Unit Dates

IB Mathematics SL Topics

California Content Standards

Chapter 1

Chapter 1 Number Patterns
1.1 Real Numbers, Relations,

and Functions
1.2 Mathematical Patterns
1.3 Arithmetic Sequences
1.4 Lines
1.5 Linear Models
1.6 Geometric Sequences

can do calculus: Infinite Geometric Series

Algebra

1.1

· Arithmetic Sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.

Sigma notation
Examples of applications, compound interest and population growth

Functions and Equations

2.1

Concept of function : domain, range; image (value).

Algebra II

22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.

23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series.

Unit Dates	Unit Dates	IB Mathematics SL Topics	California Content Standards
Chapter 2	Chapter 2 Equations and Inequalities 2.1 Solving Equations Graphically 2.2 Solving Quadratic Equations Algebraically 2.3 Applications of Equations 2.4 Other Types of Equations 2.5 Inequalities	Functions and Equations 2.2 · The graph of a functions’ its equation y = f (x). Function graphing skills: Use of a GDC to graph a variety of functions; investigation of key features of graphs. Solution of equations graphically. 2.6 The solution of The quadratic formula. Use of the discriminant	Algebra II 8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.
Unit Dates	Topics	IB Mathematics SL Topics	California Content Standards
Chapter 3	Chapter 3 Functions and Graphs 3.1 Functions 3.2 Graphs of Functions 3.3 Quadratic Functions 3.4 Graphs and Transformations 3.5 Operations on Functions 3.6 Inverse Functions 3.7 Rates of Change *can do calculus:* Instantaneous Rates of Change	Functions and Equations 2.1 Composite functions Identity Function Inverse Function 2.3 Transformations of graphs: translations; stretches; reflections in the axes. The graph of as the reflection in the line y = x of the graph of . 2.4 The reciprocal function : its graphs’ its self-inverse nature. 2.5 (Rational coefficients only) The quadratic function : its graph, y-intercept (0, c). Axis of symmetry . The form : vertex (h, k) The form : x-intercepts (p, 0) and (q, 0)	Algebra II 9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a (x-b) 2 + c. 10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function. 24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.

Unit Dates	Topics	IB Mathematics SL Topics	California Content Standards
Chapter 4	Chapter 4 Polynomial and Rational Functions 4.1 Polynomial Functions 4.2 Real Zeros 4.3 Graphs of Polynomial Functions 4.4 Rational Functions 4.5 Complex Numbers 4.6 The Fundamental Theorem of Algebra *can do calculus:* Optimization Applications	Algebra 1.3 The binomial theorem: expansion of (Missing in textbook)	Algebra II 3.0 Students are adept at operations on polynomials, including long division. 4.0 Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. 5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane. 6.0 Students add, subtract, multiply, and divide complex numbers. 7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator. Mathematical Analysis 4.0 Students know the statement of, and can apply, the fundamental theorem of algebra. 6.0 Students find the roots and poles of a rational function and can graph the function and locate its asymptotes.
Unit Dates	Topics	IB Mathematics SL Topics	California Content Standards
Chapter 5	Chapter 5 Exponential and Logarithmic Functions 5.1 Radicals and Rational Exponents 5.2 Exponential Functions 5.3 Applications of Exponential Functions 5.4 Common and Natural Logarithmic Functions 5.5 Properties and Laws of Logarithms 5.6 Solving Exponential and Logarithmic Equations 5.7 Exponential, Logarithmic, and Other Models *can do calculus:* Tangents to Exponential Functions	Algebra 1.2 Exponents and Logarithms Laws of Exponents Laws of Logarithms Change of Base Functions and Equations 2.7 · The function: The inverse function Graphs of and Solution of using logarithms 2.8 The exponential function The logarithmic function Examples of applications: compound interest, growth and decay.	Algebra II 11.0 Students prove simple laws of logarithms. 11.1 Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 11.2 Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step. 12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. 13.0 Students use the definition of logarithms to translate between logarithms in any base. 14.0 Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.
Unit Dates	Topics	IB Mathematics SL Topics	California Content Standards
Chapter 6	Chapter 6 Trigonometry 6.1 Right-Triangle Trigonometry 6.2 Trigonometric Applications 6.3 Angles and Radian Measure 6.4 Trigonometric Functions 6.5 Basic Trigonometric Identities *can do calculus:* Optimization with Trigonometry	Circular Functions and Trigonometry 3.1 The circle: radian measure of angles Length of an arc Area of a sector Radian measure may be expressed as multiples of or decimals. 3.2 Definition of and in terms of the unit circle. Given , finding possible values of without finding Definition of as Lines through the origin can be expressed as , with gradient . The identity	Trigonometry 1.0 Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians. 2.0 Students know the definition of sine and cosine as y- and x- coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions. 3.0 Students know the identity cos2 (x) + sin2 (x) = 1: 3.1 Students prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, conversely, they can prove the Pythagorean theorem as a consequence of this identity). 3.2 Students prove other trigonometric identities and simplify others by using the identity cos2 (x) + sin2 (x) = 1. For example, students use this identity to prove that sec2 (x) = tan2 (x) + 1. 9.0 Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.

