Review Notes for IB Standard Level Math

1 Review Notes for IB Standard Level math 2015, Steve @stevemuenchPlease feel free to share the link to these my worked solutions to the November 2014 my worked solutions to the May 2015 (Timezone 2) any student you believe might benefit from 3, 20151 Contents1 Rules of Basic Operations .. Rules of Roots .. Rules of Exponents .. Sequences and Series .. Arithmetic Sequences and Series .. Sum of Finite Arithmetic Series (u1+ +un) .. Partial Sum of Finite Arithmetic Series (uj+ +un) .. Geometric Sequences and Series .. Sum of Finite Geometric Series .. Sum of Infinite Geometric Series .. Example Involving Sum of Infinite Geometric Series .. Sigma Notation .. Sigma Notation for Arithmetic Series .. Sigma Notation for Geometric Series .. Sigma Notation for Infinite Geometric Series .. Defining Functions Using Sigma Notation .. Applications: Compound Interest.

2 Applications: Population Growth .. Logarithms .. Using Logarithms to Solve Equations .. Using Exponentiation to Solve Equations .. Logarithm Facts Involving 0 and 1 .. Laws of Exponents and Logarithms .. Change of Base .. Powers of Binomials and Pascal s Triangle .. Expansion of (a+b)n.. The Binomial Theorem .. Using The Binomial Theorem for a Single Term .. Example of Using Binomial Theorem .. Solving Systems of Three Linear Equations Using Substitution .. Solving Systems of Three Linear Equations Using Matrix Inverse .. Writing a System of Linear Equations in Matrix Form .. Using Matrix Inverse to Solve System of Three Linear Equations .. 242 Functions and Sets .. Union and Intersection of Sets .. Common Sets of Numbers .. Intervals of Real Numbers .. Concept of Function .. Graph of a Function .. Domain of a Function.

3 Range of a Function .. Composing one Function with Another .. Identity Function .. Inverse Function .. Determining the Inverse Function as Reflection in Liney=x.. Determining the Inverse Function Analytically .. Drawing and Analyzing Graphs with Your Calculator .. Drawing and Zooming Graph .. Finding a Maximum Value in an Interval .. Finding a Minimum Value Value in an Interval .. Finding thex-Intercepts or Zeros of a Graph in an Interval .. Finding they-Intercept of a Graph .. Vertical Asymptotes .. Graphing Vertical Lines .. Horizontal Asymptotes .. Tips to Compute Horizontal Asymptotes of Rational Functions .. Graphing Horizontal Lines .. Symmetry: Odd Functions .. Symmetry: Even Functions .. Solving Equations Graphically .. Transformations of Graphs .. Horizontal and Vertical Translations .. Reflections inx-Axis andy-Axis.

4 Vertical Stretch .. Horizontal Stretch .. Order Matters When Doing Multiple Transformations in Sequence .. Graphing the Result of a Sequence of Transformations .. Determining Where a Particular Point Moves Under a Sequence of Trans-formations .. Quadratic Functions .. Using the Quadratic Formula to Find Zeros of Quadratic Function .. Finding the Vertex If You Know the Zeros .. Graph and Axis of Symmetry .. Computing the Vertex From the Coefficients .. Using the Discriminant to Find the Number of Zeros .. Y Intercept Form .. X Intercept Form .. Binomial Squared Form .. Vertex (h,k) Form .. Reciprocal Functions .. Rational Functions .. Exponential Functions .. Continuously Compounded Interest .. Continuous Growth and Decay .. Logarithmic Functions .. 553 Circular Functions and Understanding Radians .. Represent a Part of a Circular Path.

5 The Fraction of a Complete Revolution an Angle Represents . to Measure an Angle Using Distance .. Distance on the Unit Circle Uniquely Identifies an Angle .. the Fraction of a Complete Revolution for Angle in Radians . Converting Between Radians and Degrees .. from Degrees to Radians .. from Radians to Degrees .. Length of an Arc Subtended by an Angle .. Inscribed and Central Angles that Subtend the Same Arc .. Area of a Sector .. Definition of cos and sin .. Interpreting cos and sin on the Unit Circle .. Radian Angle Measures Can Be Both Positive and Negative .. Remembering the Exact Values of Key Angles on Unit Circle .. The Pythagorean Identity .. Double Angle Identities .. Definition of tan .. Using a Right Triangle to Solve Trigonometric Problems .. Using Right Triangle with an Acute Angle .. Using Right Triangle with an Obtuse Angle.

