Formula Sheet For Igcse Maths

Your Ultimate IGCSE Maths Formula Sheet & Revision Guide

Are you feeling overwhelmed by the sheer volume of formulas needed for your IGCSE Maths exams? Don't worry, you're not alone! Many students struggle to keep track of all the different formulas and when to apply them. This comprehensive guide will not only provide you with a complete formula sheet, but also explain each formula in simple terms, offer helpful tips, and provide examples to solidify your understanding. Mastering these formulas is key to achieving a high score on your IGCSE Maths exams, so let's dive in!

Number & Algebra

This section covers the fundamental building blocks of IGCSE Maths, focusing on number manipulation and algebraic expressions.

1. Number Properties

• Prime Numbers: Numbers greater than 1 divisible only by 1 and themselves (e.g., 2, 3, 5, 7, 11).

• Factors: Numbers that divide exactly into another number (e.g., factors of 12 are 1, 2, 3, 4, 6, 12).

• Multiples: Numbers that are the product of a given number and an integer (e.g., multiples of 3 are 3, 6, 9, 12...).

• Highest Common Factor (HCF): The largest number that divides exactly into two or more numbers.

• Lowest Common Multiple (LCM): The smallest number that is a multiple of two or more numbers.

• Indices (Exponents): Rules for working with powers:

  • a^m x aⁿ = a^m+n
  • a^m ÷ aⁿ = a^m-n
  • (a^m)ⁿ = a^mn
  • a⁰ = 1
  • a^-n = 1/aⁿ
  • a^1/n = ⁿ√a
  • a^m/n = (ⁿ√a)^m

• Standard Form (Scientific Notation): Expressing numbers in the form a x 10^k, where 1 ≤ a < 10 and k is an integer.

Example: Find the HCF and LCM of 12 and 18.

• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 18: 1, 2, 3, 6, 9, 18
• HCF(12, 18) = 6
• Multiples of 12: 12, 24, 36, 48...
• Multiples of 18: 18, 36, 54...
• LCM(12, 18) = 36

2. Algebraic Manipulation

• Expanding Brackets: Removing brackets by multiplying each term inside the bracket by the term outside. For example: 3(x + 2) = 3x + 6 and (x + 2)(x + 3) = x² + 5x + 6 (using the FOIL method: First, Outer, Inner, Last).
• Factorizing: Expressing an algebraic expression as a product of its factors. For example: x² + 5x + 6 = (x + 2)(x + 3). This often involves finding common factors or using difference of squares (a² - b² = (a + b)(a - b)).
• Solving Equations: Finding the value(s) of the unknown variable that make the equation true. This may involve rearranging the equation, using inverse operations, or applying the quadratic formula (see below).
• Simultaneous Equations: Solving two or more equations with two or more unknowns simultaneously. Methods include substitution and elimination.
• Quadratic Equations: Equations of the form ax² + bx + c = 0. Solutions can be found using:
  • Factorization: If possible, factor the quadratic expression and set each factor to zero.
  • Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a

Example: Solve the quadratic equation x² + 5x + 6 = 0.

By factorization: (x + 2)(x + 3) = 0, so x = -2 or x = -3.

Geometry & Mensuration

This section deals with shapes, sizes, and their properties.

1. Basic Shapes

• Perimeter: The total distance around the outside of a shape.
• Area: The amount of space inside a shape.
• Volume: The amount of space a three-dimensional shape occupies.
• Surface Area: The total area of all the faces of a three-dimensional shape.

Formulas for common shapes:

• Rectangle:
  • Perimeter = 2(length + width)
  • Area = length × width
• Triangle:
  • Area = (1/2) × base × height
  • Pythagorean Theorem (right-angled triangles only): a² + b² = c² (where a and b are legs, c is the hypotenuse)
• Circle:
  • Circumference = 2πr or πd (where r is radius, d is diameter)
  • Area = πr²
• Cuboid:
  • Volume = length × width × height
  • Surface Area = 2(lw + lh + wh)
• Cylinder:
  • Volume = πr²h
  • Curved Surface Area = 2πrh
  • Total Surface Area = 2πr(r + h)
• Sphere:
  • Volume = (4/3)πr³
  • Surface Area = 4πr²

2. Trigonometry

• Sine Rule: a/sinA = b/sinB = c/sinC
• Cosine Rule: a² = b² + c² - 2bc cosA
• Trigonometric Ratios (in a right-angled triangle):
  • sin θ = opposite / hypotenuse
  • cos θ = adjacent / hypotenuse
  • tan θ = opposite / adjacent

Statistics & Probability

This section focuses on data analysis and chance.

1. Statistics

• Mean: The average of a set of numbers. Sum of numbers / number of numbers.
• Median: The middle value in a set of ordered numbers.
• Mode: The most frequent value in a set of numbers.
• Range: The difference between the highest and lowest values in a set of numbers.

2. Probability

• Probability of an event: Number of favorable outcomes / Total number of possible outcomes.
• Independent Events: The probability of one event does not affect the probability of another. P(A and B) = P(A) × P(B)
• Mutually Exclusive Events: Two events that cannot occur at the same time. P(A or B) = P(A) + P(B)

Vectors & Transformations

This section covers geometric transformations and vectors.

1. Vectors

• Vector Addition: Add the components of the vectors.
• Scalar Multiplication: Multiply each component of the vector by the scalar.

2. Transformations

• Translation: Moving a shape without changing its size or orientation.
• Rotation: Turning a shape about a point.
• Reflection: Flipping a shape across a line.
• Enlargement: Changing the size of a shape by a scale factor.

Tips for Mastering IGCSE Maths Formulas

• Practice Regularly: Consistent practice is key to memorizing and understanding formulas. Work through plenty of past papers and exercises.
• Understand, Don't Just Memorize: Focus on understanding the derivation and application of each formula, rather than simply rote learning.
• Use Flashcards: Create flashcards with formulas on one side and examples or explanations on the other.
• Organize Your Notes: Keep your notes and formula sheet well-organized and easily accessible.
• Identify Your Weak Areas: Regularly assess your understanding and focus on areas where you struggle.
• Seek Help When Needed: Don't hesitate to ask your teacher, tutor, or classmates for help if you're having trouble.

Frequently Asked Questions (FAQ)

Q: Do I need to memorize all these formulas?

A: While you don't need to memorize every detail, a solid understanding of the core formulas and their applications is essential. Practice will help you internalize them.

Q: What if I forget a formula during the exam?

A: Try to derive the formula if possible, or use logical reasoning and problem-solving skills to approach the problem differently.

Q: Are there any resources besides this formula sheet that can help me?

A: Utilize textbooks, online resources, and past papers to further strengthen your understanding and practice your problem-solving skills.

Conclusion

This comprehensive formula sheet and guide will serve as a valuable resource throughout your IGCSE Maths journey. Remember that consistent practice and a deep understanding of the concepts are vital for success. By combining diligent study with this guide, you'll be well-equipped to tackle the challenges of your IGCSE Maths exams with confidence. Good luck!