Maths revision

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

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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