6 Using Inverse Trigonometric Functions on Your Calculator .. Circular Functions sin, cos, and tan .. The Graph of sinx.. The Graph of cosx.. The Graph of tanx.. Transformations of Circular Functions .. Using Transformation to Highlight Additional Identities .. Determining Period from Minimum and Maximum .. Applications of the sin Function: Tide Example .. Solving Trigonometric Equations in a Finite Interval .. Solving Quadratic Equations in sin, cos, and tan .. Solutions of Right Triangles .. The Cosine Rule .. The Sine Rule .. Area of a Triangle .. 774 Vectors as Displacements in the Plane .. Vectors as Displacements in Three Dimensions .. Terminology: Tip and Tail .. Representation of Vectors .. Magnitude of a Vector .. Multiplication of a Vector by a Scalar .. Negating a Vector .. Sum of Vectors.

7 Difference of Vectors .. Unit Vectors .. Scaling Any Vector to Produce a Parallel Unit Vector .. Position Vectors .. Determining Whether Vectors are Parallel .. Finding Parallel Vector with Certain Fixed Length .. Scalar (or Dot ) Product of Two Vectors .. Perpendicular Vectors .. Base Vectors for Two Dimensions .. Base Vectors for Three Dimensions .. The Angle Between Two Vectors .. Vector Equation of a Line in Two and Three Dimensions .. Vector Equation of Line Passing Through Two Points .. Finding the Cartesian Equation from a Vector Line .. The Angle Between Two Vector Lines .. Distinguishing Between Coincident and Parallel Lines .. Finding the Point of Intersection of Two Lines .. Finding Intersection Between a Line and an Axis .. 925 Concepts .. versus Sample .. Data versus Continuous Data .. Presentation of Data.

8 Distribution Tables .. Histograms with Equal Class Intervals .. Mean .. Median .. Mode .. Cumulative Frequency .. Frequency Table .. Frequency Graphs .. Dispersion .. Range .. and Whiskers Plots .. Deviation .. Use Cumulative Frequency Graph to Find Median and Quartiles .. Computing Statistics Using Your Calculator .. Statistics for a Single List .. Statistics for a List with Frequency .. Linear Correlation of Bivariate Data .. Scatter Diagrams .. Pearson s Product-Moment Correlation Coefficientr.. Lines of Best Fit .. Equation of the Regression Line .. 1046 Probability Concepts .. Probability of an Event .. Probability of an Event s Not Occurring .. Independent, Dependent, and Mutually Exclusive Events .. Probability ofAandBfor Independent Events .. Probability ofAorBfor Mutually Exclusive Events.

9 Probability of Mutually Exclusive Events .. Probability ofAorBfor Non-Mutually Exclusive Events .. Lists and Tables of Outcomes .. Conditional Probability of Dependent Events .. Testing for Independent Events .. Venn Diagrams .. Tree Diagrams .. Probabilities With and Without Replacement .. Discrete Random Variables and Their Probability Distributions .. Explicitly Listed Probabilities .. Probability Distribution Given by a Function .. Explicit Probability Distribution Involving an Unknown .. Expected Value (Mean),E(X) for Discrete Data .. Expected Value for a Fair Game .. Binomial Distribution .. Using the Calculator for Binomial Distribution Problems .. Tip for Calculators WhosebinomCdfDoes Not Have Lower Bound .. Mean and Variance of the Binomial Distribution .. Example of Mean and Variance of Binomial Distribution .. Normal Distribution and Curves.

10 Standardizing Normal Variables to Getz-values (z-scores) .. Using the Calculator for Normal Distribution Problems .. Tip for Calculators WhosenormalCdfDoes Not Have Lower Bound .. Using Inverse Normal Cumulative Density Function .. Determining z Value and from the Probability .. 1207 Overview of Concepts for Differential Calculus .. of Change in Distance .. s Derivative Gives Instantaneous Rate of Change Using TangentLines .. Between Function and Derivative .. of Derivative Concepts .. Equations of Tangents and Normals .. Notation for Derivatives .. Graphing Derivatives with Your Calculator .. Derivatives on the TI-Nspire CX .. Derivatives on the TI-84 Silver Edition .. Computing Derivatives at a Point with Your Calculator .. Derivative at a Point on the TI-NSpire CX .. Derivative at a Point on the TI-84 Silver Edition .. Rules for Computing Derivatives.