math

• hello there and welcome to the year nine end of year exam revision video here we're going to go through the first three questions in the year nine exam not exactly the questions but the topics surrounding those questions and the types of questions you might face in the end of year exam
• how are we going to use this video well it each question pause a video and answer the question give it a proper go not just 20 seconds and then give up try really hard and then play the video to see if you are correct and if you weren't then try to remember what you need to do next time and then maybe try that question again later on to see if you've remembered how to do it if you're finding that that topic is pretty straightforward and you know how to do it feel free to skip ahead to the next topic at any point in the video and feel free to skip ahead I think this video will actually be quite a long one so skipping is absolutely fine as long as you're confident
• Topics covered in this video

  • Algebra and basic algebra skills
  • Straight line graphs
  • Standard form questions
• write down the most important ideas on a revision sheet as you go through them and then maybe do the questions on a separate sheet of paper and then you'll have a big poster at the end of it with the key ideas on the first three questions for the end of year 9 exam
• Solving algebra question


  1. Rewrite formula with numbers

  2. Perform calculations step-by-step

  3. Write final answer
• Expanding brackets


  1. Multiply first term by both terms in bracket

  2. Simplify and tidy up final answer
• Factorising


  1. Identify common factors

  2. Put common factor at front of bracket

  3. Determine what goes inside bracket
• Factorising into two brackets


  1. Try one bracket first

  2. If that doesn't work, try two brackets

  3. Expand brackets and check if it matches original expression
• Expanding brackets


  1. Multiply x by first term in second bracket

  2. Multiply first term in first bracket by second term in second bracket

  3. Add results
• Factorising


  • Identify common factor between terms
  • Divide all terms by common factor and put in first bracket
  • Factorize what's left in the bracket
• Solving equations


  1. Move smaller variable to other side

  2. Move numbers to other side

  3. Divide both sides by coefficient of variable
• 1. intercept


  The number the line starts on the y-axis
• Gradient


  The rate of change, how much y changes for each unit change in x
• Drawing straight line graphs

  1. Start at y-intercept

  2. Move along x-axis by 1, up/down by gradient

  3. Connect points
• Negative gradient means line goes downwards
• Flat gradient of 1/2 means line is very shallow
• Drawing a line on a graph

  1. Start at y-axis

  2. Right by 1, down by 3

  3. Right by 1, down by 3

  4. Right by 1, down by 3

  5. Right by 1, down by 3

  6. Right by 1, down by 3
• Drawing a line on a graph (reverse)

  Left by 1, up by 3
• Equation of a line

  y = -3x + 8
• Drawing a line on a graph

  1. Start at -4 on y-axis

  2. Right by 1, up by 1/2

  3. Right by 1, up by 1/2

  4. Right by 1, up by 1/2

  5. Right by 1, up by 1/2

  6. Left by 1, down by 1/2

  7. Left by 1, down by 1/2

  8. Left by 1, down by 1/2
• Drawing a line on a graph

  1. Start at 0 on y-axis

  2. Right by 1, down by 2

  3. Right by 1, down by 2

  4. Right by 1, down by 2

  5. Right by 1, down by 2
• Drawing a line on a graph (reverse)

  Left by 1, up by 2
• Equation of a line

  y = -2x
• Equation of a line


  y = 3x + 4
• Equation of a line

  y = 1/2x + 2
• Equation of a line

  y = 2x - 5
• Coordinate (5,4)


  Does not lie on line y = 2x - 3
• Coordinate (2,-4)


  Lies on line y = -3x + 2
• Parallel lines


  • Have the same gradient
• Finding equation of line parallel to y = 3x - 1 that intersects (4,5)


  1. Gradient is 3

  2. Substitute (4,5) into equation y = 3x + C

  3. C = -7

  4. Equation is y = 3x - 7
• Finding equation of line parallel to y = -2x + 5 that intersects (-4,1)


  1. Gradient is -2

  2. Substitute (-4,1) into equation y = -2x + C

  3. C = -7

  4. Equation is y = -2x - 7
• Finding gradient between two points (4,5) and (2,1)

  1. Change in y = 4

  2. Change in x = 2

  3. Gradient = 4/2 = 2
• Finding equation of line through (4,6) and (7,9)


  1. Gradient = (9-6)/(7-4) = 1

  2. Substitute (4,6) into y = x + C

  3. C = 2

  4. Equation is y = x + 2
• Finding equation of line through (-3,-9) and (4,-3)

  1. Gradient = (-3-(-9))/(4-(-3)) = -3/7

  2. Substitute (-3,-9) into y = -3/7x + C

  3. C = 9

  4. Equation is y = -3/7x + 9
• Standard form


  Number between 1 and 9.9 multiplied by power of 10
• Recurring or one in ten is going to be able to represent this there'll be five point six and then we need to work out how many multiples of ten we need to make five point six equal to this thing here
• Little trick to use

  1. Put decimal point between the five and six

  2. Work out how many times to multiply by 10
• Need to multiply by ten seven times to give 56 million
• Decimal is seven point zero four
• Put decimal point between the 7 and 04

  1. Go one two three four five

  2. 10 to the minus 5