𝜋
𝑟=(
) × 𝑑𝑒𝑔𝑟𝑒𝑒𝑠
180
𝑥 = cos ø
180
𝑑=(
) × 𝑟𝑎𝑑𝑖𝑎𝑛𝑠
𝜋
𝑦 = sin ø
tan ø =
𝒚 = 𝐚𝐬𝐢𝐧 𝒃𝒙 + 𝒄
sin ø
cos ø
𝒚 = 𝐚𝐜𝐨𝐬 𝒃𝒙 + 𝒄
𝑎 = 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒
2𝜋
= 𝑝𝑒𝑟𝑖𝑜𝑑
𝑏
𝑄1 ø = 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑎𝑛𝑔𝑙𝑒
𝑄2 ø = 180 − 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑎𝑛𝑔𝑙𝑒 𝑂𝑅 𝜋 − 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑎𝑛𝑔𝑙𝑒
𝑐 = 𝑚𝑒𝑎𝑛 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
𝑄3 ø = 180 + 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑎𝑛𝑔𝑙𝑒 𝑂𝑅 𝜋 + 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑎𝑛𝑔𝑙𝑒
sin2 ø + cos 2 ø = 1
𝑄4 ø = 360 − 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑎𝑛𝑔𝑙𝑒 𝑂𝑅 2𝜋 − 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑎𝑛𝑔𝑙𝑒
𝒚 = 𝒂 𝐭𝐚𝐧 𝒃𝒙 + 𝒄
𝑝𝑒𝑟𝑖𝑜𝑑 =
𝑎𝑠𝑠𝑦𝑚𝑝𝑡𝑜𝑡𝑒𝑠 =
𝜋
𝑏
( 2𝑘 + 1 𝜋)
, 𝑘 −1,0,1,2
2𝑏
𝜋
sinShortcut
( − ø) = cos ø
Turning Point
2
Quadratic Formula
𝜋
sin (Quadratic
+ ø) = cos
ø
Inequalities
2
𝜋 1. Solve equation
𝑦 = 𝑎𝑥 2 + 𝑏𝑥 +𝜋𝑐 → 𝑎 𝑥 − ℎ 2 + 𝑘
cos ( − ø) = sin ø
cos ( + ø) = −sin ø
2
2 2. Draw graph
𝑎=𝑎
3. Use graph to find
values suiting
𝑏
ℎ=−
inequality
2𝑎
Discriminant
∆= 𝑏 2 − 4𝑎𝑐
< 0  No solutions
= 0  One solution
> 0, perfect square  2x rational
> 0, x perfect square  2x
irrational
Rectangular Hyperbola
𝑦=
𝑎
+𝑘
𝑥−ℎ
Truncus
Square Root Function
𝑦=
𝑎
+𝑘
𝑥−ℎ 2
𝑦 = 𝑎√𝑥 − ℎ + 𝑘
𝑎 + 𝑏 3 = 𝑎3 + 3𝑎2 𝑏 + 3𝑎𝑏 2 + 𝑏 3
𝑎 + 𝑏 4 = 𝑎4 + 4𝑎3 𝑏 + 6𝑎2 𝑏 2 + 4𝑎𝑏 3 + 𝑏 4
Cubic Function of form:
𝑦 =𝑎 𝑥−ℎ 3+𝑘
Point of Inflection:
Index Laws
𝑎𝑚 × 𝑎𝑛 = 𝑎𝑚+𝑛
𝑎𝑚 ÷ 𝑎𝑛 = 𝑎𝑚−𝑛
𝑎−𝑛 =
1
𝑎𝑛
𝑎𝑚 𝑛 = 𝑎𝑚×𝑛
𝑎𝑏 𝑚 = 𝑎𝑚 × 𝑏 𝑚
𝑚
𝑛
𝑎 𝑛 = √𝑎𝑚
𝑎0 = 1
Prime Decomposition
Make all bases prime (when can)
before further calculations.