Unit Dates

Topics

IB Mathematics SL Topics

California Content Standards

Chapter 7

Chapter 7 Trigonometric Graphs
7.1 Graphs of the Sine, Cosine, and Tangent Functions
7.2 Graphs of the Cosecant, Secant, and Cotangent Functions
7.3 Periodic Graphs and Amplitude
7.4 Periodic Graphs and Phase Shifts
can do calculus: Approximations with Infinite Series

Circular Functions and Trigonometry

3.4

The circular functions , and : their domains and ranges; their periodic nature; and their graphs.
Composite functions of the form
Examples of applications: heights of tide, Ferris Wheel.

Trigonometry

4.0 Students graph functions of the form f(t) = A sin ( Bt + C ) or f(t) = A cos ( Bt + C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.

5.0 Students know the definitions of the tangent and cotangent functions and can graph them.

6.0 Students know the definitions of the secant and cosecant functions and can graph them.

Unit Dates

Topics

IB Mathematics SL Topics

California Content Standards

Chapter 8

Chapter 8 Solving Trigonometric Equations
8.1 Graphical Solutions to Trigonometric Equations
8.2 Inverse Trigonometric Functions
8.3 Algebraic Solutions of Trigonometric Equations
8.4 Simple Harmonic Motion and Modeling
can do calculus: Limits of Trigonometric Functions

Circular Functions and Trigonometry

3.5

· Solution of trigonometric equations in a finite interval.

Equations of the type .
Equations leading to quadratic equations in, for example, sin x.
Graphical interpretation of the above.

Trigonometry

8.0 Students know the definitions of the inverse trigonometric functions and can graph the functions.

19.0 Students are adept at using trigonometry in a variety of applications and word problems.

9.0 Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.

Unit Dates

Topics

IB Mathematics SL Topics

California Content Standards

Chapter 9

Chapter 9 Trigonometric Identities and Proof
9.1 Identities and Proofs
9.2 Addition and Subtraction Identities
9.3 Other Identities
9.4 Using Trigonometric Identities
can do calculus: Rates of Change in Trigonometry

Circular Functions and Trigonometry

3.3

Double angle formulae: ;

Double angle formulae can be established by simple geometrical diagrams and /or by use of GDC.

Trigonometry

10.0 Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs and can use those formulas to prove and/ or simplify other trigonometric identities.

11.0 Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines and can use those formulas to prove and/ or simplify other trigonometric identities.

