Maths

Understanding Measurement 1. Standard Metric Units and Conversions Metric units follow a base-10 system. Conversion involves multiplying or dividing by powers of 10. Common Units Length: millimeter (mm), centimeter (cm), meter (m), kilometer (km) Mass: milligram (mg), gram (g), kilogram (kg), tonne (t) Capacity/Volume: milliliter (ml), liter (l), cubic centimeter ($\text{cm}^3$), cubic meter ($\text{m}^3$) Conversion Factors $1\text{ cm} = 10\text{ mm}$ $1\text{ m} = 100\text{ cm} = 1000\text{ mm}$ $1\text{ km} = 1000\text{ m}$ $1\text{ kg} = 1000\text{ g}$ $1\text{ l} = 1000\text{ ml} = 1000\text{ cm}^3$ Tip: To convert from a larger unit to a smaller unit, multiply. To convert from a smaller unit to a larger unit, divide. ...

Averages and Measures of Spread 1. Types of Averages (Central Tendency) Averages provide a single value that represents a data set. Mean The sum of all values divided by the total number of values. Non-grouped data: $\text{Mean} = \frac{\sum x}{n}$. Frequency data: $\text{Mean} = \frac{\sum (f \cdot x)}{\sum f}$ (where $f$ is frequency and $x$ is the value/midpoint). Median The middle value when data is ordered from least to greatest. ...

Pythagoras’ Theorem and Similar Shapes 1. Pythagoras’ Theorem Applies only to right-angled triangles. The Formula In a right-angled triangle with legs $a, b$ and hypotenuse $c$ (the side opposite the right angle): $$a^2 + b^2 = c^2$$ Calculations Finding the Hypotenuse: $c = \sqrt{a^2 + b^2}$. Finding a Shorter Side: $a = \sqrt{c^2 - b^2}$. 2. Similarity Two shapes are similar if they have the same shape but different sizes. ...

Straight Lines and Quadratic Equations 1. Straight Line Graphs Represented on a 2D Cartesian coordinate system $(x, y)$. The Equation of a Line General form: $y = mx + c$ $m$: Gradient (slope). $c$: $y$-intercept (where the line crosses the $y$-axis). Gradient ($m$) Gradient measures the steepness: $\text{gradient} = \frac{\text{vertical change}}{\text{horizontal change}} = \frac{\text{rise}}{\text{run}}$. Calculating Gradient from Two Points: Given $(x_1, y_1)$ and $(x_2, y_2)$: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ ...

Sequences, Surds, and Sets 1. Sequences A sequence is an ordered list of numbers following a specific rule. Term-to-Term Rules Describes how to get from one term to the next. Arithmetic Sequence: Constant difference added or subtracted (e.g., $+3, +3, +3$). Geometric Sequence: Constant ratio multiplied or divided (e.g., $\times 2, \times 2, \times 2$). The $n$-th Term ($u_n$) The formula to find any term in the sequence based on its position $n$. ...