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Flashcards in C2 Deck (21):
1

y = x^2 - 1 translated by (a)
(b)

(y-b) = (x-a)^2 - 1

2

y = -f(x)

reflection in x axis

3

y = f(-x)

reflection in y axis

4

arithmetic sequence

each term is found by adding a fixed number (common difference) to the previous one

e.g u1 = a
u2 = u1 + d
u3 = u2 + d

5

formula to find a term in an arithmetic series

Un = a + (n-1)d

a being the first term
d being the common difference

6

sum of a certain number of terms

1/2n(a+l)
l being the last given term
OR
1/2n(2a+ (n-1)d)

7

geometric sequence

each term is found by multiplying the previous term by a fixed number (common ratio)

8

nth term of geometric series

U1 = a
U2 = ar
U3 = ar^2

a being first term
r being the common ratio

9

sum of a geometric series

Sn = a(1-r^n)/1-r

10

sum to infinity of a geometric series

a / 1 - r

if -1 < r < 1

11

(1 + x)^n =

1 + (n)x + (n)x^2 + (n)x^3
(1) (2) (3)

12

cosine rule

a^2 = b^2 + c^2 -2bccosA

13

sine rule

a/sinA = b/sinB

14

area of a triangle

1/2absincC

15

length of an arc

l = rθ

16

area of sector

1/2(r^2)θ

17

sin^2x + cos^2x =

1

18

sinx/cosx =

tanx

19

y = a^x

positive for all values of x
always passes through point (0,1)

20

y = a^x =

x = loga y

21

trapezium rule

1/2h(sum of end ordinates + 2(sum of interior ordinates))