# O level Math Formula Sheet (Algebra and Geometry)

The O Levels exams are a critical milestone in a student’s academic journey, and preparation is key to achieving your best results. Amidst the rigorous syllabus and complex concepts, one invaluable tool can help you streamline your revision and boost your confidence in the examination hall: the Condensed Formula Sheet.

In this article, we introduce you to a meticulously crafted, student-friendly guide that distills the essential formulas, equations, and key concepts across various topics into one comprehensive resource.

If you’re racing against time or looking for a concise overview, this condensed formula sheet is your secret weapon to mastering O Levels efficiently.

## E math formula sheet and A math formula sheet

### Conversion factors/numbers

Conversion factors are crucial in questions that involve speed, distance and time. If you are stuck with a question on how to find speed using distance and time refer to this formula sheet for a quick reference.

### Algebra

Quadratic Equations:

An equation in which the highest power of the variable is 2 is called a quadratic equation. Thus

ax2 + bx + c = 0 where a, b, c are constants and a ≠ 0 is a general equation.

Solving quadratic equations:

We can solve quadratic equation by method of,

- a) Factorization
- b) Using the quadratic formula
- c) Completing the square

Additional functions that should be practiced after the basics:

**Linear Equation**s: Solving linear equations with one variable and using algebraic techniques to rearrange equations.

**Quadratic Equations**: Understanding quadratic equations, factoring, and solving them using methods like the quadratic formula.

**Inequalities:** Working with linear and quadratic inequalities and understanding their solutions.

**Polynomials**: Manipulating and simplifying polynomials, including operations like addition, subtraction, multiplication, and long division.

**Functions:** Understanding the concept of functions, domain and range, and working with function notation.

**Coordinate Geometry:** Graphing equations on the Cartesian plane, including lines, parabolas, circles, and more.

**Simultaneous Equations:** Solving systems of linear equations with multiple variables.

### Geometry and Measurement

The basics of geometry and its rules are in the above infographic, however, it is important to note that area may also include polygons. The types of polygons and its names are as follows:

Types of Polygons and Names:

**Triangle**: A polygon with three sides. Variations include equilateral (all sides and angles are equal), isosceles (two sides and angles are equal), and scalene (all sides and angles are different).

**Quadrilateral**: A polygon with four sides. Common types include square (all sides and angles are equal), rectangle (opposite sides are equal and all angles are 90 degrees), rhombus (all sides are equal), parallelogram (opposite sides are equal and parallel), and trapezoid (one pair of opposite sides are parallel).

**Pentagon**: A polygon with five sides.

**Hexagon**: A polygon with six sides.

**Heptagon or Septagon**: A polygon with seven sides.

**Octagon**: A polygon with eight sides.

**Nonagon or Enneagon:** A polygon with nine sides.

**Decagon**: A polygon with ten sides.

Lastly, pythagoras theorem is also a key testing subject for geometry.: In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This is expressed as a^2 + b^2 = c^2. ( Find out some of the interesting facts about pythagoras in this article!)

Remember that the properties and formulas for these polygons, such as area and perimeter, can vary based on their specific characteristics. Understanding these core rules and concepts in geometry is crucial for success in O Levels mathematics and lays a strong foundation for more advanced mathematical studies.

## How is Algebra and Geometry relevant to my life?

Algebra and geometry, studied in secondary school, are highly relevant to students’ lives in various ways. Here are a few examples:

**Budgeting and Financial Planning: **Algebraic skills are crucial for creating budgets and managing personal finances. Students can use algebra to calculate expenses, income, savings, and investments.

**Home Improvement Projects: **Alternatively, a more practical usage for geometry is to measure spaces, angles, and dimensions in home improvement projects. Students can use geometric concepts to plan room layouts, calculate areas for painting or flooring, and design furniture arrangements for optimal space utilization.

**Technology and Gaming: **Algebra is the foundation of computer programming and game development. Though games are often a unique combination of art, creative thinking and mathematics, students with good algebraic skills can create code, design algorithms, and solve complex problems in the digital world. Geometry is also used extensively in graphics programming to create realistic 3D environments and characters. Following this thread of thought, many professions require algebra and geometry skills. Architects use geometry to design buildings, engineers apply algebra to solve complex equations in various fields, and scientists use both to analyze data and make predictions.

**Travel and Navigation**: Geometry is the core concept behind GPS technology and map reading. Understanding geometric principles helps students interpret maps, calculate distances, and plan travel routes efficiently.

**Problem Solving and Critical Thinking:** Both algebra and geometry foster problem-solving and critical-thinking skills. These skills are not only applicable in specific scenarios but also in everyday decision-making, from evaluating options to making informed choices.

**Data Analysis and Statistics:** Algebra is used to manipulate data, and geometry helps visualize data through graphs and charts. These skills are essential for interpreting information in news reports, scientific studies, and everyday life.

**Home and Personal Projects: **Algebra and geometry can be applied to various home and personal projects, such as designing a garden layout, calculating materials for DIY projects, or planning a trip itinerary.

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