Pure

Question 1

How to transform logarithmic graphs?

Answer 1

Write as a familiar function y=f(x) and then use normal transformation rules.

Question 2

Relationship between lines of lnx and e^x

Answer 2

Reflection of each other in the line y=x

Question 3

What does y=e^x look like?

Answer 3

Acceleration, crosses y-axis at (0,1), asymptotes of y=x and x-axis

Question 4

What does y=lnx look like?

Answer 4

Deceleration, crossing x-axis at (1,0), asymptotes of y=x and y-axis

Question 5

How to convert a circle’s equation?

Answer 5

Complete the square

Question 6

Which formula to use when r>1?

Answer 6

r^n - 1, r-1 instead of the other one (on formula sheet)

Question 7

sin2A

Answer 7

2sinAcosA

Question 8

cos2A

Answer 8

cos^2A - sin^2A, 1-2sin^2A, 2cos^2A -1

Question 9

tan2A

Answer 9

2tanA/1-tan^2A

Question 10

sec^2A

Answer 10

1+tan^2A

Question 11

cosec^2A

Answer 11

1+cot^2A

Question 12

How to write parametric equations as a function?

Answer 12

x = p(t), y = q(t)

Question 13

What is the domain of f(x)?

Answer 13

range of x

Question 14

What is the range of f(x)?

Answer 14

range of y

Question 15

How to draw functions as graphs?

Answer 15

Work out domain and range.

Question 16

domain of secx?

Answer 16

R except even multiples of pi/2

Question 17

range of secx?

Answer 17

-1≤ or ≥1

Question 18

domain of cotx?

Answer 18

R, except multiples of π

Question 19

range of cotx?

Answer 19

R

Question 20

range of cosec?

Answer 20

-1≤ or ≥1

Question 21

domain of cosec?

Answer 21

R, except multiples of π

Question 22

domain of arcsinx

Answer 22

-1 ≤ x ≤ 1

Question 23

range of arcsinx

Answer 23

[-π/2, π/2]

Question 24

domain of arccosx?

Answer 24

-1 ≤ x ≤ 1

Question 25

range of arccosx?

Answer 25

[0, π]

Question 26

how to draw arcfunctionx?

Answer 26

restrict domain of ‘normal’ function, then reflect in y=x

Question 27

domain of arctanx?

Answer 27

all real numbers

Question 28

range of arctanx?

Answer 28

[-π/2, π/2]

Question 29

cos(-A) is the same as

Answer 29

cos(A)

Question 30

sin(-A) is the same as

Answer 30

-sin(A)

Question 31

sin30

Answer 31

1/2

Question 32

cos30

Answer 32

√3/2

Question 33

tan30

Answer 33

√3/3

Question 34

sin45

Answer 34

√2/2

Question 35

cos45

Answer 35

√2/2

Question 36

tan45

Answer 36

1

Question 37

sin60

Answer 37

√3/2

Question 38

cos60

Answer 38

1/2

Question 39

tan60

Answer 39

√3

Question 40

cosine rule

Answer 40

a² = b² + c² - 2bccosA

Question 41

How can we use the discriminant?

Answer 41

It’s value tells us the number of times two lines intersect.

Question 42

when modelling parametric, what is the value of dy/dt at max/min?

Answer 42

0, like dy/dx is 0