Maths revision

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S U A J J W I G T Q L L U V G B S P G P S
R H J D F L C D S S K D A Q P G N I Q E N
I X O I D T I N N G R O D B A E O C C P M
N I G D E A R M O X N U L X R H I Q D W D
T E U O F N C L I H B B X W A S T B M S B
E K Q T I G L B T J D L F W M C A I O K J
R E S P R E E M C M K E S I E P U N H F S
S I O R F N S C A H Q A A F T K Q O W W X
E O M O M T A C R A G N D R R J E M E E Y
C B Q D S F N W F L P G I R I M N I S Y G
T B I U K O D L L D P L Y C C F A A P F N
I W U C R R E X A M T E V G E R I L D J R
N O M T J M L W I E A F M E Q D S T P K T
G P H T T U L X T H G O C B U P E H F F S
L V S X S L I J R L Y R R T A A T E M W A
I S P K A A P C A Q D M T Q T I R R O V S
N N O P J E S W P C U U A H I V A E O Y Q
E A V A T Q E Q F Q B L F I O L C O U E X
S U T U M T S K O G U A J B N Y F M A J V
V R M Q A G T Q G S P E U O S M M T A T E
W P T M B V K H N N O M W R Q E Q H F T R

Clues

  • Circle centre (0,0) radius 1, cartesian - x^2+y^2=r^2. If centre (a,b) x=rcos[angle]+a y=rsin[angle]+b and cartesian - r^2=(x-a)^2+(y-b)^2. Ellipses cartesian - x^2/a^2+y^2/b^2=1 (7, 3, 8)
  • cos[angle] = a1b1+a2b2+a3b3/|a|.|b|, a.b = a1b1+a2b2+a3b3 = |a|.|b| x cos[angle] (3, 7)
  • If it is an improper fraction, use the Remainder Thereom to find the number that is divisible, and then use the partial fractions method. If it has x(x^2 -1) partial fractions becomes A/x + Bx+c/x^2 -1 (7, 9)
  • Make t the subject and put into an equation, make the cartesian according to y. If substitution doesn't work, for instance x=t^2+1/t and y=t^2-1/t, add them together (9, 9)
  • Parallel lines = multiples, Intersect = value for h* and u* are the same. If does neither = Skew lines (12, 5)
  • sin(2A) = 2sinAcosA, cos(2A) = cos^2A-sin^2A (6, 5, 8)
  • tan(A+B) = tanA+tanB/1-tanAtanB, tan(A-B) = tanA-tanB/1+tanAtanB, tan(2A) = 2tanA/1-tan^2A (7, 8)
  • to coverge |ax| (8, 7)
  • Translate - a add a to function for x, b add b to the function for y. Stretch (xd) multiply x function by d, Stretch (yd) multiply y function by d. Reflection (xd) multiply y function by -1, Reflection (yd) multiply x function by -1 (10, 9)

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