pure

Question 1

tan^2, sec^2

Answer 1

1 + tan^2 = sec^2

Question 2

cot^2, cosec^2

Answer 2

1 + cot^2 = cosec^2

Question 3

Vieta quadratic equations

Answer 3

p+q = -b/a
pq = c/a

Question 4

Vieta cubic equations

Answer 4

p+q+r = -b/a
pq + qr +pr = c/a
pqr = -d/a

Question 5

derivative from 1st principes

Answer 5

lim h->0
f(x+h)−f(x) / h

Question 6

cos differentiation

Answer 6

-sin

Question 7

tan differentiation

Answer 7

sec^2

Question 8

cot differentiation

Answer 8

-cosec

Question 9

sec differentiation

Answer 9

sec x tan x

Question 10

cosec differentiation

Answer 10

-cosec x cot x

Question 11

even vs odd function

Answer 11

EVEN: f(-x) = f(x)
ODD: f(-x) = -f(x)

Question 12

second derivative local min/max

Answer 12

local max if negative
local min if positive

Question 13

parametric integration

Answer 13

x = f(t)
y = g(t)

to find new bounds plug in the x values and solve for t

integrate f’(t) g(t)
(differentiate x and leave y alone)

Question 14

log rules

Answer 14

log(1) = 0
log(ab) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(a^n) = n log(a)

Question 15

n
∑ 1
i= 1

Answer 15

n
∑ 1 = n
i= 1

Question 16

n
∑ i
i= 1

Answer 16

n
∑ i = n(n+1)/2
i= 1

Question 17

n
∑ i^2
i= 1

Answer 17

n
∑ i^2 = n(n+1)(2n+1)/6
i= 1

Question 18

n
∑ i^3
i= 1

Answer 18

n
∑ i^3 = (n^2 (n+1)^2)/4
i= 1

Question 19

n
∑ a+(i-1)d
i= 1

(arithmetic)

Answer 19

n
∑ a+(i-1)d = n/2(2a + (n-1)d)
i= 1

OR n/2(a1 + an)
where a1 is first term and an is last

Question 20

n
∑ ar^i-1
i= 1

(geometric)

Answer 20

n
∑ ar^i-1=a(1-r^n)/1-r
i= 1

Question 21

∞
∑ ar^i-1
i= 1

Answer 21

∞
∑ ar^i-1=a/1-r
i= 1

Question 22

nth term of geometric series

Answer 22

an = ar^(n-1)

Question 23

nth term of arithmetic series

Answer 23

an = a1 + (n-1)d

Question 24

integral of ln(x)

Answer 24

x ln(x) - x

Question 25

binomial expansion formula
(1+a)^n

Answer 25

1 + na +n(n-1)/2! a^2 + n(n-1)(n-2)/3!a^3 + …

Question 26

turn (2+3x)^-3 into correct form

Answer 26

2^-3 (1+3x/2)^-3

Question 27

partial fraction case

Answer 27

quadratic / (factor)(quadratic)
–>
A/factor + Bx+C/quadratic

Question 28

integration by parts

Answer 28

∫AB = A∫B - ∫(A’∫B)

Question 29

quotient rule

Answer 29

f’(x)g(x) - f(x)g’(x) / g(x) ^2