12𝑛 × 18−2𝑛
3 × 22 𝑛 × 32 × 2 −2𝑛
=
1
33𝑛
Base Rule – make bases same before solving
Graphs of
Exponentials
𝑦 = 𝑎 𝑥−ℎ + 𝑘
Dilations:
Multiplying a by dilation
factor dilates from x axis
Multiplying x by dilation
factor dilated from y
axis
Reflections:
Multiplying a by -1
reflects in x axis
Multiplying x by -1
reflects in y axis
Translations:
Translated h (flip sign)
units horizontal and k
units vertical
Log Laws
𝑎 𝑥 = 𝑦 = log 𝑎 𝑦 = 𝑥
log 𝑎 𝑚 + log 𝑎 𝑛 = log 𝑎 𝑚 × 𝑛
log 𝑎 𝑚 − log 𝑎 𝑛 = log 𝑎 𝑚 ÷ 𝑛
log 𝑎 𝑚𝑝 = 𝑝 log 𝑎 𝑚
log 𝑎 𝑎 = 1
log 𝑎 1 = 0
Log Solving Rule
log 𝑏 𝑐 =
log 𝑎 𝑐
log 𝑎 𝑏
…where a is any base
Log Graphs
𝑦 = log 𝑎 𝑥 − ℎ + 𝑘
Dilations:
Multiplying log by dilation factor
dilates away from x axis
Multiplying x by dilation factor of a
dilates by 1/a away from y axis
Reflections:
Multiplying log by -1 reflects in x
axis
First Principles
Differentiation
𝑓 𝑥+ℎ −𝑓 𝑥
ℎ→0
ℎ
𝑓 ′ 𝑥 = lim
𝑓 𝑥 = 𝑥 𝑛 , 𝑓 ′ 𝑥 = 𝑛𝑥 𝑛−1
Solves to find instantaneous rate of change
(gradient at a point) for a graph, when
coordinates subbed into derivative…
Finding point where tangent makes ø
angle…
𝑚 = tan ø =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑟𝑖𝑠𝑒
=
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑟𝑢𝑛
1. Solve for ø to find the gradient
2. Take gradient and make equal derivative
3. Sub x coordinate found from derivative
into original equation to find y coordinate
Antidifferentiation
𝑥 𝑛 𝑑𝑥 =
𝑥 𝑛+1
+𝑐
𝑛+1
Finds the original equation.
Limits
lim 𝑓 𝑥
𝑥→𝑎
Always factorise first!
Sub a into x to solve once
factorised.
Function is differentiable
if f(x) is continuous at
this point, and a tangent
can be drawn at the
point (the point is not an
endpoint or cusp).
Tangent Line (CAS):
Menu  4  9
Normal Line (CAS):
Menu  4  A
Absolute Maximum
Maximum value of
function over given
domain. May not be a
stationary point, may be
an endpoint of domain.
Absolute Minimum
Minimum value of
function over given
domain. May not be a
stationary point, may be
an endpoint of domain.
Stationary Points
Probability Equations
Independent Events
Pr 𝐴′ = 1 − Pr 𝐴
Events are independent if:
Pr 𝐴 ∪ 𝐵 = Pr 𝐴 + Pr 𝐵 − Pr 𝐴 ∩ 𝐵
Pr 𝐴 ∩ 𝐵 = Pr 𝐴 × Pr 𝐵
Pr 𝐴|𝐵 =
Pr 𝐴 ∩ 𝐵
Pr 𝐵
Pr A|B = Pr A
Pr B|A = Pr B
Pr 𝐴 ∩ 𝐵 = Pr 𝐴|𝐵 × Pr 𝐵
Pr 𝐴 = Pr 𝐴|𝐵 × Pr 𝐵 + Pr 𝐴|𝐵′ × Pr 𝐵′
CAS
binomPDF – Menu 5 5 A
The probability of getting _
(can be blank for distribution
table) successes where
probability of success is _
and number of trials is _.
binomCDF – Menu 5 5 B
The probability of getting _ ,
_ or _ successes where
probability of success is _
and number of trials is _,
with lower and upper
bounds included.
Is a subset of
(within or eqaual
to)