## MATH

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SCIENCE ENGLISH SOCIAL SCIENCE WORLD LANGUAGE ELECTIVES

4 years of English = A-G standards **C requirement **

**ALGEBRA I****ALGEBRA II****GEOMETRY****PRE-CALCULUS****AP CALCULUS**

**ALGEBRA I - 9th Grade **- **Moderate** • Homework: 0-30 minutes nightly Grading: 50% tests, 15% homework, 15% class/group work, 20% quizzes/Do Now.

**DESCRIPTION** Instructional time should focus on four critical areas: 1) deepen and extend understanding of linear and exponential relationships; 2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving and using quadratic fractions; 3) extend the laws of exponents to square and cube roots; 4) apply the linear models to data that exhibits a linear trend.

**ALGEBRA II - 9th & 10th Grades - ****Difficult** • Homework: 30-60 minutes nightly* Grading: Three term grades are given each semester. 40% class/homework, 20% quizzes, 40% tests. To calculate the semester grade, each term grade is weighted at 30% and the final counts for 10%. Grades are based on the standard scale of: A= 90-100 / B= 89-90 / C = 70-79 / D= 60-69 / F= <60.

**PREREQUISITES** Freshman students must have a C or better in Algebra 1; required scores on the SFUSD end-of-year proficiency test.

**DESCRIPTION** The coursework begins with a review of elementary techniques and concepts and quickly moves into graphing functions with an emphasis on range and domain. Linearity, including linear systems, are studied in depth, concluding with applications and modeling, and followed by quadratic functions which include graphing, root computations, imaginary numbers and modeling. By the second semester, the content shifts to exponents and logarithms, again solidifying the ideas through modeling, in this case using exponential and logarithmic functions. The next topics are: rational expressions with an emphasis on factoring; radicals, which includes simplification, rationalization, and extraneous solutions; and conic sections, higher degree functions, arithmetic and geometric sequences and series. and probabilities and statistics.

**GEOMETRY **- **10th & 11th Grades - Moderate **• Homework: 0-30 minutes nightly. Grading: 15% homework, 50% quizzes, 15% group quiz, 20% Do Nows (warm ups). To calculate the semester grade, each term grade is weighted at 30% and the final counts for 10%. Grades from A through F are based on the standard scale of:

- A+ = 97-100
- A = 93-96
- A- = 90-92

- B+ = 87-89
- B = 83-86
- B- = 80-8

- C+ = 77-79
- C = 73-76
- C- = 70-72

**PREREQUISITE** Algebra I, Algebra II

Topics include: sets, real numbers, lines, planes, angles, triangles, congruence, proofs, geometric inequalities, perpendicular lines and planes in space, parallel lines and planes, polygonal regions and their areas, similarity, plane coordinate geometry, circles, spheres, sectors, trigonometry, symmetry, transformations, and solids. Emphasis will be on developing theoretical and analytical thinking skills, and curriculum will be based on Common Core Standards. Click here for ADDITIONAL NOTES.

**PRE-CALCULUS **- **11th & 12th Grades - Moderate **• Homework: 60 minutes daily. Grading scale: tests 50%, quizzes: 20%, classwork: 15%, homework: 15%. Each grading period counts for 1⁄4 of the final grade with the final exam also counting as 1⁄4 of this grade.

**PREREQUISITES** Students must successfully complete algebra, geometry, advanced algebra with a grade of C or better: algebra, geometry, advanced algebra.

**DESCRIPTION** This pre-calculus course is divided into two sections. Section one, first semester, is made up of advanced algebra topics such as graphing and solving functions, conics, logarithms, and complex numbers. Section two, second semester, is made up of trigonometric topics such as graphing, identities, applications, and various rules for solving functions. Both semesters are a preparation for the skills needed to succeed in an AP calculus course. Semester 1 (Grading Periods 1-3) and Semester 2 (Grading Periods 4-5) details below.

**Grading Period 1 **

Functions- Characteristics

- Piecewise graphs
- Transformations
- Composites

Polynomial and Rational Functions

- Quadratic Functions
- Power Functions
- Rational Functions
- Polynomial Functions

** **

**Grading Period 2**

Zeros of a Polynomial Function

- Complex numbers
- Complex zeros
- Polynomial and rational inequalities

Exponential/ Logarithmic Functions

- Inverse functions
- Exponential functions
- Logarithmic functions
- Logarithmic and exponential functions
- Compound interest/ growth/ decay

**Grading Period 3**

Analytic Geometry

- Conics
- Parabolas, ellipses, and hyperbolas

Sequences

- Arithmetic and geometric sequences

Counting and probability

- Sets and counting
- Permutations and combinations

**Grading Period 4**

Trigonometric Functions

- Angles
- Trigonometric functions
- Properties of trig functions
- Graphs of sine, cosine, tangent, cotangent, cosecant, and secant

**Grading Period 5**

Analytic Trigonometry

- Trig identities

**AP CALCULUS **- **12th Grade - Difficult **• Homework: 60 minutes daily. Grading scale: tests 50%, quizzes: 20%, classwork: 15%, homework: 15%. Each grading period counts for 1⁄4 of the final grade with the final exam also counting as 1⁄4 of this grade.

**PREREQUISITES** Students must successfully complete the following courses with at least a C or better: algebra, geometry, advanced algebra, pre-calculus.

**DESCRIPTION** This AP calculus AB course is equivalent to a college semester of calculus and will cover topics such as limits and continuity, derivatives, applications of the derivative, rate of change, Mean Value Theorem, Riemann sums, average value, integration, applications of integration, Fundamental Theorem of Calculus, slope fields, applications of anti-differentiation and separable differential equations. Students are expected to take the AP exam at the end of this course. See course syllabus below.

**Limits and Continuity**

- Graphical representation
- algebraic representation
- applications

**The Derivative**

- Graphical representation
- Difference quotients
- Formal definition
- Rules for differentiation
- Implicit derivatives
- Explicit derivatives

**Applications of the Derivative**

**Curve analysis**- Max and Min
- Increasing and decreasing behavior
- Inflection points
- Concavity
- Optimization problems
- Particle motion
- Calculator representation
- Related rates
- Applications

**Anti-Derivatives**

**Substitution Roundtable**- Differential equations
- Slope fields

**The Definite Integral**

- Riemann Sums
- Fundamental Theorem of Calculus
- Applications
- Area
- Volumes of solids of revolution