Schedule for Topics #1 & #2 (Algebra and Functions)
IB Mathematics HL Year 1 (Examination 2007)
Topic 1/2 - Algebra integrated Functions and Equations
(A) List of Topics and Content to be Taught
| Topic | Objective | Content | Teaching Emphasis |
| 1 | 1.1 - Sequences and Series | 1.1 - Arithmetic Sequences and Series and Sigma Notation | concepts, graphs, formulas, applications |
| 1.2 - Geometric Sequences and Series and Sigma Notation | concepts, graphs, formulas, applications | ||
| 1.3 - Applications of Sequences & Series | financial applications, population growth | ||
|
2 |
1.2 - Exponents |
2.1 - Exponent Laws and zero, negative, rational exponents; notations | algebra focus, simplifying, numerical evaluations |
| 2.2 - Exponential Eqns | algebra and graphing | ||
| 2.3 - Applications | word problems | ||
| 3 | 1.2 - Logarithms | 3.1 - Introduction to Logarithms | Notation, numerical evaluation, conversion (l <=> e) |
| 3.2 - Laws of Logarithms | algebra focus, computation | ||
| 3.3 - Solving Equations | algebra, computation, exponential eqns, applications | ||
| 3.4 - Applications of Logarithms | applications, algebraic computations | ||
| 4 | 1.2 - Natural Logarithms | 4.1 - The number e and its applications and the natural logarithm | concept, computation, applications |
| 4.2 - Natural Logarithms, Laws and Equations | |||
| 4.3 - Applications of Natural Logarithms and e | problem solving focus | ||
| 5 | 2.1 - Function Concepts | 5.1 - Function Concepts | |
| 6 | 2.2 - Graphs of Functions | 6.1 - Exponential and Logarithmic Functions (2.7 & 2.8 in Syllabus) | |
| 6.2 - Inverse and Composite Functions | |||
| 6.3 - Reciprocal Functions (2.3 & 2.4 in Syllabus) | |||
| 6.4 - Inverse functions (2.3 in Syllabus) | |||
| 6.5 - Absolute Value Functions (2.3 in Syllabus) | |||
| 7 | 2.5 - Quadratic Functions | 7.1 - Graphs of Quadratic Functions - roots, axis of symmetry, domain, vertex | |
| 7.2 - Forms of Quadratic Equations - Factored and Vertex Form | |||
| 7.3 - Solving Quadratic Equations (2.6 in Syllabus) | |||
| 7.4 - Discriminants (2.6 in Syllabus) | |||
| 8 | 2.6 - Transformations of Functions | 8.1 - Stretches, Translations, Reflections | |
| 8.2 - Inverses as Reflections | |||
| 9 | 2.7 - Complex numbers | 9.1 - Introduction to Complex numbers | |
| 9.2 - Cartesian Form of Complex Numbers | |||
| 9.3 - Modulus-Argument form of Complex Numbers | |||
| 9.4 - Operations with Complex Numbers (+,-,x,/) (1.6 in Syllabus) | |||
| 9.5 - The Complex Plane | |||
| 10 | 1.7 - Complex Numbers | 10.1 - De Moivre's theorem | |
| 10.2 - Powers and Roots of a Complex Numbers | |||
| 11 | 1.8 - Complex Numbers | 11.1 - Roots of Polynomial Equations | |
| 12 | 2.10 - Polynomial Functions | 12.1 - Polynomial Functions | |
| 12.2 - Remainder Theorem and Factor Theorem | |||
| 13 | 2.9 - Inequalities | 13.1 - Inequalities in one variable |
things already done or things need to review:
| 1.3a | Binomial Expansion | LATER ON IN THE COURSE |
|
| 1.3b | Counting Principles | Already done but needs to be reviewed later on | |
| 1.4 | Proof by Induction | LATER ON IN THE COURSE |
timing/Pacing ==> recommend 20+26 hours ==> 46 hours which is 35 80 minute classes
(B) Tentative Schedule for Math Methods, SL, Year 1
| Feb 6
L56 1.1 - Arithmetic Sequences and Series and Sigma Notation |
Feb 7 | Feb 8
L57 1.2 - Geometric Sequences and Series and Sigma Notation |
Feb 9 | Feb 10
L58 1.3 - Applications of Sequences & Series |
| Feb 13
L59 2.1 - Exponent Laws and zero, negative, rational exponents; notations |
Feb 14 | Feb 15
L60 Topic 5 Exam |
Feb 16 | Feb 17
L61 2.2 - Exponential Eqns |
| Feb 20
L62 2.3 - Applications of Exponents |
Feb 21 | Feb 22
L63 3.1 - Introduction to Logarithms |
Feb 23 | Feb 24
L64 3.2 - Laws of Logarithms |
| Feb 27
L65 3.3 - Solving Equations |
Feb 28 | Mar 1
L66 3.4 - Applications of Logarithms |
Mar 2 | Mar 3
Holiday |
| Mar 6
Holiday |
Mar 7 | Mar 8
L67 4.1 - The number e and its applications and the natural logarithm |
Mar 9 | Mar 10
L68 4.2 - Natural Logarithms, Laws and Equations 4.3 - Applications of Natural Logarithms and e |
| Mar 13
L69 5.1 - Function Concepts |
Mar 14 | Mar 15
L70 6.1 - Exponential and Logarithmic Functions (2.7 & 2.8 in Syllabus) |
Mar 16 | Mar 17
L71 6.2 - Inverse and Composite Functions |
| Mar 20
L72 6.3 - Reciprocal Functions |
Mar 21 | Mar 22
L73 6.4 - Inverse functions |
Mar 23 | Mar 24
L74 6.5 - Absolute Value Functions |
| Mar 27
L75 7.1 - Graphs of Quadratic Functions - roots, axis of symmetry, domain, vertex |
Mar 28 | Mar 29
L76 7.2 - Forms of Quadratic Equations - Factored and Vertex Form |
Mar 30 | Mar 31
L77 7.3 - Solving Quadratic Equations 7.4 - Discriminants |
| Apr 3
L78 8.1 - Stretches, Translations, Reflections |
Apr 4 | Apr 5
L79 8.2 - Inverses as Reflections |
Apr 6 | Apr 7
L80 9.1 - Introduction to Complex numbers 9.2 - Cartesian Form of Complex Numbers 9.5 - The Complex Plane 11.1 - Roots of Polynomial Equations |
| Apr 10
L81 9.1 - Introduction to Complex numbers 9.2 - Cartesian Form of Complex Numbers 9.5 - The Complex Plane 11.1 - Roots of Polynomial Equations |
Apr 11 | Apr 12
L82 9.4 - Operations with Complex Numbers (+,-,x,/) (1.6 in Syllabus) |
Apr 13
Holiday |
Apr 14
Holiday |
| Apr 17
Holiday |
Apr 18
Holiday |
Apr 19
Holiday |
Apr 20
Holiday |
Apr 21
Holiday |
| Apr 24
L83 9.3 - Modulus-Argument form of Complex Numbers |
Apr 25 | Apr 26
L84 9.3 - Modulus-Argument form of Complex Numbers |
Apr 27 | Apr 28
L85 10.1 - De Moivre's theorem |
| May 1
L86 10.2 - Powers and Roots of a Complex Numbers |
May 2 | May 3
L87 12.1 - Polynomial Functions |
May 4 | May 5
L88 12.2 - Remainder Theorem and Factor Theorem |
| May 8
L89 12.2 - Remainder Theorem and Factor Theorem |
May 9 | May 10
L90 13.1 - Inequalities in one variable |
May 11 | May 12
L91 |