VCE Foundation Mathematics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Mean

The sum of all data values divided by the number of values. It uses every observation and is strongly affected by extreme values or outliers.

Median

The middle value when data is arranged in order. For an even number of values, average the two middle values. It resists outliers.

Interquartile range

The difference between the upper quartile and lower quartile, IQR = Q3 − Q1. It measures the spread of the middle half of the data.

Outlier rule

A data value is treated as an outlier if it lies below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR.

Relative frequency

The count for a category divided by the total number of observations. All relative frequencies in a table add to one.

Complement rule

For any event E, the probability it does not occur is P(not E) = 1 − P(E). Useful when the complement is easier to count.

Independent events

Two events are independent when one occurring does not change the probability of the other, so P(A and B) = P(A) × P(B).

Mutually exclusive events

Events that cannot happen at the same time, so P(A and B) = 0 and P(A or B) = P(A) + P(B).

Expected frequency

The predicted number of times an event occurs, found by multiplying its probability by the number of trials. It is a long-run average.

Stratified sampling

A sampling method where the population is split into groups and each group contributes a number proportional to its size.

Index laws

Rules for powers: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m−n), (a^m)^n = a^(mn), and a^0 = 1 for nonzero a.

Compound interest formula

Total amount after n periods is A = P(1 + r)^n, where P is the principal and r is the decimal rate per period.

Simple interest

Interest calculated only on the original principal: I = P × r × t, with r as a decimal rate and t the time in periods.

Percentage change

Change expressed relative to the original value: (new value − old value) ÷ old value × 100%. A negative result is a decrease.

Gradient formula

The slope between two points: m = (y2 − y1) ÷ (x2 − x1). It describes the vertical change per unit of horizontal change.

Linear equation form

y = mx + c describes a straight line, where m is the gradient and c is the y-intercept, the value of y when x is zero.

Perpendicular gradients

Two lines are perpendicular when their gradients multiply to −1, so one gradient is the negative reciprocal of the other.

Axis intercepts

The x-intercept is found by setting y = 0 and solving; the y-intercept is found by setting x = 0 and solving.

Direct proportion

A relationship of the form y = kx, graphed as a straight line through the origin. The ratio y ÷ x stays constant.

Pythagoras' theorem

In a right-angled triangle, a² + b² = c², where c is the hypotenuse opposite the right angle. Used to find unknown side lengths.

Circle formulas

Circumference C = 2πr and area A = πr², where r is the radius. The diameter equals twice the radius.

Volume of a prism

Volume equals the area of the uniform cross-section multiplied by the length or height of the prism. Applies to cylinders too.

Similar figures

Shapes with equal matching angles and side lengths in a constant ratio k. Areas scale by k² and volumes by k³.

Unit conversions

Length: 1 m = 100 cm. Area: 1 m² = 10 000 cm². Volume: 1 m³ = 1 000 000 cm³, and 1 L = 1000 cm³.

Standard deviation

A measure of how far data values typically sit from the mean. A larger value indicates greater spread in the data.

Five-number summary

The minimum, lower quartile, median, upper quartile and maximum of a data set, used to draw a box plot.

Misleading graph features

Truncated vertical axes, uneven scale intervals or three-dimensional effects can exaggerate differences. Check the scale before interpreting.

Venn diagram addition rule

For two events, P(A or B) = P(A) + P(B) − P(A and B). The overlap is subtracted so it is not counted twice.

Without replacement

When items are not returned, the total and the favourable count both decrease after each draw, so probabilities change between draws.

Testing independence

Events are independent if P(A and B) equals P(A) × P(B), or equivalently if P(A given B) equals P(A).

Inequality sign reversal

When solving an inequality, multiplying or dividing both sides by a negative number reverses the direction of the inequality sign.

Quadratic formula

For ax² + bx + c = 0 with a not zero, the solutions are x = (−b ± √(b² − 4ac)) ÷ 2a.