Maths

• how do we find the gradient of a perpendicular bisector?
• what is the equation for the midpoint of a line?


  X1+X2/2 Y1+Y2/2
• what is the minimum and maximum in a quadratic graph?

  minimum is the dent and the maximum is the slope
• -X squared is positive
• anything divided by 0.5 is doubled eg. 4 / 0.5 = 8
• to calculate the circumference of a circle, use 2πr (pi times radius)
• Character adjectives

  
• what is the formula for the volume of a cone?


  1/3 * π * r^2 * h
• what is the formula for the volume of a pyramid? 


  1/3 x base area x perpendicular height
• what is factorising a quadratic?
• what is factorising a quadratic?

  put it into 2 brackets 2xsqaured + 5x -9
• always rearange to get an 0 in a quadratic equation asked to be solved by factorising!
• the difference of 2 squares equation will always look like 16x squared + or --25 just get the square root of bothe of the sides
• Always factorise algebraic fractions first.
• Vector


  A journey from a start point to an end point that can be drawn on a grid
• Column vectors describe a journey from a start point to an end point and can be drawn onto a grid
• In this video, vectors will be represented using algebra instead of counting squares
• Vector notation


  Using bold letters to represent vectors (e.g. A, B)
• Reverse direction of a vector


  Reverse the direction of the arrow and change the sign of all the terms
• Describing a vector from X to Y


  1. Go from X to O (negative A)

  2. Then go from O to Y (positive B)

  3. The vector from X to Y is A + B
• Given information in a diagram


  • OQ is 5A
  • QR is 3B - A
  • OP is B
• Finding the vector from Q to P


  1. Go from Q to O (negative 5A)

  2. Then go from O to P (positive B)

  3. The vector from Q to P is -5A + B
• Finding the vector from P to R


  1. Go from P to Q (positive 5A - B)

  2. Then go from Q to R (3B - A)

  3. The vector from P to R is 4A + 2B
• Finding the vector from P to S


  1. Go from P to R (4A + 2B)

  2. Then go from R to S (negative 5A)

  3. The vector from P to S is A + 2B
• OABC is a parallelogram
• Vector BC


  Same as vector OA, both are 2A
• Vector AC


  Same as vector OB, both are 6B
• Finding the vector from A to M


  AM is half of AC, which is 3B
• Finding the vector from O to M

  1. Go from O to A (2A)

  2. Then go from A to M (3B)

  3. The vector from O to M is 2A + 3B
• Finding the vector from O to N


  ON is half of OC, which is 3B + A
• Finding the vector from N to B


  1. Go from N to O (negative 3B - A)

  2. Then go from O to B (6B)

  3. The vector from N to B is 3B - A
• OC is 5 times OB, so OC is 5B
• BC is 4B
• Finding the vector from A to X


  AX is 3/4 of AB, which is 3/4 of (-3A + B)
• Finding the vector from X to Y

  1. XB is 1/4 of AB

  2. BY is 2/7 of BC
• Ratios are used to find the position of points X and Y on the lines
• When analysing vectors, you may be tempted to try and convert fractions into decimals but in most cases writing your answers as fractions is going to be easier in vectors questions
• Finding the vector from X to Y


  1. Go from X to B (vector XB)

  2. Go from B to Y (vector BY)
• Vector XB


  1/4 of the vector AB
• Vector BY


  2/7 of the vector BC