Unit Dates

Topics

IB Mathematics SL Topics

California Content Standards

Chapter 10

Chapter 10 Trigonometric Applications
10.1 The Law of Cosines
10.2 The Law of Sines
10.3 The Complex Plane and Polar Form for Complex Numbers
10.4 DeMoivre’s Theorem and nth Roots of Complex Numbers
10.5 Vectors in the Plane
10.6 Applications of Vectors in the Plane
can do calculus: Euler’s Formula

Circular Functions and Trigonometry

3.6

· Solution of triangles.

The cosine rule:
The sine rule:
Area of a triangle as

· Appreciation of Pythagoras’ Theorem as a special case of the cosine rule.

The ambiguous case of the sine rule.
Applications to problems in real-life situations, such as navigation.

Vectors

5.1

Vectors as displacements in the plane and in three dimensions.

Components of a vector; column representation.

Algebraic and geometric approaches to the following topics:

The sum and difference to two vectors; the zero vector, the vector –v ; multiplication by a sclar, kv; magnitude of a vector, ; unit vectors; base vectors i, j, and k; position vectors .

5.2

The scalar product of two vectors

;

Perpendicular vectors; parallel vectors

The angle between two vectors.

5.3

Representation of a line as r = a + tb.

The Angle between two lines

5.4

Distinguish between coincident and parallel lines.

Finding points where lines interesects

(Note: This textbook only covers two-dimensional vectors. Therefore vectors are represented as i and j. )

Trigonometry

12.0 Students use trigonometry to determine unknown sides or angles in right triangles.

13.0 Students know the law of sines and the law of cosines and apply those laws to solve problems.

14.0 Students determine the area of a triangle, given one angle and the two adjacent sides.

15.0 Students are familiar with polar coordinates. In particular, they can determine polar coordinates of a point given in rectangular coordinates and vice versa.

16.0 Students represent equations given in rectangular coordinates in terms of polar coordinates.

17.0 Students are familiar with complex numbers. They can represent a complex number in polar form and know how to multiply complex numbers in their polar form.

18.0 Students know DeMoivre's theorem and can give n th roots of a complex number given in polar form.

Mathematical Analysis

1.0 Students are familiar with, and can apply, polar coordinates and vectors in the plane. In particular, they can translate between polar and rectangular coordinates and can interpret polar coordinates and vectors graphically.

2.0 Students are adept at the arithmetic of complex numbers. They can use the trigonometric form of complex numbers and understand that a function of a complex variable can be viewed as a function of two real variables. They know the proof of DeMoivre's theorem.

Linear Algebra

7.0 Students demonstrate an understanding of the geometric interpretation of vectors and vector addition (by means of parallelograms) in the plane and in three-dimensional space.

12.0 Students compute the scalar (dot) product of two vectors in n- dimensional space and know that perpendicular vectors have zero dot product.

Unit Dates

Topics

IB Mathematics SL Topics

California Content Standards

Chapter 11

Chapter 11 Analytic Geometry
11.1 Ellipses
11.2 Hyperbolas
11.3 Parabolas
11.4 Translations and Rotations of Conics
11.5 Polar Coordinates
11.6 Polar Equations of Conics
11.7 Plane Curves and Parametric Equations
can do calculus: Arc Length of a Polar Graph

Mathematical Analysis

5.0 Students are familiar with conic sections, both analytically and geometrically:

5.1 Students can take a quadratic equation in two variables; put it in standard form by completing the square and using rotations and translations, if necessary; determine what type of conic section the equation represents; and determine its geometric components (foci, asymptotes, and so forth).

5.2 Students can take a geometric description of a conic section - for example, the locus of points whose sum of its distances from (1, 0) and (-1, 0) is 6 - and derive a quadratic equation representing it.

Unit Dates

Topics

IB Mathematics SL Topics

California Content Standards

Chapter 12

Chapter 12 Systems and Matrices
12.1 Solving Systems of Equations
12.2 Matrices
12.3 Matrix Operations
12.4 Matrix Methods for Square Systems
12.5 Nonlinear Systems
can do calculus: Partial Fractions

Matrices

4.1

Definition of a matrix: the terms “elements”, “row”, “column” and “order”.

