Syllabus for SDHS PreCalc
Section 1: Linear Equations
Section 2: Introduction to Derivatives, Normal and Tangent lines
Skills:
· Understand and use derivatives of polynomials to analyze rates of change
· Use derivatives to determine minima and maxima
· Use derivatives to help find the equation for tangent and normal lines at particular locations on a function
Section 3: Imaginary Numbers and Solving Quadratic Equations
Skills:
Page 28,29 Written exercises 1- 32
-
Factoring
-
Completing the square
-
Quadratic formula
Problems: page 35, 1-30
Section 4: Operations with Polynomials
Skills:
- Be able to add/subtract/multiply/divide polynomials
skill check 6
- Be able to factor trinomials by completing the square, using common patterns, and using quadratic formula
- Be able to factor out common factors from a polynomial
- Be able to evaluate polynomials at a particular value
- Be able to estimate roots of a quadratic using the graphing calculator
- Find maxima and minima using derivatives (first derivative equals zero; for maxima, second derivative is negative, for minima, second derivative is positive) problems starting page 71, 1-4,9c 10c, A1, A2
Problems in book page 55 5-11, 13
page 78 1-6 all, artificial substitution and division not necessary, use polynomial division as shown on page 58
Handout on factoring
See http://www.algebra-online.com/sum-difference-cubes-1.htm for turotial on difference/sum of perfect cubes
See http://www.algebra-online.com/factoring-polynomials-6.htm for factoring turotial
Section 5: Inequalities and Absolute Values
Chapter 3 in Purple Book
Important concepts:
Solving and graphing inqualities of one variable including absolute values
Finding solution sets and optima of simultaneous linear inequalities
Solution set of nonlininear inequalities
Problem sets:
page 98-99
pages 103-104
pages 106-107
pages 112-113
modified process for graphing calculator: enter inequalities and graph, examine values at edges for objective function
Section 7: Functions
Functional notation
Domain/Range
What makes a function a function
Inverses
Rational Functions
Section 8: Exponents and Logarithms
Chapter 5 Advanced Mathematics
Section 9: Trigonometry
for students who've already had some Trig - there's more!
The nine trig functions and the unit circle
Identities and proofs
Domain/Range of trig functions
Graphs and Derivatives
Section 10: Conic Sections
Skills:
Recognize and be able to graph and solve equations involving conic equations including:
Circles
Elipses
Hyperbolas
Parabolas
Day 1: Equations of Circles and intersections of lines and circles
Skills (10): be able to determine the equation of a circle from its description and graph freehand a circle from its equation. Be able to algebraically determine the intersection of a line and circle.
Problems page 222, 223 1,3,5,7,8,9,10,13,14,15,16,29, 31
Skill Check
Day 2/3: Ellipses
Review and Quiz Circles
New Skills (11): identify foci, major and minor axes of symmetry, and vertices; understand transformations on ellipses; determine where an ellipse and a line cross.
Problems pages 228-230: 1-6, 12-15, 22, 23, 24-27
Skill Check
Day 4/5: Hyperbolas
New Skills (12): To determine equations of hyperbolas and to graph them; to identify, vertices, asymptotes and foci of hyperbolas
Problems pages 235-237: 1,3,5,7,11,13,15,17, 19,21,30,31
Skill Check
Section 11: Simplifying Expressions and Using Standard Forms
When checking answers and comparing results, equivalent expressions/functions may look very different. When working with complicated functions, operations can be greatly simplified if the functions are simplified as far as possible before undertaking operations. These are some of the rasons why it is important to be able to factor polynomials completely, simplify rational functions, simplify expressions with radicals, and put rational expressions involving radicals or complex numbers into a standard form.
Section 12: Vector Operations
Operations will include:
Vector addiction and subtraction
Scalar Multiplication
Problems page 422 Class exercises 1-8, 10-17
Written Excersizes 9, 11, 13, 15
Algebraic and Parametric Representation of Vectors
Problems page 428-430
class exercises 1-6
written 1,3,5,9,21,23
written p 435 1,3,5,7,19,23
Unit 1 Linear Equations.doc
Section 6 Linear Programming Examples.doc
Comments (0)
You don't have permission to comment on this page.