Tasmania TCE Everyday Adult Standard - Mathematics flashcards

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

Order of operations

Evaluate brackets first, then indices, then multiplication and division from left to right, then addition and subtraction from left to right.

Percentage of a quantity

Convert the percentage to a decimal and multiply: 15% of 80 equals 0.15 times 80, which is 12.

Percentage change formula

Divide the amount of change by the original value and multiply by 100. A rise from 40 to 50 is 25%.

Ratio sharing

Add the ratio parts, divide the total by that sum to find one unit, then multiply by each part.

Metric length conversions

One kilometre is 1000 metres, one metre is 100 centimetres, and one centimetre is 10 millimetres.

Area of a triangle

Area equals half the base multiplied by the perpendicular height, measured in square units.

Circle circumference and area

Circumference equals pi times diameter; area equals pi times radius squared, using pi about 3.14.

Speed distance time

Distance equals speed multiplied by time. Time equals distance divided by speed. Keep units consistent throughout.

Volume of a rectangular prism

Volume equals length times width times height in cubic units. One thousand cubic centimetres equals one litre.

Angle sum of a triangle

The three interior angles of any triangle always add to 180 degrees, whatever its shape or size.

Pythagoras' theorem

In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides.

Interior angle of a regular polygon

Subtract two from the number of sides, multiply by 180, then divide by the number of sides.

Similar shapes

Similar shapes have equal matching angles and proportional sides. A scale factor k multiplies lengths by k and areas by k squared.

Transformations

Translation slides, reflection flips, rotation turns and enlargement scales a shape. Only enlargement changes side lengths.

Mean median mode

Mean is the total divided by the count; median is the middle ordered value; mode is the most frequent value.

Range of data

The range is the highest value minus the lowest value. It measures spread rather than the centre of the data.

Probability of an event

Divide the number of favourable outcomes by the total number of equally likely outcomes. Results lie between 0 and 1.

Complementary probability

The probability an event does not happen equals one minus the probability it does happen.

Independent events rule

For independent events, multiply the individual probabilities to find the chance both occur, such as two heads in a row.

Median with even count

When the ordered data has an even number of values, the median is the mean of the two middle values.

Simple interest formula

Interest equals principal times annual rate as a decimal times time in years. The principal stays fixed each year.

Compound interest formula

Balance equals principal times one plus the annual rate raised to the number of compounding periods.

GST calculation

Australian GST is 10%. Add it by multiplying by 1.10; remove it by dividing a GST-inclusive price by 1.10.

Discount multiplier

A discount of 25% means paying 75% of the marked price, so multiply the price by 0.75.

Unit price comparison

Divide total cost by quantity to find cost per gram, litre or item. The lower unit price is better value.

Gross pay calculation

Multiply ordinary hours by the hourly rate, then add overtime hours multiplied by the overtime rate.

Budget surplus and deficit

A budget has a surplus when total income exceeds total expenses, and a deficit when expenses exceed income.

Estimation check

Round each number to one significant figure, compute mentally, and compare the result with the calculated answer to catch errors.

Working backwards

To check a solution, reverse each operation in the calculation and confirm you return to the starting value.

Combined rate problem

When workers and time are inversely related, their product stays constant, so doubling the workers halves the time needed.

Irrelevant information

Some values in a word problem may not be needed. Identify the quantity asked for before choosing which numbers to use.

Justifying an answer

State the calculation performed and include the correct unit so another person can follow and check the reasoning.