HSC Mathematics Standard 1 key terms

A letter or symbol standing for a quantity that can change or is not yet known. In formulas and equations it represents a number you may need to find.

A combination of numbers, variables and operations without an equals sign, such as 3x + 5. It can be simplified or evaluated but not solved.

Terms with exactly the same variable part, such as 4x and 7x, which can be combined by adding or subtracting their coefficients to simplify an expression.

The number multiplying a variable in a term. In 6y the coefficient is 6; in -x it is -1. It tells how many of that variable there are.

An equation in which the variable appears only to the first power, such as 2x + 7 = 15. Solving it means finding the value that makes both sides equal.

The operation that undoes another: addition undoes subtraction, multiplication undoes division. Used to isolate a variable when solving equations step by step.

A value of the variable that makes an equation true. Checking by substituting it back into the original equation confirms whether the solution is correct.

Replacing a variable with a given number to evaluate an expression or check a solution. Order of operations must then be followed carefully.

A rule written as an equation linking quantities, such as A = lw or C = 2πr. Substituting known values lets you calculate the unknown quantity.

Changing the subject of a formula by applying inverse operations to both sides, for example rewriting d = st as t = d ÷ s.

A statement comparing quantities that are not necessarily equal, using symbols such as <, >, ≤ or ≥. Solutions form a range of values rather than a single number.

Two or more equations involving the same variables that must be satisfied at the same time. Their solution is the pair of values true for both equations.

The steepness of a straight line, found as rise divided by run or the change in y divided by the change in x between two points.

The point where a line crosses the vertical axis, written as the value of y when x equals zero. In y = mx + b it equals b.

The straight-line graph of a linear relationship, drawn from a table of values or from its gradient and y-intercept. Straightness shows a constant rate of change.

The total distance around the outside of a two-dimensional shape, found by adding the lengths of all sides or applying a formula for circles and sectors.

The amount of surface enclosed by a two-dimensional shape, measured in square units such as cm². Formulas differ for rectangles, triangles, circles and composite shapes.

The amount of space occupied by a three-dimensional object, measured in cubic units such as m³. Found by multiplying a cross-sectional area by a length or height.

The amount a container can hold, usually measured in millilitres or litres. One cubic centimetre equals one millilitre, linking volume and capacity conversions.

The perimeter of a circle, calculated as π times the diameter or 2π times the radius. It is a length, so it uses ordinary units such as centimetres.

The distance from the centre of a circle to any point on its edge, equal to half the diameter. It appears in circle formulas for circumference and area.

A figure made by joining simpler shapes such as rectangles, triangles and semicircles. Its area or perimeter is found by working with the separate parts.

The total area of all the outer faces of a three-dimensional object, measured in square units. It is found by adding the areas of each face or using a formula.

Changing a measurement from one unit to another using a factor, such as multiplying by 100 to change metres to centimetres, or by 1000 for litres to millilitres.

The ratio between a drawing or model and the real object, for example 1:100. It converts measured lengths on a plan into actual distances.

A diagram drawn proportionally smaller or larger than the real object. Lengths on the drawing are converted to real lengths using the stated scale.

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides, written a² + b² = c². Used to find unknown side lengths.

The longest side of a right-angled triangle, opposite the right angle. It is the side isolated in Pythagoras' theorem when finding a missing length.

A ratio of two sides of a right-angled triangle linked to an angle, namely sine, cosine or tangent. These ratios allow unknown sides or angles to be calculated.

The angle measured upward from the horizontal to a line of sight to an object above. Used with trigonometry to find heights and distances.

Interest calculated only on the original amount invested or borrowed, using I = PRN, where R is the decimal rate per period and N the number of periods.

Interest calculated on both the original amount and previously earned interest, so the balance grows faster than with simple interest over the same period.

The original sum of money invested or borrowed, before any interest is added. It is the starting value in interest and loan calculations.

The percentage charged or earned on money over a period, usually quoted per year. It must be written as a decimal and adjusted for the compounding period.

The decrease in the value of an asset over time. Straight-line depreciation subtracts a fixed amount each year, while declining-balance depreciation uses a percentage.

A general rise in prices over time, which reduces the purchasing power of money. It is often modelled with a percentage increase applied repeatedly.

Money received for work, including wages, salaries, overtime and commission. Gross earning is the total before tax and other deductions are removed.

Total income earned in a pay period before any deductions such as tax, superannuation or union fees are subtracted from the amount.

The amount actually received after all deductions are subtracted from gross pay. It is also called take-home pay.

An amount removed from gross pay before it is paid, such as income tax, superannuation or salary sacrifice. Deductions reduce take-home pay.

The average found by adding all values and dividing by how many there are. It uses every data value, so extreme outliers can pull it noticeably.

The middle value of an ordered data set, or the average of the two middle values when the count is even. It is not affected by extreme values.

The value or values that occur most often in a data set. A set may have no mode, one mode, or several modes if values tie for most frequent.

The difference between the largest and smallest values in a data set. It is a simple measure of spread but depends only on the two extreme values.

A data value that lies unusually far from the rest of the data. Outliers can strongly affect the mean and range but barely affect the median.

A measure of how spread out data values are around the mean. A larger value means values are more widely scattered from the average.

A table listing each value or class of data with the number of times it occurs. It is used to organise data and calculate statistics efficiently.

A graph of a frequency distribution with bars touching, used for numerical data grouped into classes. Bar height shows the frequency of each class.

The proportion of times an outcome occurs, found by dividing its frequency by the total number of trials. It can be written as a fraction, decimal or percentage.

A number from 0 to 1 describing how likely an event is. For equally likely outcomes it equals favourable outcomes divided by total possible outcomes.

The strength and direction of a relationship between two variables shown on a scatter plot. It may be positive, negative or close to zero.

A straight line drawn through a scatter plot to model the trend of the data. It can be used to estimate values not actually measured.

A graph plotting one variable against another as individual points. It reveals patterns, trends and possible relationships between the two variables.

The difference between the upper quartile and lower quartile of a data set. It measures the spread of the middle half of the data and ignores outliers.

The minimum, lower quartile, median, upper quartile and maximum of a data set. It provides the values needed to draw a box plot.