MATHEMATICS
Except for the remedial levels (Integrated Math courses) and Advanced Placement Calculus, the mathematics courses at Alter High School are separated into honors B and C levels.
In the C level material is presented with emphasis on review, practice and application. Concepts are developed primarily through example. The student at this level will do exercises designed to check the grasp of the concepts and his/her ability to apply these ideas in basic situations. Some challenging problems will be assigned as the student demonstrates understanding.
In the B level the concepts are developed with some theory and proof (Geometry B uses direct proof fairly extensively). In addition to basic problems the student at this level will do exercises that are more challenging and that call for more sustained application.
In the honors level a rigorous approach is taken to developing mathematical theory. Proof is used as a tool extensively. In addition to basic and intermediate level exercises, the student will do challenging problems requiring higher level thinking skills. Success in handling these problems will depend on the student’s ability to evaluate given information, to discover relationships that are not obvious, and to reason out a method of solution. Prerequisites for AP and Honors classes may not be waived.
Placement into freshman classes is determined by the High School Placement Test, grade school curriculum and eighth grade teacher observation of performance. Placement of all non-freshmen is based on the average of the first three quarters in the current math course. However, all Algebra 2 courses carry an additional prerequisite from Algebra I as noted in the individual course descriptions. The present teacher’s signature is required to guarantee the prerequisites (minimum stated for each course) are met.
All students are to have a TI84+ graphing calculator.
COMPUTER PROGRAMMING
Grade 11, 12 Elective Full Year 1 Credit
Prerequisite: Enrollment in or completion of Honors or regular (B) Geometry and the computer teacher’s signature. This is not a math course, yet is preparation for college courses in computer science and engineering.
Description: This course teaches the computer language C++. Students will be required to write, compile, execute, debug, store, and retrieve programs.
HONORS ALGEBRA 1
Grade 9 Elective Full Year 1 Credit
Prerequisite: Placement determined by the Math Department
Description: This course enriches the Algebra I concepts with an in depth study of theory and problem solving. Additional topics include direct proofs, factoring cubics, simplifying zero and negative integral exponents, solving systems of three equations in three variables, and an introduction to irrational numbers.
ALGEBRA 1 B
Grade 9 Elective Full Year 1 Credit
Prerequisite: Placement determined by the Math Department
Description: In addition to the concepts presented in Algebra I C, this course includes transforming formulas, combined inequalities, absolute value equations/inequalities, and functions and relations.
ALGEBRA 1 C
Grades 9, 10, 11 Elective Full Year 1 Credit
Prerequisite: Grade 9 - Placement determined by Math Department
Grades 10 and 11 – A grade of A or at least a B- in Integrated Math must be attained
Description: This course is an introduction to the study of the structure of the algebra of the real number system. It is designed to help the student recognize the techniques and properties of algebra as reflections of this structure and to be able to apply algebraic concepts and skills to equations, inequalities, and problem solving.
HONORS GEOMETRY
Grade 9, 10 Elective Full Year 1 Credit
Prerequisite: A in Algebra I B and teacher recommendation; C+ in Honors Algebra I
Description: In addition to the concepts presented in Geometry B, this course presents geometry as a mathematical system, uses proof to develop all topics covered, develops the understanding and use of locus and coordinate geometry topics and quadrilaterals, properties of circles, areas and perimeters of polygons and circles, special right triangle properties and the Pythagorean theorem, coordinate geometry of a line, and an introduction to the two column proofs for congruent triangles.
GEOMETRY B
Grade 9, 10 Elective Full Year 1 Credit
Prerequisite: A- in Algebra I C; C- in Algebra I B; D in Honors Algebra I
Description: In addition to the concepts presented in Geometry C, this course includes use of two column deductive proofs to introduce and explore many topics, an introduction to indirect and paragraph proofs, an introduction to right triangle trigonometry, and area and volumes of 3-dimensional figures.
GEOMETRY C
Grade 10, 11, 12 Elective Full Year 1 Credit
Prerequisite: D in Integrated Algebra 1/Basic Geometry; D in Algebra I C; D+ or D (only) in Algebra I B
Description: This course includes the use and understanding of the language of geometry, spatial relationships of lines and planes, properties of polygons with emphasis on triangles and quadrilaterals, properties of circles, areas and perimeters of polygons and circles, special right triangle properties and the Pythagorean theorem, coordinate geometry of a line, and an introduction to the two column proofs for congruent triangles.
