SACE Stage 2 Essential Mathematics flashcards

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

Simple interest formula

Interest I = P × r × t, where P is principal, r the annual rate as a decimal, and t the time in years. Total amount is P(1 + rt).

Compound interest formula

A = P(1 + r/n)^(nt), where n is the number of compounding periods per year and t is years. Interest earned equals A minus P.

Continuous compound growth

A = Pe^(rt) applies when interest compounds continuously, with e approximately 2.71828. Used for limiting cases of frequent compounding.

Straight-line depreciation

Value falls by a fixed amount each period: value = P − (P × r × t). The graph of value against time is a straight line.

Reducing-balance depreciation

Value = P(1 − r)^t, where r is the decimal rate lost each period. Each period's loss is a percentage of the current value, not the original.

Percentage change

Percentage change = (new value − old value) / old value × 100. A positive result is an increase; a negative result is a decrease.

Unit conversion by cancellation

Multiply by a fraction equal to 1, such as 1000 m / 1 km, arranging units so the unwanted unit cancels and only the desired unit remains.

Scale factor for areas

If lengths are multiplied by factor k, areas are multiplied by k². A 1:100 scale drawing has areas 10 000 times smaller than reality.

Rounding only at the end

Keep full calculator precision through intermediate calculations and round only the final answer, otherwise rounding errors accumulate and distort the result.

Rearranging a formula

Undo operations in reverse order to isolate the unknown; whatever is done to one side must be done to the other to preserve equality.

Rate multiplied by time

Quantity = rate × time. Rearranged forms are rate = quantity / time and time = quantity / rate; used for speed, wages and flow problems.

Finding the original amount

After a percentage change, divide by the multiplier: original = final / (1 ± r). For a 20% increase, divide the final value by 1.2.

Mean of a data set

The sum of all values divided by the number of values. The mean is affected by extreme values more than the median is.

Median of a data set

Order the values from smallest to largest; the median is the middle value, or the average of the two middle values when the count is even.

Mode of a data set

The value or values occurring most frequently. A data set may have no mode, one mode, or several modes.

Range and interquartile range

Range = maximum − minimum. IQR = Q3 − Q1, describing the spread of the middle 50% and resisting distortion by outliers.

Standard deviation meaning

A measure of how far values typically sit from the mean. A larger standard deviation means the data are more spread out.

Comparing two data sets

Compare a measure of centre (mean or median) and a measure of spread (range, IQR or standard deviation) together, since either alone can mislead.

Area of a circle

A = πr², where r is the radius. Circumference is C = 2πr; use the radius, not the diameter, in both formulas.

Area of a triangle

A = ½ × base × height, where the height is perpendicular to the chosen base. Any side may be used as the base.

Volume of a prism

Volume = area of the uniform cross-section × length (or height). Applies to rectangular, triangular and cylindrical solids.

Volume of a cylinder

V = πr²h, where r is the base radius and h the height. Capacity in litres equals volume in cm³ divided by 1000.

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.

Perimeter of composite shapes

Add the lengths of all outer boundary edges only; internal dividing lines are excluded because they are not part of the perimeter.

Total cost of a loan

Total repayments = regular payment × number of payments. Interest paid = total repayments − amount originally borrowed.

Budget surplus or deficit

Surplus = income − expenses when positive; deficit when negative. Fixed costs stay constant, variable costs change with usage.

Simple probability

P(event) = number of favourable outcomes / total number of equally likely outcomes. Every probability lies between 0 and 1 inclusive.

Complementary probability

P(not A) = 1 − P(A). Useful when counting non-occurrence directly is harder than counting the event itself.

Expected frequency

Expected number of occurrences = probability of the event × number of trials. Actual results vary around this value by chance.

Relative frequency

Relative frequency = number of times an event occurred / number of trials. With many trials it estimates the true probability.

Reading tables and graphs

Check axis labels, units and scale intervals before interpreting. A broken or non-zero axis can exaggerate apparent differences between values.

Misleading data displays

Watch for truncated axes, inconsistent scales, three-dimensional effects and selective time ranges, all of which can distort the impression a graph gives.