3rd Form Revision for EOY 1

• Powers


  • Squares (e.g., 3^2 = 9)
  • Cubes (e.g., 2^3 = 8)
• Roots


  • Square root (e.g., √16 = 4)
  • Cube root (e.g., √27 = 3)
• Using a calculator


  Use power and root functions for harder calculations (e.g., 5^3, √81)
• Fractional powers


  x^(1/n) = n√x
• Negative powers


  x^(-n) = 1/x^n
• Laws of indices


  1. Multiplying: a^m × a^n = a^(m+n)

  2. Dividing: a^m ÷ a^n = a^(m-n)

  3. Power of a power: (a^m)^n = a^(mn)
• Standard form


  • Large numbers: 4,500,000 = 4.5 × 10^6
  • Small numbers: 0.00032 = 3.2 × 10^-4
• Calculating with standard form

  Multiply/divide numbers normally, add/subtract exponents
• Prime factors


  Breaking down a number into primes (e.g., 60 = 2^2 × 3 × 5)
• HCF (Highest Common Factor)


  The largest factor that divides two numbers
• LCM (Lowest Common Multiple)


  The smallest number that is a multiple of both numbers
• Substituting numbers into formulae


  Replace variables with given numbers (e.g., if y = 3x + 2 and x = 4, then y = 3(4) + 2 = 14)
• Working with indices


  Follow laws of indices to simplify expressions (e.g., 2^3 × 2^4 = 2^7)
• Expanding brackets


  a(b + c) = ab + ac
• Collecting like terms


  Combine terms with the same variable (e.g., 3x + 5 + 2x - 3 = 5x + 2)
• Factorising algebraic expressions


  Find common factors and use them to factorise (e.g., 6x + 9 = 3(2x + 3))
• Generating formulae


  Create expressions based on given relationships (e.g., area A of rectangle = length l × width w, so A = l × w)
• Changing the subject of a formula

  Rearrange formula to solve for a different variable (e.g., from y = 3x + 2 to x = (y - 2)/3)
• Solving simple equations


  Isolate the variable (e.g., 2x + 3 = 7 becomes 2x = 4, so x = 2)
• Solving harder linear equations

  Use similar steps but may involve more operations (e.g., 3(x - 1) = 2x + 4 becomes 3x - 3 = 2x + 4, so x = 7)
• Solving equations with brackets and fractions

  Expand and simplify (e.g., 2x - 3/4 = 2/4 becomes 2x - 3 = 8, so 2x = 11 and x = 11/2)