| Grade 9 | Grade 10 | Grade 11 | Grade 12 |
|---|---|---|---|
| Algebra I (L, S, A) Algebra II (A) |
Geometry (L, S) Geo/Trig (A *Algebra II (A) |
Algebra II (L, S, A) *Intro to Calculus (A) | *Trig & Topics (S) *Intro to Calculus (A) *AP Calculus (A) *Applications of Math (L) |
|
Introduction: The members of the department recognize the increasing
importance of mathematics in our students’ lives. Not only will they need math
skills and competency in the applied sciences, but they will also use math as an
indispensable language in such fields as business, economics, and the social
sciences. Our immediate aim therefore is to develop students’ proficiency in,
and understanding of, the mathematical techniques they will need in college and
their careers.
We recognize the specific need in today’s society for the development of
the appreciation of order, pattern, and precision as a means of stimulating
imagination and of developing the students’ powers of analysis and reasoning.
Students will use the TI-83 graphing calculator to enhance their powers of
analysis.
Freshman Placement: Upon acceptance into Queen of Peace High School, any student who has successfully completed an Algebra I course in his/her grammar school will be given an internal placement exam to determine if he/she qualifies for the Algebra II Accelerated course.
Algebra I (L, S, A) Grade 9 Required full year course (4 credits) Accelerated Level: This course offers exceptional students a commitment to in-depth study of first year algebra. It will cover all the topics listed in the Scholastic Level at a depth and pace which will present a suitable challenge for students with superior ability in mathematics. Occasionally this class will make use of computers to discover and reinforce a variety of mathematical concepts. Some use will also be made of graphing calculators. Scholastic Level: This course is a thorough study of the first year of algebra for students with average to good mathematical ability. Topics include the field axioms and other properties, number sets, linear equations, linear inequalities, absolute value, linear graphing, developing and solving systems of equations, operations with polynomials, simplifying rational and radical expressions, solving rational equations, and solving quadratic equations, including a study of the quadratic formula. Throughout the course, various applications are introduced with an emphasis on logic. Lasallian Level: This course focuses on the key topics that provide a strong foundation in the essentials of the first year of algebra. It begins with a review of operations with real numbers combined with an introduction to the use of variables. It includes: solving linear equations and inequalities, the concept of absolute value, operations with polynomials, factoring, simplifying rational expressions, graphing linear equations, and fundamental laws of exponents. Significant experiential instructional methodology will be employed to strengthen student’s foundation in this academic discipline. Geometry (L, S) Geometry/Trigonometry (A) Grade 10 Required full year course (4 credits) Accelerated Level: This course is a thorough study of Euclidean Geometry with emphasis on developing logical reasoning. Topics include: perpendicular and parallel lines and planes, congruent and similar polygons, right triangles, circles, perimeter, area and volume. The course also includes introductory topics in trigonometry: definitions of the trigonometric functions, unit circle, Law of Sines, use of tables, and Law of Cosines. These topics will be covered at a depth and pace which will present a suitable challenge for students with superior ability in mathematics. The students will use computers on occasion to assist in their skills of observation. SAT material is also reviewed. Prerequisites: Approval of current Math teacher and Member of Administration Minimum of 85% average in Algebra I (A) Scholastic Level: This course is designed to aid the student in the development of logical reasoning and creative thinking through the use of proofs and algebraic applications. This geometric system includes the basic undefined terms, parallel, perpendicular and congruent lines, congruent and similar polygons, Right triangles, circles, perimeter and area of familiar polygons. SAT material is also reviewed. Prerequisites: Algebra I (S) or Algebra I (L) with a grade of 75 or higher 15 Lasallian Level: This course focuses on the key topics that provide a strong foundation in the essentials of geometry through the use of proofs and algebraic applications. This geometric system includes the basic elements of point, line, plane, perpendicular lines, parallel lines and planes, congruent and similar polygons, right triangles, Pythagorean Theorem, circles, and perimeter and area of familiar polygons. SAT material is also reviewed. Significant experiential instructional methodology will be employed to strengthen student’s foundation in this academic discipline. Prerequisites: Algebra I (L) Algebra II (L, S) Grade 11; Algebra II (A) Grade 9, 10, 11 Required full year course (4 credits) Accelerated Level: This course allows the superior student an opportunity to demonstrate a potential to take Advanced Placement Mathematics. An emphasis is placed on word problems to develop the student’s ability to translate physical situations into