Pure (Important Stuff)

Question 1

integral of cosecxcotx

Answer 1

-cosecx + c

Question 2

integral of secxtanx

Answer 2

secx + c

Question 3

integral of cosec^2x

Answer 3

-cotx

Question 4

derivative of tanx

Answer 4

sec^2x

Question 5

integral of tan x

Answer 5

-lncosx

tanx = sinx/cosx, f’(x)/f(x)

Question 6

sin2x =

Answer 6

2sinxcosx

Question 7

cos2x =

Answer 7

• cos^2x - sin^2x
• 2cos^2x - 1
• 1 - 2sin^2x

Question 8

sec^2 x =

Answer 8

1 +tan^2 x

Question 9

cosec^2 x =

Answer 9

1 + cot^ x

Question 10

if part of the function differentiates to give the whole function then

Answer 10

the integral is the function

Question 11

integral of sec^2x

Answer 11

tanx + c

Question 12

convex curve

Answer 12

curve is below chord

second derivative > 0

Question 13

concave curve

Answer 13

curve is above chord

second derivative < 0

Question 14

Odd function geometrically

Answer 14

rotational symmetry about origin

Question 15

even function geometrically

Answer 15

symmetric with respect to y axis

Question 16

odd function

Answer 16

f(-x) = -f(x)

Question 17

even function

Answer 17

f(-x) = f(x)

Question 18

f’‘(X) a^x =

Answer 18

a^xlna

Question 19

perpendicular gradients

Answer 19

m * m = -1

Question 20

gradient of a reflection in the line y= x

Answer 20

1/ gradient of object point

Question 21

points of an inverse / normal function reflected in y = x

Answer 21

x and y swap