Paper 1

Question 1

a =

Answer 1

3

Question 2

binomial theorem

Answer 2

1 + 4x - 8x^2 + 32x^3

Question 3

logarithms

Answer 3

log base 2 3

Question 4

completing the square

Answer 4

2(x + 1)^2 + 7
y-intercept (0,9)
minimum (-1, 7)

Question 5

range of possible values for k

Answer 5

k-4

Question 6

circle

Answer 6

sub y in as soon as possible

Question 7

geometric proof:

Answer 7

(1) : Sn = a + ar + ar^2 + … + ar^(n-1)
(2) : rSn = ar + ar^2 + ar^3 + … + ar^n
(1) - (2): Sn - rSn = a + ar^n

Question 8

prove by contradiction

Answer 8

• assume
• DOTS: (2p - q)(2p + q) = 25
• as +ve: (2p - q) < (2p + q)
• (2p + q) > 0
• 2p + q = 25
• 2p - q = 1
• solve (p = 6.5)

Question 9

deriving the equation

Answer 9

• sub in values
• use brackets
• B = 51.6
• A = 69.6
• A becomes maximum

Question 10

finding the tangent for r

Answer 10

• set b^2 - 4ac = 0

- 9 +/- 3 root 5