Maths Algebra Skill 1

• Pro numerals


  Letters used to represent one or more numbers
• Variables


  Letters used to represent one or more numbers
• a times b


  Written as ab (no multiplication sign)
• a divided by b

  Written as a/b (as a fraction)
• a times a


  Written as a^2 (a squared)
• Expression


  A combination of numbers and pro numerals combined with mathematical operations
• Expressions


  • 2a - 3c + 4xy
• Term


  A part of an expression with only pro-numerals, numbers, multiplication and division signs
• Terms


  • 9a, 10cd, 3x/5, 2b, 3xy
• Coefficient


  The number in front of a pro numeral
• Constant term


  A term that does not contain any variables
• Identifying terms in an expression

  • a + b - 12c + 5
• Sum

  Addition of numbers
• Difference


  Subtraction of numbers
• Product

  Multiplication of numbers
• Quotient

  Division of numbers
• Square


  A number multiplied by itself
• Writing expressions from word descriptions

  1. Sum of three and k

  2. Product of m and 7

  3. 5 added to one half of k

  4. Sum of a and b is doubled
• Pro numerals


  Letters used to represent one or more numbers in a given base. They are often used in mathematical expressions to make them more concise and easier to read.
• Digits

  The individual symbols used to represent numbers in a positional numeral system. In the decimal system, the digits are "0, 1, 2, 3, 4, 5, 6, 7, 8, 9".
• Purpose of pro numerals

  To make mathematical expressions more concise and easier to read. They are also used in certain mathematical systems where there are not enough standard digits to represent all of the numbers.
• Substitution


  Replacing a variable with a specific value in an expression
• Substituting a value for a variable

  1. Find the expression

  2. Replace the variable with brackets and the value

  3. Simplify the expression
• Substituting values


  • 2 + x = 5 (when x = 3)
  • 2 + (-3) = -1
  • 2x^2 - 10 (when x = -3) = 18 - 10 = 8
  • 2(-3)^2 - 3(-3) + 5 = 18 - 9 + 5 = 14
  • 2(-3)(-2) - 2(-3)^2(-2) = 12 - 24 = -12
• Putting the value in brackets when substituting is a powerful way to do it
• The operations outside the brackets remain outside the brackets when substituting
• Following BIDMAS (brackets, indices, division/multiplication, addition/subtraction) is important when simplifying after substitution
• Substituting values with multiple variables follows the same process
• Collecting like terms

  Adding up the coefficients of the same variable
• Collecting like terms

  • a + a + a + a = 4a
  • 3c + 2c = 5c
  • 8y - 3y = 5y
  • w + w = 2w
• When adding different letters, you cannot simplify, you can only collect like terms
• Collecting like terms

  • a + c = a + c
  • x^2 + x^2 = 2x^2
  • 5c + 5c - 12c = 10c - 12c = -2c
  • x + x + 2x + 5 + 3 = 4x + 8
• Collecting like terms

  • 4a + 2c + 5a + 9c = 9a + 11c
  • 8a + 7w + 2w - 3a = 5a + 9w
  • 6s + 4t - 8s - 5t = -2s - t
  • 10x - 5y - x - 2y = 9x - 7y
• Expand a single bracket

  Multiply the terms inside the bracket by the term outside
• Expanding brackets


  1. Multiply the term inside the bracket by the term outside

  2. Combine the results
• Expanding 4(x + 2)


  • 4 * x = 4x
  • 4 * 2 = 8
  • Result: 4x + 8
• Expanding brackets with a positive number outside


  Multiply each term inside by the number outside, keep the signs
• Expanding 9(9x + 4)

  • 9 * 9x = 81x
  • 9 * 4 = 36
  • Result: 81x + 36
• Expanding 3(2x - 7)

  • 3 * 2x = 6x
  • 3 * -7 = -21
  • Result: 6x - 21
• Expanding brackets with a variable outside

  Multiply each term inside by the variable outside