Pure year 2

Question 1

Start by assuming its not true

Answer 1

Use steps to lead to something impossible

Question 2

In proofs

Answer 2

how can rational and irrational numbers be differentiated?

Question 3

What is Q?

Answer 3

The set of all rational numbers

Question 4

What does the modulus of a number do?

Answer 4

Make it not negative

Question 5

When f(x) >= 0

Answer 5

the modulus of f(x) =

Question 6

When f(x) < 0

Answer 6

the modulus of f(x) =

Question 7

How to sketch y = modulus(ax+b) ?

Answer 7

Sketch y = ax+b

Question 8

What is domain and range?

Answer 8

Domain = all possible inputs

Question 9

A mapping is a function if every input has a distinct output

Answer 9

functions can be what or what?

Question 10

What type of function is fg(x)?

Answer 10

Composite

Question 11

What is the inverse of f(x)?

Answer 11

f⁻¹(x)

Question 12

What does y=f(x) look like in relation to y=f⁻¹(x)?

Answer 12

A reflection in the line y=x

Question 13

How do the domains and ranges of inverse functions relate?

Answer 13

The domain of f(x) is the range of f⁻¹(x)

Question 14

How to sketch y = modulus(f(x))?

Answer 14

Sketch f(x)

Question 15

How to sketch y = f(modulus(x))?

Answer 15

Sketch f(x) for x>=0

Question 16

What does f(x+a) do?

Answer 16

Translation left by a

Question 17

What does f(x) + a do?

Answer 17

Translation up by a

Question 18

What does f(-x) do?

Answer 18

Reflect in the y-axis

Question 19

What does -f(x) do?

Answer 19

Reflect in the x-axis

Question 20

What does f(ax) do?

Answer 20

Horizontal stretch of scale factor 1/a

Question 21

What does af(x) do?

Answer 21

Vertical stretch of scale factor a

Question 22

Formula for nth term of an arithmetic sequence

Answer 22

Un = a + (n-1)d

Question 23

Formula for the sum of the first n terms of an arithmetic sequence

Answer 23

Sn = (n/2)(2a + (n-1)d)

Question 24

Formula for the nth term of a geometric sequence

Answer 24

Un = ar^(n-1)

Question 25

Formula for the sum of the first n terms of a geometric series

Answer 25

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

Question 26

What is a convergent series?

Answer 26

A geometric series where |r| < 1

Question 27

Formula for the sum to infinity of a convergent geometric series

Answer 27

S∞ = a/(1-r)

Question 28

Explain sigma notation

Answer 28

Greek capital letter sigma

Question 29

What does a recurrence relation do? with general rule

Answer 29

Defines each term of a sequence as a function of the previous term

Question 30

Expand (1+x)^n

Answer 30

1 + nx + ((n(n-1))/2!)x^2 + ((n(n-1)(n-2))/3!)x^3 + …

Question 31

Expand (a+bx)^n

Answer 31

(a^n)(1+(b/a)x)^n

Question 32

When is the expansion of (1+x)^n valid?

Answer 32

When |x| < 1

Question 33

When is the expansion of (a+bx)^n valid?

Answer 33

When |x| < |a/b|

Question 34

What is a radian?

Answer 34

A measure of angles

Question 35

sin(π - θ)

Answer 35

sin(θ)

Question 36

sin(π + θ)

Answer 36

-sin(θ)

Question 37

sin(2π - θ)

Answer 37

-sin(θ)

Question 38

cos(π - θ)

Answer 38

-cos(θ)

Question 39

cos(π + θ)

Answer 39

-cos(θ)

Question 40

cos(2π - θ)

Answer 40

cos(θ)

Question 41

tan(π - θ)

Answer 41

-tan(θ)

Question 42

tan(π + θ)

Answer 42

tan(θ)

Question 43

Arc length formula in radians

Answer 43

l = rθ

Question 44

Area of a sector in radians

Answer 44

A = (1/2)(r²)(θ)

Question 45

When θ is small and in radians

Answer 45

sin(θ) ≈

Question 46

When θ is small and in radians

Answer 46

tan(θ) ≈

Question 47

When θ is small and in radians

Answer 47

cos(θ) ≈

Question 48

Which equation links sec and cos?

