𝑀𝐴𝑇𝐻𝑆 𝑌𝑅7 ꨄ

• Algebra rules


  • 1. Never write the multiplication sign
  • 2. Never write the divide sign
  • 3. Always write numbers before letters
• Solving an equation


  Finding the value of an unknown variable
• Types of sequences


  • Arithmetic (add or subtract the same number from each term)
  • Geometric (multiply by the same number each time to make the next term)
  • Fibonacci (add the two previous terms together to make the next term)
  • Square numbers (square the sequence)
  • Cube numbers (cube the sequence)
• Vertical graphs


  Equations written in the form x=c, where c represents any number. Cuts the x-axis at the point [c,a].
• Horizontal graphs


  Equations written in the form y=c, where c represents any number.
• Linear graphs


  • Form a straight line, have the equation y=mx+c or can be rearranged into this form
• Quadratic graphs


  • The highest power of x is x^2, the graph forms a parabola
• Cubic graphs


  • The highest power of x is x^3, the graph has a distinctive shape
• Expanding single brackets


  Multiply the term outside the bracket by the term inside the bracket
• Significant figures


  The number of digits excluding zeros at the beginning or end
• Rounding using significant figures


  Keep the overall place value of the number the same
• Estimation


  Round all numbers in the question to 1 significant figure
• Percentage


  The number of parts per 100
• Converting fractions, decimals and percentages

  1. Fraction to decimal: divide numerator by denominator

  2. Decimal to percentage: multiply by 100

  3. Percentage to fraction: put over 100 and simplify
• Expressing a number as a percentage of another


  Put the numbers into a fraction and then convert to a percentage
• Protractor


  Used to measure angles
• Constructing SAS triangles


  1. Draw side AB

  2. Use protractor to mark angle of 68° from point B

  3. Use ruler to draw line of 5cm from B to C

  4. Join A to C to complete triangle
• Constructing ASA triangles


  1. Draw side AB

  2. Use protractor to mark angle of 38° from point A

  3. Use protractor to draw long line from A

  4. Use protractor to mark angle of 108° from point B

  5. Use ruler to draw line from B to meet point C
• Types of averages


  • Mean (sum of values / number of values)
  • Mode (most common number, can have two answers)
  • Median (middle number, only one answer)
• Range


  The difference between the biggest and smallest values
• Angles


  • Angles around a point total 360°
  • Angles on a straight line total 180°
  • Vertically opposite angles are equal
• Types of triangles


  • Scalene (no equal angles)
  • Isosceles (a pair of equal angles and sides)
  • Equilateral (all angles and sides are equal)
• Kites


  • Have one pair of equal opposite angles
  • Diagonals are perpendicular and cross at 90°
• Quadrilaterals


  • Angles add up to 360°
• Parallel lines


  • Always the same distance apart (equidistant), never meet
• Types of angles between parallel lines

  • Corresponding angles (equal)
  • Alternate angles (equal)
  • Co-interior angles (add to 180°)
• Divisible by


  When you divide one number by another, the answer is a whole number
• Divisibility Rules


  • A number is divisible by 2 if the last digit is 0, 2, 4, 6, or 8
  • A number is divisible by 3 if the sum of the digits is divisible by 3
  • A number is divisible by 4 if the last two digits is divisible by 4
  • A number is divisible by 5 if the last digit is 0 or 5
  • A number is divisible by 6 if it is divisible by 2 and 3
  • A number is divisible by 7 if you cross off the last digit, double it and subtract, and the new number is divisible by 7
  • A number is divisible by 8 if the last 3 digits is divisible by 8
  • A number is divisible by 9 if the sum of the digits is divisible by 9
  • A number is divisible by 10 if the last digit is 0
  • A number is divisible by 11 if you subtract the last digit from the number formed by the remaining digits, and the new number is divisible by 11
  • A number is divisible by 12 if it is divisible by 3 and 4
• Factor


  A whole number that divides exactly into another number
• Factors of 15


  • 1, 3, 5, 15
• Factors of 80


  • 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
• Highest Common Factor (HCF)


  The largest number that goes into two or more numbers exactly
• Finding the HCF


  1. Find the prime factors of each number

  2. Multiply the shared prime factors together

  3. The answer is the highest common factor
• Triangular numbers


  Numbers that can be represented as an equilateral triangle
• Cubed numbers


  The product of a number that has been multiplied by itself three times
• Fibonacci numbers


  Each term in the sequence is the sum of the previous two terms
• Lowest Common Multiple (LCM)


  The lowest number that is a multiple of two or more numbers
• Finding the LCM


  1. Find the prime factors of each number

  2. Find the highest common factor

  3. Multiply the HCF by the unused prime factors
• Subtracting a negative number means add
• If a negative thing happens to a negative person, that's a positive thing