HSC Mathematics Standard 2 key terms

A letter or symbol standing in for an unknown or changing number in an expression, equation or formula. It lets you write general rules and solve for missing values.

An equation in which every pronumeral appears to the first power only, so its graph is a straight line. Solving it means finding the value that makes both sides equal.

Replacing pronumerals in a formula or expression with given numbers, then evaluating the result using the correct order of operations. Used constantly in measurement and finance formulas.

A rule written as an equation linking quantities, such as area equals length times width. You substitute known values into it to calculate an unknown quantity.

Changing the subject of a formula or equation by performing the same inverse operations to both sides. Essential for isolating an unknown before substituting values.

Two or more equations that must be satisfied at the same time by the same values of the pronumerals. Solved by substitution or elimination, or graphically at the point of intersection.

A measure of how steep a straight line is, calculated as the rise divided by the run between two points. A negative gradient means the line slopes downwards.

Estimating a value between two known data points, often by reading from a line of best fit. It is generally more reliable than predicting outside the observed range.

Predicting a value outside the range of observed data by extending a trend or line of best fit. It is less reliable because the pattern may not continue beyond the data.

A statement comparing two quantities that are not necessarily equal, using symbols such as less than, greater than, or at most. Solutions form a range rather than a single value.

The endpoint value of a range allowed by an inequality or rounding, such as the smallest and largest numbers that round to a given figure. Important in measurement error questions.

The total distance around the outside of a closed two-dimensional shape, found by adding all side lengths. For a circle the special name is circumference.

The amount of flat surface enclosed by a two-dimensional shape, measured in square units. Formulas differ for rectangles, triangles, circles and composite figures.

The perimeter of a circle, calculated as pi times the diameter or twice pi times the radius. It is a length, so it is measured in linear units.

A shape made by combining simpler shapes such as rectangles, triangles and semicircles. Its area or perimeter is found by adding or subtracting the parts.

The amount of three-dimensional space occupied by a solid, measured in cubic units. Found by multiplying a cross-sectional area by a length or height.

The amount a container can hold, usually measured in litres or millilitres. Converting between capacity and volume relies on the fact that one cubic centimetre equals one millilitre.

The total area of all outer faces of a three-dimensional solid, measured in square units. Useful for problems about painting, wrapping or coating objects.

Changing a measurement from one unit to another by multiplying or dividing by a conversion factor, such as metres to centimetres. Units must be consistent before calculating.

The meaningful digits in a measurement, starting from the first non-zero digit. Answers are often rounded to a given number of these to reflect measurement precision.

The difference between a measured or rounded value and the true value, always taken as positive. It is often at most half the smallest unit of measurement used.

The absolute error expressed as a percentage of the true or accepted value. It allows comparison of accuracy between measurements of different sizes.

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Used to find unknown lengths and distances.

A ratio linking an angle in a right-angled triangle to two of its sides, namely sine, cosine and tangent. Used to find unknown sides or angles.

The angle measured upwards from a horizontal line to a line of sight above it. Paired with angles of depression in problems involving heights and distances.

A direction measured clockwise from north, written as a three-digit angle. Used to describe journeys and positions on maps and diagrams.

A diagram in which all lengths are reduced or enlarged by the same ratio to represent a real object. The scale links drawing lengths to actual lengths.

Interest calculated only on the original principal for the whole term, using the formula interest equals principal times rate times time. The interest amount stays constant each period.

Interest calculated on the principal plus previously earned interest, so the balance grows by a fixed percentage each period. It produces faster growth than simple interest.

The original amount of money borrowed or invested, before any interest is added. It forms the base for calculating simple or compound interest.

An increase in the value of an asset over time, often modelled by repeated percentage increase. Depreciation is the corresponding decrease in value.

A decrease in the value of an asset over time, calculated either by a fixed amount each year or as a percentage of the declining value.

A general rise in prices over time, which reduces the purchasing power of money. Often modelled with compound percentage increases.

The income remaining after allowable deductions are subtracted from gross income, used to work out income tax payable.

The total amount earned before any deductions such as tax, superannuation or union fees are taken out. Net pay is what remains after deductions.

The amount an employee actually receives after all deductions are subtracted from gross pay. Also called take-home pay.

The average found by adding all scores and dividing by how many there are. It is affected strongly by extreme values.

The middle score when data are arranged in order, or the average of the two middle scores for an even count. It is resistant to outliers.

The difference between the upper and lower quartiles, describing the spread of the middle half of the data. It is less affected by outliers than the range.

A measure of how far scores typically spread from the mean. A larger value means the data are more widely scattered.

A bell-shaped, symmetric distribution of data centred on the mean. Roughly 68 percent of scores lie within one standard deviation and 95 percent within two.

The number of standard deviations a score lies above or below the mean. It allows comparison of scores from different distributions.

A number between negative one and one describing the strength and direction of a linear relationship between two variables. Values near zero indicate a weak relationship.

A straight line drawn through a scatterplot to summarise the overall trend, used to make predictions. It may be fitted by eye or by least squares.

A graph plotting one variable against another as points, used to reveal the form, direction and strength of a relationship.

The number of times an outcome occurs divided by the total number of trials, giving an estimated probability. It tends to approach the true probability as trials increase.

A table classifying data by two categorical variables, with totals for rows and columns. It is used to calculate conditional and joint relative frequencies.

A number between zero and one describing how likely an event is, where zero means impossible and one means certain.

A diagram of vertices joined by edges, used to model connections such as roads or pipes. It can be analysed for paths, degrees and connectivity.

A point or node in a network where edges meet, representing an object or location. Its degree is the number of edges attached to it.

A connection or link between two vertices in a network, sometimes carrying a weight such as distance or cost.

The number of edges meeting at a vertex. In a network, exactly two vertices must have odd degree for an Eulerian trail to exist.

A route through a network that uses every edge exactly once, starting and finishing at different vertices. It exists only when exactly two vertices have odd degree.

A route that traverses every edge of a network exactly once and returns to its starting vertex. It exists only when every vertex has even degree.

A network in which each edge is labelled with a number, such as distance, time or cost. Weighted networks are used to find minimum-cost paths and spanning trees.

The set of edges of smallest total weight that connects all vertices of a weighted network without forming a cycle. Found using algorithms such as Prim's.

The longest path through a project network, which determines the minimum time needed to complete the whole project. Activities on it cannot be delayed without delaying the project.

The amount of delay an activity can tolerate without delaying the whole project, found from earliest and latest start times. Activities on the critical path have zero float time.