C3

Question 1

if y=eˣ, then x = ?

Answer 1

ln(y)

Question 2

ln(a) + ln(b) = ?

Answer 2

ln(ab)

Question 3

ln(a) - ln(b) = ?

Answer 3

ln(a/b)

Question 4

kln(a) = ?

Answer 4

ln(aᵏ)

Question 5

ln(e) = ?

Answer 5

1

Question 6

ln(1) = ?

Answer 6

0

Question 7

ln(eˣ) = ?

Answer 7

x

Question 8

eˡⁿˣ = ?

Answer 8

x

Question 9

lnx is the inverse of ?

Answer 9

eˣ

Question 10

eˣ is the inverse of ?

Answer 10

lnx

Question 11

How do you display the root of two lines?

Answer 11

Intersection

Question 12

How do you show that a root lies between 4 & 5?

Answer 12

input x=4 into f(x)
input x=5 into f(x)
if there is a sign change then root lies between the two values of x

Question 13

What form must equations be in for iteration?

Answer 13

x =

Question 14

What value should you first input into iteration?

Answer 14

lowest value of restriction range

Question 15

How should you treat reflections?

Answer 15

As stretches

Question 16

If stretches & translations are in different axes, then the order ____ ?

Answer 16

Doesn’t matter

Question 17

If stretches & translations are both in the y axes, then the order ____ ?

Answer 17

Stretch, then translate

Question 18

If stretches & translations are both in the x axes, then the order ____ ?

Answer 18

Translate, then stretch

Question 19

when does |x|= x?

Answer 19

when x≥0

Question 20

when does |x| = -x?

Answer 20

when x≤0

Question 21

If |x| = k, then x = ?

Answer 21

x = ±k

Question 22

If |x| = |y| then x² =, x = ?

Answer 22

x² = y², x = ±y

Question 23

Restrictions when |x| ≤ k

Answer 23

-k ≤ x ≤ k

Question 24

Restrictions when |x| ≥ k

Answer 24

x ≥ k or x ≤ -k

Question 25

If |𝓍| ≤ |y|, then 𝓍² ____ ?

Answer 25

𝓍² ≤ y²

Question 26

y = eˣ, dy/d𝓍 = ?

Answer 26

dy/d𝓍 = eˣ

Question 27

y = eᶠ⁽ˣ⁾, dy/d𝓍 = ?

Answer 27

dy/d𝓍 = f'(𝓍)eᶠ⁽ˣ⁾

Question 28

y = ln𝓍, dy/d𝓍 = ?

Answer 28

dy/d𝓍 = 1/x

Question 29

y = ln(f(𝓍)), dy/d𝓍 = ?

Answer 29

dy/d𝓍 = f'(x)/f(x)

Question 30

y = [f(𝓍)]ⁿ, dy/d𝓍 = ?

Answer 30

dy/d𝓍 = nf'(x)[f(x)]ⁿ⁻¹

Question 31

If y = u⋅v, then dy/d𝓍 = ?

Answer 31

dy/d𝓍 = vu' + uv'

Question 32

If y = u/v, then dy/d𝓍 = ?

Answer 32

dy/d𝓍 = (vu' - uv')/v²

Question 33

dy/d𝓍 x d𝓍/dy = ?

Answer 33

1

Question 34

d𝓍/dy = ?

Answer 34

1/(dy/d𝓍)

Question 35

cosec𝓍 = ?

Answer 35

1/sin𝓍

Question 36

sec𝓍 = ?

Answer 36

1/cos𝓍

Question 37

cot𝓍 = ?

Answer 37

1/tan𝓍 = cos𝓍/sin𝓍

Question 38

CAST = ?

Answer 38

C - only cosine is positive (270-360) (repeats at 360-α) A - All trig are positive (0-90) S - only sine is positive (90-180) (repeats at 180-α) T - only tan is positive (180-270) (repeats at 180+α)

Question 39

sin(A+B) = ?

Answer 39

sinAcosB + cosAsinB

Question 40

sin(A-B) = ?

Answer 40

sinAcosB - cosAsinB

Question 41

cos(A+B) = ?

Answer 41

cosAcosB - sinAsinB

Question 42

cos(A-B) = ?

Answer 42

cosAcosB + sinAsinB

Question 43

tan(A+B) = ?

Answer 43

(tanA + tanB)/(1 - tanAtanB)

Question 44

tan(A-B) = ?

Answer 44

(tanA - tanB)/(1 + tanAtanB)

Question 45

sin2A = ?

Answer 45

2sinAcosA

Question 46

cos2A = ?

Answer 46

= cos²A - sin²A = 1 - 2sin²A = 2cos²A - 1

Question 47

tan2A = ?

Answer 47

2tanA/(1 - tan²A)

Question 48

sin4A = ?

Answer 48

2sin2Acos2A

Question 49

asinθ + bcosθ can also be written as?

Answer 49

Rsin(θ±α) or Rcos(θ±α)

Question 50

How do you write in the form Rcos(θ±α) from | Acos𝓍 - Bsin𝓍?

Answer 50

``` Equate cos𝓍 & sin𝓍 terms so Rcosα = A & Rsinα = B ∴ tanα = B/A R² = A² + B² R = √(A² + B²) ```

Question 51

What does R give?

Answer 51

max/min value

Question 52

tanA = ?

Answer 52

sinA/cosA

Question 53

sin²A + cos²A = ?

Answer 53

1

Question 54

secA = ?

Answer 54

1/cosA

Question 55

cosecA = ?

Answer 55

1/sinA

Question 56

cotA = ?

Answer 56

1/tanA = cosA/sinA

Question 57

cosec²A = ?

Answer 57

1 + cot²A

Question 58

sec²A = ?

Answer 58

tan²A + 1

Question 59

∫eᶠ⁽ˣ⁾ d𝓍 = ?

Answer 59

eᶠ⁽ˣ⁾/f'(𝓍) + c

Question 60

∫1/𝓍 d𝓍 = ?

Answer 60

ln|𝓍| + c

Question 61

Reverse chain rule only works for?

Answer 61

Linear functions inside bracket

Question 62

∫(a𝓍 + b)ⁿ d𝓍 = ?

Answer 62

1/(a(n+1) ⋅ (a𝓍 + b)ⁿ⁺¹ + c

Question 63

∫f'(𝓍)/f(𝓍) d𝓍 = ?

Answer 63

ln|f(𝓍)| + c

Question 64

∫n⋅f'(𝓍)/f(𝓍) d𝓍 = ?

Answer 64

n⋅ln|f(𝓍)| + c

Question 65

Volume of revolution around the 𝓍 - axis?

Answer 65

Vₓ = π ᵇ∫ₐ [f(𝓍)]²

Question 66

Volume of revolution around the y - axis?

Answer 66

Vᵧ = π ᵇ∫ₐ [g(y)]²

Question 67

Volume of revolution between two curves?

Answer 67

Vₓ = π ᵇ∫ₐ [f(𝓍)]² - π ᵇ∫ₐ [g(𝓍)]²

Question 68

Define: 𝓍∈R

Answer 68

𝓍 belongs to the set of real numbers

Question 69

When are functions one-to-one?

Answer 69

When each member of 𝓍 maps to only one member of y

Question 70

How to find the vertex of a graph?

Answer 70

Complete the square | min/max point @ (-p,q)

Question 71

Properties of Inverse functions

Answer 71

reflections in y=𝓍 | only one-to-one functions have an inverse