1. Integrate

Answer:

(4 marks)

2a. Show that is always positive

Answer has a vertex of (-4,1) which is >0. The coefficient is positive, so the curve opens upwards. Hence, it is always positive

b. A number plus three is squared. It is greater than the square of the original number:

-Sometimes?

-Always?

-Never?

Explain why

Therefore, sometimes true.

3a Given A and B, find AB: A was (4i+5j) and B was (-5i-2j)

Find AB=OB-OA= -9i+3j

b)

4a. l

_{1}: 4y-3x=10

l

_{2}goes through two points A(1,5) and B(-1,8)

Are these lines parallel, perpendicular or neither?

The gradients are neither equal or negative recipricols of each other, hence neither.

5a.The logs did not have the same coefficient so the substraction law could not be applied.The student did rather than

b. Solve the log equation correctly to get

6a. £15 is not a sensible price, since the profit is negative (prove with

b.

Smallest value of x is £7.22

c.i) Maximum profit is when

Therefore P=100

Profit= £100,000

ii)

x=9

£9.00

7a. sinx=0.6

Therefore,

b.

8a. velocity for the minimum cost

I've written ?

b. Cost associated with that £243.16 *Pretty sure this is wrong, but it's what I've written down

9a. Show (x+2) was a factor of g(x)

b. Fully factorise it to

c.i) x<=-2 OR

ii)

10. Show from first principals that differentiates to

11a. Binomial expansion of the first three terms in ascending terms of x

b. the first two terms of are 128 and 36x.

Find a and b

128=512a

b=

12a. Rearrange the trig equation

b. 16.1, 40, 80

13a

b.P was the value of the painting in 1980. Q was the rate of change in the value of the painting

c. Value of painting 30 years later: £2,000,000.00

14a equation of circle:

i) centre (3,-5)

ii) radius 5

b) Find the values of k when y=kx intersects the circle twice

Use discriminant by plugging y=kx into equation of circle

15a line equation:

Integrate C between 2 and 4=10

Area of triangle:

10+36=46.(10 marks)

I've got a lesson now so I'll add more detail later if I still remember!