Mathematics

Symmetry 1. Key vocabulary Line of symmetry: A line that divides a shape into two matching mirror-image halves. Rotational symmetry: A shape matches its original position after a rotation of less than one complete turn. Order of rotational symmetry: The number of times a shape matches itself during one complete turn of $360^\circ$. Axis of rotational symmetry: A line about which a shape or solid can be rotated and remain unchanged. Plane of symmetry: A flat plane that divides a solid into matching mirror-image halves. A shape can have line symmetry, rotational symmetry, both, or neither. ...

Core quadratic graphs and graphical solutions; Supplement (Extended) reciprocal, cubic, exponential, tangent, derivative, and stationary-point work. Focus on required graph features: roots, symmetry, turning points, asymptotes, end behaviour, and gradients.

Scatter Diagrams and Correlation 1. Bivariate Data Bivariate data consists of pairs of values for two different variables recorded for the same subject. Example: Height and weight of students. The goal is to determine if there is a relationship (correlation) between the two variables. 2. Scatter Diagrams A scatter diagram plots bivariate data on a Cartesian plane. X-axis: Independent variable. Y-axis: Dependent variable. Each pair $(x, y)$ is plotted as a single point. ...

Scale Drawings, Bearings and Trigonometry 1. Scale Drawings Scale drawings represent real-life objects or areas at a reduced size while maintaining proportions. Scale Factors A scale is written as $\text{Drawing Distance} : \text{Real Distance}$ (e.g., $1 : 50,000$). Finding Real Distance: $\text{Real Distance} = \text{Drawing Distance} \times \text{Scale Factor}$. Finding Drawing Distance: $\text{Drawing Distance} = \text{Real Distance} \div \text{Scale Factor}$. 2. Bearings Bearings are used for navigation to specify direction. ...

Further Solving of Equations and Inequalities 1. Simultaneous Equations Two linear equations with two unknowns (usually $x$ and $y$) that must be solved simultaneously. Methods of Solution Elimination: Multiply equations so that coefficients of one variable are the same (or opposites), then add or subtract the equations to eliminate that variable. Substitution: Rearrange one equation to express one variable in terms of the other (e.g., $x = \dots$), then substitute this expression into the second equation. Worked example (elimination): Solve ...