Question 1

1. G = 8

   M = 7

   D = 5

2. 15/24

3. 20/24 = 0.833

   19/23 = 0.826

   18/22 = 0.818

   0.833 x 0.824 x 0.818 = 0.56

Question 2

1. 4, 4

2. 2log3 + log5 = logA

   log9 + log5 = logA

   log45 = logA

   A = 45

3. 2log3 + logB = log180

   log9 + logB = log180

   logB = log(180/9)

   B = 20

Question 3

1. Tn = 110n

2. 256 x r^(n-1)

   256(1/2)^5

   = 8

3. 256(1/2)^(n-1) = 1

   1/2^(n-1) = 1/256

   (2^-1)^n-1 = 2^-8

   -n+1=-8

   -n=-9

   n=9

   T=110(9)

   = 990 minutes past

Question 4

1. line = x=4

   5, 3.5

2. 2

3. y = 0.5 (x-4)^2 - 1

   = 0.5 (x^2 - 8x + 16) -1

   = 1/2x^2 - 4x + 8 - 1

   = 1/2x^2 - 4x + 7

4. 0 = 0.5 (x-4)^2 - 1

   2 = (x-4)^2

   ± √2 = x-4

   x = 4 ± √2

   x = 5.4

   x = 2.6

Question 5

1. cosC = (a^2 + b^2 - c^2) / 2ab

   C = cos^-1 (20^2 + 12^2 - 28^2) / 2(20)(12)

   C = 120

2. 20:15 = 0.75

   12:9

   EC = 9