mathematical sentences. The field axioms and other properties will be studied with an introduction to the concept of proof. The student will be able to solve equations involving rational expressions, radical expressions, quadratic functions, and exponential and logarithmic functions. Additional topics include a study of functions, graphs in two and three dimensions, conic sections, and introductions to matrices, and sequences and series. SAT material is also reviewed. Prerequisite: Approval of current Math teacher and Member of Administration Minimum of 85% average in Algebra I (A) Scholastic Level: This course is designed to challenge the average to above average student. Linear equations, systems of equations and inequalities, matrices and determinants begin the curriculum path. Working with quadratic equations, functions, powers roots and radicals are skills that are introduced and worked with intensely in this course. As a continuance in the curriculum, exponential and logarithmic functions, polynomial and rational functions are included. SAT material is also reviewed. Prerequisite: Minimum average of 75% in Algebra I (S) and Geometry (S) Lasallian Level: This course is a study of topics of algebra with an emphasis placed on the study of equations and inequalities, including linear, rational, radical, and quadratic. Throughout the course there is an application to word problems involving rate and proportions. Additional topics include functions and their graphs, complex numbers, and introductions to logarithms and basic conic sections. SAT material is also reviewed. Significant experiential instructional methodology will be employed to strengthen student’s foundation. Prerequisite: Algebra I (L) and Geometry (L) Introduction to Calculus (A) Grade 11, 12 Elective full year course (4 credits) This course provides a background in function theory necessary for the study of calculus. This includes basic graphing techniques, transformations, combinations, and properties of functions. The concept of limit will be discussed from both a graphical and arithmetic viewpoint and used in the development of the derived function, slope of a curve, and the determination of tangents and normals to curves. Types of functions studied are: polynomial, rational, general algebraic, exponential, logarithmic, and trigonometric. Sequences, polar coordinates, polar graphs and vectors will also be studied. Fundamental and supplemental concepts, as well as applications, will be explored through the use of graphing calculator and/or computer-based projects and assignments. NOTE: Introduction to Calculus is designated as the first half of the Advanced Placement course in calculus. Juniors choosing Introduction to Calculus should have the desire, willingness, and motivation to continue with the second half of the sequence which is Advanced Placement Calculus. A graphing calculator is required for this course. Prerequisites: Approval of current Math teacher and Member of Administration Geo/Trig (A), Algebra I (S, A), Algebra II (A) with a minimum average of 80 in each. A student currently taking Algebra II (S) who has maintained an average of at least 90 would be considered. Advanced Placement Calculus (A) Grade 12 Elective full year course (4 credits) This course is a study of differential and integral calculus with applications. It is the continuation of the Introduction to Calculus course. Topics include “max-min” problems, rate of change and related rates, area between curves, volumes of revolution and solids of known cross-section, surface area, Mean Value Theorem, and techniques of integration. The course is the equivalent of the first two semesters of a college calculus course. Students will take the standardized Advanced Placement exam in May and may receive college placement and/or credit for the course depending on the test results and the policy of the receiving college. As with Introduction to Calculus, graphing calculator and/or computer-based projects and assignments will be used to broaden the scope of topics discussed in class. A graphing calculator is required for this course. Prerequisite: Approval of current Math teacher and Member of Administration Introduction to Calculus (A) with an average of at least 80%. AP Test required. Trigonometry and Topics (S) Grade 12 Elective full year course (4 credits) This course is for students who wish to prepare for college mathematics. Several algebraic topics are covered which include: graphing functions, logarithms, binomial theorem, and probability. The trigonometric topics include: angles, trigonometric functions, Laws of Sines and Cosines, polar coordinates, vectors, inverse trigonometric functions, and DeMoivre’s Theorem. A graphing calculator is required for this course. Prerequisite: Algebra II (L) with an average of 80, or Algebra II (S) with an average of 75, or permission of department chair. Applications of Mathematics (L) Grade 12 Elective full year course (4 credits) This course is designed to help the students put their math skills to work in practical, everyday, real-life situations. The course will deal with such topics as: Income, Checking Accounts, Types of Insurance, Loans, Buying Automobiles, Investments, Budgets, and the use of Credit Cards. Prerequisites: This course is open to seniors who have taken Algebra I (L), Algebra II (L), and Geometry. |