Answer 48

sec = 1/cos

Question 49

Which equation links cosec and sin?

Answer 49

cosec = 1/sin

Question 50

Which equation links tan and cot?

Answer 50

cot = 1/tan

Question 51

Which equation links sin

Answer 51

cos and cot?

Question 52

Which equation links sin and cos?

Answer 52

sin²θ + cos²θ = 1

Question 53

Which equation links tan and sec?

Answer 53

1 + tan²θ = sec²θ

Question 54

Which equation links cot and cosec?

Answer 54

1 + cot²θ = cosec²θ

Question 55

Expand sin(A+B)

Answer 55

sinAcosB + cosAsinB

Question 56

Expand sin(A-B)

Answer 56

sinAcosB - cosAsinB

Question 57

Expand cos(A+B)

Answer 57

cosAcosB - sinAsinB

Question 58

Expand cos(A-B)

Answer 58

cosAcosB + sinAsinB

Question 59

Expand tan(A+B)

Answer 59

(tanA + tanB)/(1 - tanAtanB)

Question 60

Expand tan(A-B)

Answer 60

(tanA - tanB)/(1 + tanAtanB)

Question 61

Sin2A =

Answer 61

2sinAcosA

Question 62

Cos2A =

Answer 62

cos²A - sin²A

Question 63

Tan2A =

Answer 63

(2tanA)/(1 - tan²A)

Question 64

For R Sin or Cos (x ± α)

Answer 64

what does R =

Question 65

For the parametric equations x=p(t) and y=q(t)

Answer 65

with the Cartesian equation y=f(x)

Question 66

Differentiate sin(kx)

Answer 66

k cos(kx)

Question 67

Differentiate cos(kx)

Answer 67

-k sin(kx)

Question 68

Differentiate e^(kx)

Answer 68

k e^(kx)

Question 69

Differentiate ln(x)

Answer 69

1/x

Question 70

Differentiate a^(kx)

Answer 70

(a^(kx))(k)(ln(a))

Question 71

What is the chain rule?

Answer 71

dy/dx = dy/du × du/dx

Question 72

How to get from dx/dy to dy/dx?

Answer 72

dy/dx = 1 / (dx/dy)

Question 73

What is the product rule?

Answer 73

If y=uv

Question 74

What is the quotient rule?

Answer 74

If y=u/v

Question 75

Differentiate tan(kx)

Answer 75

k sec²(kx)

Question 76

Differentiate cosec(kx)

Answer 76

-k cosec(kx)cot(kx)

Question 77

Differentiate sec(kx)

Answer 77

k sec(kx)tan(kx)

Question 78

Differentiate cot(kx)

Answer 78

-k cosec²(kx)

Question 79

How to do implicit differentiation?

Answer 79

Differentiate the y like an x then multiply it by dy/dx

Question 80

What is the point called where a curve changes from concave to convex or vice versa?

Answer 80

The point of inflection

Question 81

Integration of x^n

Answer 81

(x^(n+1)) / (n+1)

Question 82

Integration of e^x

Answer 82

e^x

Question 83

Integration of 1/x

Answer 83

ln(x)

Question 84

Integration of cos(x)

Answer 84

sin(x)

Question 85

Integration of sin(x)

Answer 85

-cos(x)

Question 86

Integration of sec²(x)

Answer 86

tan(x)

Question 87

Integration of cosec²(x)

Answer 87

-cot(x)

Question 88

Formula for integration by parts

Answer 88

∫u dv = uv - ∫v du

Question 89

Distance of the origin to the point (x

Answer 89

y

Question 90

Limit of dx → 0 for sigma f(x) when x = a and b on the top

Answer 90

∫ from a to b of f(x) dx

Question 91

Distance of the origin to the point (x

Answer 91

y

Question 92

Distance between the points (x₁

Answer 92

y₁

Question 93

How are unit vectors on the 3D axes denoted?

Answer 93

i

Question 94

If the vector a = xi + yj + zk makes an angle θ with the positive x-axis

Answer 94

how do you find it?