IB SL Math Review
Topic 1&2: Algebra, Functions-
Sequences:
○ Arithmetic = Addition
○ Geometric = multiplication
○ d = the slope
○ Sn = (n/2)u1+un
Quadratic Equations:
y = ax 2 + b x + c y = a( x - h)2 + k, vertex = (h,k )
○ Axis of Symmetry: x = (b)/2a
○ To find y-intercept: plug 0 in for x
○ To find x-intercept: plug 0 in for y
Exponential Growth and Decay:
A = P ( 1 + r)t Basic Growth, Decay or Yearly compound interest
○ A = Current or final amount
○ P = Principal or starting amount
○ r = interest rate
○ t = time
A = P ( 1 + (r)/(n) )nt ompound interest multiple times per year
C
rt rt
A = P e = C e Continuous compounding, or continuous growth, decay
Inverse Functions:
f -1(x) = the inverse of f(x)
○ y = ex ↔
y = ln(x)
2
○ y = x ↔ y = √x
Logs:
○ e and ln are inverses
○ a = bx ↔ y = logba
○ a = ex ↔ x = ln(a) = logea
logA + logB = log(AB)
logA - logB = logA/B
logan = n l og(a)
Binomial Expansion:
(a + b)n = (n)|(r)(a)r(b)n-r = _anb0 + _an-1b1 + _an-2b2 + .... + _a1bn-1 + _a0bn
Pascal’s Triangle
○ Number of terms in the expansion in one more than the exponent given
, Ex. (3 + x)4 has five terms
○ To find the (n)|(r) part on the calculator, type n first, then go to Math⟶PRB⟶nCr and then
type r
○ nCr=(n!)/(n-r)!r!
○ Remember:
1. n = Exponent given on top of the entire equation
2. The two exponents in the set up have to add up to n
3. r can be either the two exponents in the set up
Linear Regressions:
○ Diagnostics and stat plot need to be on while graphing
○ Turn on diagnostics: 2nd⟶0⟶diagnostics on
○ Turn on stat plot: y= ⟶click the stat plot icon
○ Extrapolation- when the values given stretch outside a given range of data
○ Interpolation- when the values given are inside a range of data
○ r is the correlation coefficient
○ The highest r can be is 1(means strong positive correlation)
○ The lowest r can be is -1(means strong negative correlation)
○ Worst correlation is 0
○ To get a linear regression line: Stat⟶Calc⟶LinReg
○ Mean: type values into L1(and maybe L2), then go to Stat⟶Calc⟶1 var stats
Topic 3: Circular Function and Trigonometry-
Sine Equations to Model Table of Values:
y = AsinB( x-C) + D
○ A = Amplitude⟶ (Max - Min)/2
○ B = (2π)/Period
○ C = phase shift or shift left/right
○ D = Vertical shirt and center line⟶ (Max + Min)/2
Trig Intro:
(All Strippers Take Cash)⟶(All Sin Tan Cos)
○ SOH CAH TOA
○ sin2Ө = 2sinӨcosӨ
Topic 1&2: Algebra, Functions-
Sequences:
○ Arithmetic = Addition
○ Geometric = multiplication
○ d = the slope
○ Sn = (n/2)u1+un
Quadratic Equations:
y = ax 2 + b x + c y = a( x - h)2 + k, vertex = (h,k )
○ Axis of Symmetry: x = (b)/2a
○ To find y-intercept: plug 0 in for x
○ To find x-intercept: plug 0 in for y
Exponential Growth and Decay:
A = P ( 1 + r)t Basic Growth, Decay or Yearly compound interest
○ A = Current or final amount
○ P = Principal or starting amount
○ r = interest rate
○ t = time
A = P ( 1 + (r)/(n) )nt ompound interest multiple times per year
C
rt rt
A = P e = C e Continuous compounding, or continuous growth, decay
Inverse Functions:
f -1(x) = the inverse of f(x)
○ y = ex ↔
y = ln(x)
2
○ y = x ↔ y = √x
Logs:
○ e and ln are inverses
○ a = bx ↔ y = logba
○ a = ex ↔ x = ln(a) = logea
logA + logB = log(AB)
logA - logB = logA/B
logan = n l og(a)
Binomial Expansion:
(a + b)n = (n)|(r)(a)r(b)n-r = _anb0 + _an-1b1 + _an-2b2 + .... + _a1bn-1 + _a0bn
Pascal’s Triangle
○ Number of terms in the expansion in one more than the exponent given
, Ex. (3 + x)4 has five terms
○ To find the (n)|(r) part on the calculator, type n first, then go to Math⟶PRB⟶nCr and then
type r
○ nCr=(n!)/(n-r)!r!
○ Remember:
1. n = Exponent given on top of the entire equation
2. The two exponents in the set up have to add up to n
3. r can be either the two exponents in the set up
Linear Regressions:
○ Diagnostics and stat plot need to be on while graphing
○ Turn on diagnostics: 2nd⟶0⟶diagnostics on
○ Turn on stat plot: y= ⟶click the stat plot icon
○ Extrapolation- when the values given stretch outside a given range of data
○ Interpolation- when the values given are inside a range of data
○ r is the correlation coefficient
○ The highest r can be is 1(means strong positive correlation)
○ The lowest r can be is -1(means strong negative correlation)
○ Worst correlation is 0
○ To get a linear regression line: Stat⟶Calc⟶LinReg
○ Mean: type values into L1(and maybe L2), then go to Stat⟶Calc⟶1 var stats
Topic 3: Circular Function and Trigonometry-
Sine Equations to Model Table of Values:
y = AsinB( x-C) + D
○ A = Amplitude⟶ (Max - Min)/2
○ B = (2π)/Period
○ C = phase shift or shift left/right
○ D = Vertical shirt and center line⟶ (Max + Min)/2
Trig Intro:
(All Strippers Take Cash)⟶(All Sin Tan Cos)
○ SOH CAH TOA
○ sin2Ө = 2sinӨcosӨ