4.2

· Algebra of matrices: equality; addition; subtraction; multiplication by a scalar.

Multiplication of matrices.
Identity and zero matrices.

4.3 (Missing in textbook)

Determinant of a square matrix.
Calculation of 2X2 and 3x3 determinants.
Inverse o f a 2X2 matrix.
Conditions for the existence of the inverse of a matrix.
Elementary treatment only.
Obtaining the inverse of a 3X3 matrix using a GDC.

4.4

Solution of systems of linear equation using inverse matrices (a maximum of three equations in three unknowns).

Only systems with a unique solution need be considered.

Linear Algebra

3.0 Students reduce rectangular matrices to row echelon form.

4.0 Students perform addition on matrices and vectors.

5.0 Students perform matrix multiplication and multiply vectors by matrices and by scalars.

9.0 Students demonstrate an understanding of the notion of the inverse to a square matrix and apply that concept to solve systems of linear equations.

10.0 Students compute the determinants of 2 x 2 and 3 x 3 matrices and are familiar with their geometric interpretations as the area and volume of the parallelepipeds spanned by the images under the matrices of the standard basis vectors in two-dimensional and three-dimensional spaces.

11.0 Students know that a square matrix is invertible if, and only if, its determinant is nonzero. They can compute the inverse to 2 x 2 and 3 x 3 matrices using row reduction methods or Cramer's rule.

Unit Dates

Topics

IB Mathematics SL Topics

California Content Standards

Chapter 13

Chapter 13 Statistics and Probability
13.1 Basic Statistics
13.2 Measures of Center and Spread
13.3 Basic Probability
13.4 Determining Probabilities
13.5 Normal Distributions
can do calculus: Area Under a Curve

Statistics and Probability

6.1

Concepts of populations, sample, random sample and frequency distribution of discrete and continuous data.

6.2

· Presentation of data: frequency tables and diagrams, box and whisker plots.

· Grouped data:

· mid-interval values. Interval width. Upper and lower interval boundaries, frequency histograms.

· A frequency histogram uses equal class intervals.

· Treatment of both continuous and discrete data.

6.3

Mean, median, mode; quartiles, percentiles.

Range; interquartile range; variance; standard deviation.

6.4

Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles.

6.5

Concepts of trial, outcome, equally likely outcomes, sample space (U) and event.

The probability of an event A as

The complementary events A and A’ (not A);

P(A) +P(A’) = 1.

6.6

Combined events, the formula:

for mutually exclusive events.

6.7

Conditional probability; the definition .

Independent events; the definition

6.8

Use of Venn diagrams, tree diagrams and tables of outcomes to solve problems.

6.9

Concept of discrete random variables and their probability distributions.
Expected value (mean), E(X) for discrete data.

6.10

Binomial distribution.
Mean of the binomial distribution.

6.11

Normal distribution.
Properties of the normal distribution.
Standardization of normal variables.

Statistics and Probability

1.0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.

2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.

3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.

4.0 Students are familiar with the standard distributions (normal, binomial, and exponential) and can use them to solve for events in problems in which the distribution belongs to those families.

5.0 Students determine the mean and the standard deviation of a normally distributed random variable.

6.0 Students know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations.

7.0 Students compute the variance and the standard deviation of a distribution of data.

8.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.

Unit Dates

Topics

IB Mathematics SL Topics

California Content Standards

Chapter 14

Chapter 14 Limits and Continuity
14.1 Limits of Functions
14.2 Properties of Limits
14.3 The Formal Definition of Limit (Optional)
14.4 Continuity
14.5 Limits Involving Infinity
can do calculus: Riemann Sums

Calculus

7.1 Informal ideas of limit and convergence.

(Textbook is missing most IB Calculus Topics)