INTEGRATED ALGEBRA 1
Grade 9 Elective Full Year 1 Credit
Prerequisite: Placement by the Math department
Description: This course paired with Integrated Algebra 1/Basic Geometry is designed to be a two-year course covering Algebra 1 C topics and an introduction to basic Geometry topics. This course is designed for the student who needs to explore basic algebraic concepts at a slower pace than the Algebra 1 C course. Math review topics and pre-algebra topics will be integrated with an introduction to the study of the structure of algebra of the real number system. Emphasis on review of techniques and applications of algebraic concepts will be used.
INTEGRATED ALGEBRA 1 / BASIC GEOMETRY
Grade 10 Elective Full Year 1 Credit
Prerequisite: D or above in Integrated Algebra I
Description: This course is paired with Integrated Algebra 1 to give the student a full year of Algebra and an introduction to basic Geometry topics. It will review and strengthen previously introduced Algebra 1 topics and will introduce new topics to complete an Algebra 1 course. As time allows, Basic Geometry topics will be introduced to help the student prepare for Geometry C.
HONORS ALGEBRA 2 - TRIG
Grades 10, 11 Elective Full Year 1 Credit
Prerequisite: A+ in Geometry B and Algebra I B; C+ in Honors Geometry and Honors Algebra I
Description: In addition to the concepts in the other Algebra 2 courses, this course includes algebraic proofs of real number properties and absolute value, solving linear equations using determinants, working with trigonometric identities and graphs of sine and cosine functions.
ALGEBRA 2 B - TRIG
Grades 10, 11 Elective Full Year 1 Credit
Prerequisite: A in Geometry C and B in Algebra I C; C- in Geometry B and Algebra I B; D in Honors Geometry and C in Honors Algebra I
Description: In addition to the concepts presented in Algebra 2 C, this course includes beginning trigonometry (degree and radian measures on the unit circle, the six basic trigonometric identities, solving triangles, Law of Sines, Law of Cosines) and co-function formulas, and exponential and logarithmic equations.
ALGEBRA 2 C
Grades 11, 12 Elective Full Year 1 Credit
Prerequisite: D in Algebra I C and Geometry C; D in Algebra I B and D in Geometry B
Description: This course reviews and strengthens Algebra I concepts such as solving linear equations and inequalities, solving quadratic equations and inequalities by factoring, linear graphing, and word problem solving. This course includes solving quadratic equations by completing the square and the quadratic formula, radicals and radical equations, linear equations in two variables, zero and negative exponents, and complex numbers.
HONORS PRECALCULUS
Grades 11, 12 Elective Full Year 1 Credit
Prerequisite: C or better in Honors Algebra 2
Description: In addition to concepts presented in the other Precalculus courses, this course will also include coordinate geometry proofs, defining “e” and natural logarithms, polar graphing, power series, mathematical induction, an introduction to derivatives.
PRECALCULUS B
Grade 11, 12 Elective Full Year 1 Credit
Prerequisite: C in Algebra 2 B; D in Honors Algebra 2
Description: This course will include analytic geometry of all conic sections, trigonometric formulas, equations and identities, advanced graphing, polar coordinates with complex numbers, vectors, binomial theorem with probability, first derivative theory and practice, and an introduction to graphing calculators.
ALGEBRA III/TRIGONOMETRY
Grade 12 Elective Full Year 1 Credit
Prerequisite: D+ or better in Algebra 2 C; C- or D+ (only) in Algebra 2 B
Description: This course is paired with Algebra 2 C to give students the opportunity for a complete Algebra 2 course and an introduction to Precalculus. Topics include trigonometry, polynomial functions, exponents, logarithms, conic sections, basic operations with complex numbers, and probability and statistics.
SELECTED MATH TOPICS
Grade 12 Elective Full Year 1 Credit
Prerequisite: C or lower in Algebra 2B
Description: This course is for students who need a fourth year of math, but not at the PreCalculus level. Topics include, but are not limited to: Set Theory, Logic, Number Theory, Probability, and Statistics.
HONORS CALCULUS
Grade 12 Elective Full Year 1 Credit
Prerequisite: B- in Precalculus B; D or C- (only) in Honors Precalculus
Description: This course covers topics in elementary functions, differential and integral calculus comparable first year courses in colleges and universities. Topics include properties of functions, limits, derivatives of elementary, composite, implicitly defined, inverse, and logarithmic functions, applications of the derivative, techniques of integration and applications of the integral.
ADVANCED PLACEMENT CALCULUS
Grade 12 Elective Full Year 1 Credit
Prerequisite: A+ in Precalculus B; B- in Honors Pre-Calculus
Description: Advanced Placement Calculus emphasizes a multi-representational approach to Calculus with concepts, results and problems being expressed geometrically, numerically, analytically and verbally. Broad concepts and widely applicable methods are emphasized. Technology is used regularly to reinforce the relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results. It is expected that students enrolled in AP Calculus will take the AP Calculus exam in May at the prevailing fee.
