Maths

Numbers, Fractions, Decimals, and Percentages

Number Types and Operations

•  Integers: Whole numbers including positive, negative, and zero ().

•  Fractions: Represent parts of a whole in the form , where  is the numerator and  is the non-zero denominator.

•  Decimals: Numbers expressed using a decimal point based on powers of .

•  Percentages: Fractions with a denominator of , represented using the symbol .

•  Formula:

2. Ratio and Proportion

Ratios

•  Compares quantities of the same unit in the form .

•  Simplifying ratios involves dividing both sides by their highest common factor.

Proportions

•  An equation stating that two ratios are equal: .

•  Direct Proportion: As one variable increases, the other increases at a constant rate ().

•  Inverse Proportion: As one variable increases, the other decreases ().

3. Algebra, Inequalities, Sequences, Functions, and Graphs

Algebra and Expressions

•  Algebraic Expressions: Combinations of variables, numbers, and operators (e.g., ).

•  Solving Equations: Finding variable values that make an equation true (e.g., ).

Inequalities

•  Expressions involving inequality symbols (, , , ).

•  Solving inequalities follows equation rules, except multiplying or dividing by a negative number reverses the inequality sign.

Sequences

•  An ordered list of numbers following a specific rule.

•  Arithmetic Sequence: Common difference , with the  term given by

•  Geometric Sequence: Common ratio , with the  term given by

Functions and Graphs

•  Functions: A relation  mapping each input  to exactly one output.

•  Linear Graphs: Equation of a straight line , where  is the gradient and  is the .

4. Statistics

Descriptive Statistics

•  Measures of Central Tendency:

•  Mean: Sum of values divided by count ().

•  Median: Middle value when ordered.

•  Mode: Most frequent value.

•  Measures of Spread:

•  Range:

•  Standard Deviation:

Data Presentation

•  Bar Charts & Histograms: Categorical and continuous data visualization.

•  Box Plots: 5-point summary displaying distribution and quartiles.

•  Scatter Plots: Relationships and correlation between two variables.

5. Probability

Basic Concepts

•  Probability of an Event:

•  Complementary Events:

6. 2D and 3D Shapes, Maps, Scales, and Transformations

Shapes

•  2D Shapes: Polygons defined by length and width.

•  3D Shapes: Polyhedra with vertices, edges, and faces.

Maps, Scales, and Transformations

•  Scale Factor:

•  Transformations: Translation, Reflection, Rotation, and Enlargement.

7. Measurement of 2D and 3D Shapes

2D Measurement

•  Perimeter: Distance around boundary.

•  Area:

•  Circle:

•  Triangle:

3D Measurement

•  Volume:

•  Cylinder:

•  Sphere:

•  Surface Area: Sum of all face areas.