SACE Stage 2 Essential Mathematics key terms

Replacing a number with a nearby value that has fewer significant figures or decimal places, chosen according to a stated level of accuracy. Answers are usually rounded to the precision the question specifies.

The digits of a number that carry meaningful information about its precision, counted from the first non-zero digit. Leading zeros are not counted, so 0.00450 has three significant figures.

The number of digits written after the decimal point in a number. Rounding to two decimal places keeps only two digits to the right of the point.

A way of writing very large or very small numbers as a value between 1 and 10 multiplied by a power of ten, such as 3.2 x 10^5. It makes the order of magnitude easy to see.

The approximate size of a quantity expressed as a power of ten. Two values differ by one order of magnitude when one is about ten times the other.

Producing an approximate answer by rounding values or using sensible benchmark numbers. Estimation is used to check whether a calculated answer is reasonable.

The size of the difference between an approximate or measured value and an accepted value, written as a percentage of the accepted value. It measures accuracy of an estimate or measurement.

The difference between a measured or estimated value and the true or accepted value, written as a positive amount without reference to the true value. It has the same units as the quantity.

A comparison of two or more quantities of the same kind, written with a colon such as 3:5 or as a fraction. Ratios describe relative size, not actual amounts.

A statement that two ratios are equal, allowing an unknown quantity to be found. Solving a proportion usually involves cross-multiplying the two fractions.

A relationship in which one quantity increases at the same rate as another, so their ratio stays constant. Doubling one value doubles the other.

A relationship in which one quantity increases while the other decreases so that their product stays constant. Doubling one value halves the other.

The fixed multiplier that links two quantities in a proportional relationship, often written k. In y = kx, k is the constant of proportionality.

The number by which every length in a figure is multiplied to produce a similar figure. Areas change by the square of the scale factor and volumes by its cube.

Shapes that have the same shape but possibly different size, with matching angles equal and matching sides in the same ratio. Corresponding lengths share a common scale factor.

Shapes that are identical in both shape and size, so one can be moved onto the other exactly. All matching sides and angles are equal.

The total distance around the outside boundary of a flat shape. It is found by adding the lengths of all sides and is measured in linear units.

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

The amount of flat space enclosed by a circle, found using pi multiplied by the radius squared. The result is measured in square units.

The area of the pie-shaped region of a circle bounded by two radii and an arc. It equals the fraction of the full circle multiplied by the circle's area.

The distance along a curved part of a circle's boundary between two points. It equals the fraction of the circumference corresponding to the angle at the centre.

The total area of all outer faces of a three-dimensional object, measured in square units. For a prism it is the sum of the areas of its flat faces.

The amount of three-dimensional space an object occupies, measured in cubic units. For a prism or cylinder it is the cross-sectional area multiplied by the length or height.

The amount a container can hold, usually measured in litres or millilitres. One litre equals 1000 cubic centimetres, linking capacity to volume.

A flat pattern that can be folded to form a three-dimensional object. Nets help in working out surface area by showing every face laid out.

The rule that in a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides. It is used to find unknown side lengths.

The longest side of a right-angled triangle, lying opposite the right angle. Its length can be found from the other two sides using Pythagoras' theorem.

A ratio of two sides of a right-angled triangle, such as sine, cosine or tangent, linked to one of the acute angles. These ratios allow unknown sides or angles to be calculated.

The angle measured upwards from the horizontal to a line of sight to an object above. It is used with trigonometric ratios to find heights and distances.

The angle measured downwards from the horizontal to a line of sight to an object below. It is often equal to the angle of elevation from the object back to the observer.

Changing a measurement from one unit to another by multiplying or dividing by a conversion factor. Correct conversion keeps the physical quantity unchanged.

A comparison of two quantities with different units, such as kilometres per hour or dollars per kilogram. Rates are often used to describe how one quantity changes with another.

The total distance travelled divided by the total time taken, giving a single rate for a journey. It is not necessarily the speed at any one moment.

Interest calculated only on the original amount invested or borrowed, using the formula I = Prn. The interest earned stays the same each period.

Interest calculated on the original amount plus any interest already added, so the balance grows by a fixed percentage each period. It grows faster than simple interest.

The original amount of money borrowed or invested, before any interest is added. Interest calculations use the principal as their starting value.

The decrease in the value of an asset over time, often calculated as a fixed percentage of its value each period. It reduces value in a way similar to compound interest.

The average found by adding all values in a data set and dividing by how many values there are. It is affected strongly by unusually large or small values.

The middle value of a data set when the values are arranged in order. If there is an even number of values, the median is the mean of the two middle values.

The value that occurs most often in a data set. A data set may have no mode, one mode, or more than one mode.

A measure of how spread out the values in a data set are around the mean. A larger standard deviation means the values are more widely scattered.

A bell-shaped, symmetric distribution of data centred on the mean, common in measurements of natural quantities. Known proportions of values fall within one, two and three standard deviations of the mean.