IB Math Curriculum YEAR 1 & 2
1) Topic 1 Quadratics (Chap 6 IB Math SL book)
A) Review Radicals & Complex Numbers
B) Solving Quadratic Equations
C) Completing the Square
D) Graphing
E) Vertex form
F) Modeling
G) Writing equations
H) Quad-Linear Systems
I) Word Problem Applications
2) Topic 1 Binomial Expansion ( Chap 7 IB Math SL)
3) Topic 2 Functions (Chap1 IB Math SL)
A) Domain & Range
B) Graphs
C) Transformations
D) Composition of Functions
E) Inverse Functions
F) Rational Fn’s & asymptotes
4) Topic 2 Exponential & Logarithmic Functions(Chap 3 and 4)
A) Basic Rules of Exponents
B) Rational exponents
C) Factoring
D) Word problems
E) Exponential Fn
F) Graphing Exp Fn
G) e & ex
H) Compound Interest
I) Logs
J) Properties of Logs
K) Solving exp & log equations
5) Topic 3 Circular Functions and Trig (Chap 8)
A) Right Triangle Trig
B) Area of triangle
C) Area of sector
D) Area of segment
6) Topic 3 Non Right Triangle Functions (Chap 9)
A.)Law of sines
B.)Ambiguous Case
C.)Law of cosines
D.)Navigation
E.)Surveying
7) Topic 3 Graphing TrigFunctions (Chap10)
A) Graphing Trig functions
B) Latitude sine & cosine curve
C) Transformations w/trig fn
D) Inverse Trig fn
8) Topic 3 Solving Trig Equations (Chap10)
A) Solving Trig eq’ns
B) Sine & Cosine Curves
C) Solving more difficult trig Equations usu=ing double angles and identity
D) Trig Models
E) Double Angles
F) Trig identies
9) Topic 1 Series & Sequences ( Chap 2)
A) Definition & notation
B) Arithmetic Sequences & Series
C) Geometric Sequences & Series
D) Applications
10) Topic 1 Linear Equations (Chapter 1 in Advanced Mathematics)
A) Slopes
B) Midpoint
C) Distance
D) Equations of lines
E) Parallel & Perpendicular Lines
11) Topic 4 Vectors ( Chap 12)
A) Add/ Subtract/Scalar
B) Magnitude
C) Midpoint
D) Scalar Product
E) Unit Vector
F) Angles between 2 vectors
12)Topic 4 Lines and Planes in Space ( Chap 13)
A) Equation of a line
B) Applications 2-D & 3-D
C) Parallel, intersecting, coincident, non-intersecting
YEAR 2
13.)Topic 5 Probability & Statistics
{IB Math 2 Start with Statistics}
A) Conditional Probability
B) Venn Diagram
C) Statistical Independence
D) Probability Distribution
E) Expectation of X
F) Discrete Random Variables
G) Binomial distribution
H) Normal Distribution
I) Inverse of standard normal distribution
J) Frequency tables & histograms
K) Vocab
L) Mean, median & mode
M) Variance
N) Standard deviation
O) Quartiles
13.) Topic 6 Limits
A) Properties of limits
B) Evaluating limits analytically
C) Continuity Intermediate Value Thm
D) Infinite limits
14.) Topic 6 Derivatives
A) Limit Process/Tangent Line
B) Basic Differentiation
C) Product Rule
D) Quotient Rule
E) Chain Rule
15.) Topic 6 Applications of Derivatives
A) Extrema
B) Mean Value Thm/ Rolle’s Thm
C) 1st Derivative Test
D) 2nd Derivative Test
E) Limits @ Infinity (review)
F) Curve Sketching
G) Optimization
H) Newton-Raphson Method
I) Linear Approximation
J) Rectilinear Motion
K) Physics Applications
16.) Topic 6 Integration
A) Area
B) Reimann Sums/ Definite Integrals
C) Indefinite Integrals
D) Fundamental Thm of Calculus
E) Integration by substitution (simple)
F) Trapezoidal & Simpson’s Rule (Simpson’s Rule Optional)
17.) Topic 6 Application of Integrals
A) Area between 2 curves
B) Disc Method
C) Washer Method
D) Cross Sectional Area
E) Shell Method (if time)
F) U substitution
18.) Topic 6 Diff & Integrals of Logarithmic & Exponential F’n
A) Natural Log Fn
B) Derivative of ln
C) Integration of ln
D) Inverses
E) Derivative of Exponential fn
F) Integration of Exponential fn
G) Bases other than e (Derivative & Integration)
19.) Review for IB Exam (need at least 3 weeks)
20.) Internal Assessment –An Exploration -6 – 12 page paper
21.) Extra Topics for After IB Exam
A) Related Rates ( Calculus)
B) Shell Methods
C) Integration by Parts
D) Polynomials (Chap 2 in Advanced Mathematics)
E) Long Division
F) Synthetic Division
G) Determining the roots
H) Basic sketches of graphs (rational fn too)
I) Rational Root Theorem