Maths semester exam - 2024

Salary and wages

Weekly pay x 52 = annual pay

Annual pay ÷ 12 = monthly pay

Monthly pay x 12 = annual pay

Annual pay ÷ 52 = weekly pay

Annual pay ÷ 26 = fortnightly pay

Penalty rates

Time and a half = 1.5

Double time = 2

Double time and a half = 2.5

Simple interest

I = pin

Compound interest

A = p( 1 + i )ⁿ

Expressing rates

First quantity/second quantity

Rate = distance/time

Speed = distance/time

Time = distance/speed

Scale factor

length of image/length of object

Area and volume in scale factor

SF = n

Area = n²

Volume = n³

Pythagoras theorem

a² + b² =c²

c² - b² =a²

c² - a² = b²

Trigonometry

SOH CAH TOA

Finding an angle

Inverse sine = sin^-1

Inverse cosine = cos^-1

Inverse tangent = tan^-1

Determining if triangle is right angled

a² + b² always = c²

Pythagoras only works on right angled triangles

Types of data

Categorical - words

Ordinal - goes in order

Nominal - not able to go in order

Numerical - numbers

Discrete - whole numbers

Continuous - decimal places or fractions

Population - collecting data from every individual in a group

Sample - collecting data from only parts of an identified group

Proportionality

y = kx

Percentage frequency

count/total x 100

Mean

sum of scores/number of scores

Median

(n+1/2)

Range

Highest score - lowest score

Mode

Most frequently occurring

Interquartile range

IQR = Q3 - Q1

Complementary event

Pr (A) + pr (A’) = 1

Theoretical probability

p (event) = number of favourable outcomes/number of possible outcomes

Relative frequency / experimental probability

freq of outcome/ total number of trials

Expected number of results

probability of outcome x number of trials