, often flagged as beyond one and a half interquartile ranges from a quartile. It may be a recording error or a genuine extreme case.

A symmetric bell-shaped model for a continuous variable, described by its mean and standard deviation. About 68 percent of values lie within one standard deviation of the mean and about 95 percent within two.

The number of standard deviations a value lies above or below the mean, found by subtracting the mean and dividing by the standard deviation. It allows comparison of values from different distributions.

A number between minus one and one measuring the strength and direction of a straight-line association between two numerical variables. It says nothing about causation.

The straight line that best summarises a linear relationship in a scatterplot, usually found by least squares. It is used to predict one variable from the other within the observed range.

Using a model fitted to observed data to predict values outside the range of that data. It is risky because the pattern may not continue beyond the observed region.

A relationship of the form y equals mx plus c, where the graph is a straight line with constant slope. It describes quantities changing by a fixed amount each step.

A relationship in which the variable appears as an exponent, giving repeated multiplication by a constant factor. It models growth or decay at a constant percentage rate per period.

The turning point of a parabola, where the graph reaches its maximum or minimum value. In context it often represents the optimal price, time or quantity.

The U-shaped curve produced by a quadratic relationship, opening upward when the squared term's coefficient is positive and downward when it is negative. It models many optimisation problems.

A set of vertices joined by edges, used to represent connections such as roads, pipes or tasks. Labels or numbers on edges may represent distances, times or costs.

A point or node in a network, representing an object such as a town, junction or task. Vertices are joined by edges, and their number of connections is called the degree.

A connection between two vertices in a network, drawn as a line or arc. An edge may be directed, allowing travel one way only, or undirected, allowing travel both ways.

A square table with a row and column for each vertex, where an entry records whether, or how many, edges join the corresponding pair. It allows network properties to be computed by matrix operations.

A network in which each edge carries a number representing cost, distance or time. Weighted graphs are used to find shortest paths and minimum spanning trees.

The set of edges connecting all vertices of a weighted network with the smallest possible total weight and no cycles. It is found by repeatedly choosing the cheapest safe edge.

A matrix whose entries give the proportions moving from each state to each other state in one step. Powers of it describe the distribution after several steps.

A distribution that no longer changes when the transition matrix is applied, reached eventually in many repeated processes. It represents long-run proportions rather than a stopping point.

The longest chain of dependent tasks in a project network, which determines the shortest possible completion time. Any delay on it delays the whole project.

The amount by which a task can be delayed without delaying the whole project. Tasks on the critical path have zero float.

A rule in which the next term equals a constant times the current term plus a fixed amount. Depending on that constant, the sequence may grow, decay or settle at a fixed value.

An ordered list of numbers in which each term after the first is obtained by adding a fixed amount. Its graph against term number is a straight line.

An ordered list of numbers in which each term after the first is obtained by multiplying by a fixed factor. It grows or decays exponentially rather than steadily.

A model in which a quantity grows quickly at first but slows as it approaches a limiting value called the carrying capacity. It produces an S-shaped curve rather than unlimited growth.