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Math - Year 12 > Extension > Flashcards

Extension Flashcards

1
Q

What is column vector notation?

A

Representation of a vector in the form (a
b)

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2
Q

When is maximum height reached?

A

When the projectile’s vertical velocity is 0

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3
Q

What is component form?

A

Representation of a vector in the form xi + yj

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4
Q

What proves if vectors are parallel?

A

u . v = +/- |u||v|

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5
Q

What is the horizontal equation of acceleration?

A

ẍ = 0

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6
Q

What is the horizontal equation of velocity?

A

ẋ = Vcosθ

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7
Q

What is the horizontal equation of displacement?

A

x = Vtcosθ

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8
Q

What is the vertical equation of acceleration?

A

ÿ = -g

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9
Q

What is the vertical equation of velocity?

A

ẏ = -gt + Vsinθ

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10
Q

What is the vertical equation of displacement?

A

y = -1/2gt^2 + Vtsinθ + h

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11
Q

What can (x,y) for vectors also be written as?

A

(Vcosθ, Vsinθ)

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12
Q

What is the equation for the acceleration vector?

A

a = -gj

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13
Q

What is the equation for the velocity vector?

A

v = Vcosθi + (-gt + Vsinθ)j

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14
Q

What is the equation for the displacement vector?

A

r = Vtcosθi + (-1/2gt^2 + Vtsinθ + h)j

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15
Q

How do you find time of flight?

A

Let vertical component (j) of r(t) equal 0 then solve for t

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16
Q

How do you find the range of flight?

A

Substitute time of flight into the horizontal component (i) of r(t)

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17
Q

How do you find the maximum height of a projectile using time of flight?

A

Half the time of flight and substitute into the j component of r(t)

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18
Q

How do you find the maximum height of a projectile using velocity?

A

Let the vertical component (j) of v(t) equal 0 then solve t and sub into r(t)

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19
Q

What is the formula to find a unit vector?

A

1/|a| x a

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20
Q

What is the projection of a onto b?

A

projba = a . b / |a|^2 X a

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21
Q

How do you find the Cartesian equation of vector displacement?

A

Rearrange x to get t on its own and then sub in y
Make sure final equation only has tan

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22
Q

How do you find the maximum range?

A

Change θ but not velocity

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23
Q

What degree gives the maximum range?

A

45

24
Q

How do you find speed?

A

|V(t)|

25
Q

What is the angle of projection for horizontal or waterfall?

A

0

26
Q

What is the relationship between f(x) and g(x) when they are inverse?

A

f(x) = 1/g’(x)

27
Q

What is the shape of cos^-1 graph?

A

Starts at (-1,π) passes through π/2 and ends at (1,0)

28
Q

What is the shape of sin^-1 graph?

A

Starts at (-1,-π/2) passes through the origin and ends at (1,π/2)

29
Q

What is the shape of tan^-1 graph?

A

Sideway tan function which starts in the negative y, passes through the origin and finishes in the positive asymptotes at y=+/-π/2

30
Q

How do you calculate the volume of a graph rotated around the y axis?

A

π ∫x^2 dy

31
Q

How do you calculate the volume of a graph rotated around the x axis?

A

π ∫y^2 dx

32
Q

When do you permutations?

A

When order matters

33
Q

What do you do if there are repetitions in a permutation?

A

n!/r!
n - number of items
r - number of repetition

34
Q

How do you calculate a circle arrangement?

A

(n-1)!

35
Q

How do you calculate a bracelet or necklace arrangement?

A

(n-1)!/2

36
Q

When do you use combinations?

A

When order doesn’t matter

37
Q

What is the pigeonhole principle statement?

A

By the pigeonhole principle…

38
Q

What should be stated at the beginning of a pigeonhole principle question?

A

Let the … be pigeons and the … pigeonholes

39
Q

What is the pigeonhole principle?

A

If there are n pigeons in k pigeonholes at least one of the holes contain n/k or more pigeons

40
Q

How do you calculate the smallest number needed using the pigeonhole principle?

A

n=mk+1

41
Q

Rules for square root function graphing?

A
  • Does not exist in y < 0
  • Has the same x intercepts
  • New graph under old when y > 1
  • New graph intercepts at y = 1
  • New graph above the old when y < 1
42
Q

Rules for reciprocal functions graphing?

A
  • x intercepts give vertical asymptotes
  • Intersect at y=+/- 1
  • When y > 1 inverse is <1
  • When y < 1 inverse is >1
  • When original increases inverse decreases and vice versa
43
Q

Rules for y =|f(x)| graphing?

A
  • When f(x) > 0 graph is same as y=f(x)
  • When f(x) < 0 y-values are made positive
44
Q

Rules for y = f(|x|) graphing?

A
  • When x > 0 the graph is the same
  • When x < 0 graph on right hand side reflected across the y-axis
45
Q

Rules for y^2 function graphing?

A

Same as square root but also reflected in the x-axis

46
Q

Rules for y = f(|x|) graphing?

A
  • When x > 0 the graph is the same
  • When x < 0 graph on right hand side reflected across the y-axis
47
Q

What is E(p^)?

A

p

48
Q

What is Var(p^)?

A

p(1-p)/n

49
Q

a^2+b^2+g^2

A

(a+b+g)^2-(ab+ag+bg)

50
Q

What is an even function?

A

f(x) = f(-x)

51
Q

What is an odd function?

A

-f(x) = f(-x)

51
Q

Rules for y^2 function graphing?

A

Same as square root but also reflected in the x-axis

51
Q

Rules for square root function graphing?

A
  • Does not exist in y < 0
  • Has the same x intercepts
  • New graph under old when y > 1
  • New graph intercepts at y = 1
  • New graph above the old when y < 1
51
Q

Rules for reciprocal functions graphing?

A
  • x intercepts give vertical asymptotes
  • Intersect at y=+/- 1
  • When y > 1 inverse is <1
  • When y < 1 inverse is >1
  • When original increases inverse decreases and vice versa
52
Q

Rules for y =|f(x)| graphing?

A
  • When f(x) > 0 graph is same as y=f(x)
  • When f(x) < 0 y-values are made positive
53
Q

What is the formula for the dm/dt for water concentration?

A

Concentration pumped in x volume rate pump in - concentration pump out x volume rate pumped out

kg/L x L/h - m/V x L/h

Math - Year 12 (2 decks)

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