Notes

(I substituted theta for x in some of the questions like trig functions for easier typing)

1) 2x7/2+c (3)

2) i) 21/3 + 21/4 + 21/5 + 21/6 +21/7 = 22.95(2)

ii)d=5 so U10=a+9x5
U10=a+45

S10=10/2[2a+9x5]
S10=10a+225(3)

3) (2.4-3.6)/(2.2-2) = -6(2)

4) i) (6,-3/2)(2)

ii) (2,-3)(2)

5) a2=b2+c2-2bcCosA
AC=8.72cm(3)

6)half r squared theta equation

1/2x12.42x2.1=161.448

area of a trianlge 1/2absinc

1/2x12.4x12.4xsin2.1= 66.3635...

161.448-66.3635... =95.1cm2(4)
7)150=a/(1-r)
24=ar

simultaneous equations

24/r=a

150=(24/r)/(1-r)
150r-150r2=24
150r-150r+24=0
r=4/5 a=30
r=1/5 a=120(5)

8)(√sin2x)/tanx
sinx/(sinx/cosx)
cosxsinx/sinx
cosx (3)

9)
tan2x=3
2x=71.6
x=35.8 (3)
(draw the graph and stuff)
180 + 35.8 = x=215.8

also 125.78 and 305.78

10)
3x+1=52x
3xx3=25x
xlog103+log103=xlog1025
log103=xlog1025-xlog103
log103=x(log1025-log103)
x=0.518 (4)

11)
i)dy/dx=1+8x-3
then differentiate again for the show that thing.(3)

ii)0=1+8x-3
x=-2
sub into original equation of curve to give y value
(-2,-3)
sub in x value to second derivative and it should come out negative so is therefore maximum. Or you could find the gradient either side. (5)

iii)7y-x+34 (5)

12)
i) 1/2x3x[9+9.1+2(10.7+11.7+11.9+11.0)]
163.05m2(4)

ii)A)11-10.872(just sub in the equation to get the 10.872 value)
=0.128(2)

B)ya'll know how to integrate...
161.72m2(4)

13) This one might be slightly tricky because a graph has to be drawn but these are the answers I got so there will probably be a range of accepted values.

i)h=a x 10bt
log10h=log10a x 10bt
log10h=log10a + log1010bt
log10h=log10a + btlog1010
log10h=log10a + bt(2)

ii) graph should be a straight line, I got my y intercept as -0.24. (4)

iii) find the gradient of your line. I think mine was 0.0289
h=10-0.24+0.0289t(4)
iv)sub in 60 as t into the above equation.
=31.188...
then take away the thickness it had melted up to 50 years because the question asked for how much it would melt in the ten year span between 2010 and 2020
31.188...-15.9 = 15.289 (2)

v) I don't know if it wanted something about extrapolation of results here, or he fact that it is an exponential or something about climate change may affect the rate in which the glacier melts. (1)