PRE-CALCULUS ICOURSE DESCRIPTION: Pre-Calculus I is an advanced course of study of pre-calculus algebra. Emphasis is placed on the complex number system, equation theory, trigonometry, analytic geometry, combinatorics, and the introductory concepts of calculus. It is a rigorous course which draws greatly on the student’s knowledge of Algebra I and II, as well as Geometry. The Ti-83 Plus graphing calculator will be used throughout the course. Project work will also be incorporated - usually one project each semester will be assigned.
Students enrolled in this course will become members of the PEP Squad. These students will be required to provide nine periods of tutorial help in a quarter to a student in lower level course including students in the Lower School.
COURSE OBJECTIVES: The course will enable the student to increase his understanding of Algebra II topics; to establish the foundation for calculus through the introduction of calculus-oriented concepts; to further refine his ability to solve problems by emulating the orderly, logical and systematic approaches to algebra; to gain an appreciation for its interrelationship with other fields of mathematics, science and business; to develop skills and attitudes that will enable him to interpret and utilize mathematics in modern life; to recognize that there may be more than one way to effectively arrive at a conclusion or solution by finding alternate methods for solving problems; to recognize that some problems may have no practical solution; and to communicate and cooperate with other students.
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Chapter |
Competencies |
Assessment |
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Chapter 1 Linear and Quadratic Functions |
The student will review the coordinate geometry of lines and the various methods of finding the real and imaginary roots of quadratic equations. The student will graph linear and quadratic functions and find the coordinates of any points of intersection of two lines or of a line and a parabola. Using slope along with the distance and midpoint formulas, students verify properties of special quadrilaterals and find equations of medians, altitudes, and perpendicular bisectors of sides of various triangles. Students will also solve a variety of real-world problems for which linear or quadratic functions are models |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 2 Polynomial Functions |
The student will solve polynomial equations, both with and without the use of technology, and draw graphs of polynomial functions. Students also find maximum and minimum points on quadratic and cubic graphs and then apply this knowledge to extreme-value problems from physics, business and manufacturing. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 3 Inequalities |
The student will solve and graph linear and polynomial inequalities in one or two variables. The students also solve and graph absolute-value inequalities and graph the solution sets of systems of inequalities. The students will set up and solve linear programming models using a function’s maximum or minimum value on a feasible region. They will analyze the graph and determine reasonable solutions. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 4 Functions |
The student will build on his knowledge of polynomial functions from Chapters 1 and 2. The student will explore the relationship between the graph of a function and an algebraic rule for the function. The student will gain an appreciation for the importance of the concept of function to the fields to which mathematics is applied. The student will consider functions of more than one variable, and they will use functions to solve real-world problems. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 5 Exponents and Logarithms |
Students will study the laws of exponents and logarithms, and then apply them to real-life situations. The student will simplify exponential expressions and investigate exponential growth and decay models. The student will also work with natural logarithms and apply them and the natural exponential function, ex, to compound interest problems. The student will simplify logarithmic expressions, examine models based on logarithms, and solve exponential equations using logarithms. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 6 Analytic Geometry |
The student will use the analytic methods to prove some familiar theorems from geometry, and to find equations of circle, ellipses, hyperbolas, and parabolas. After examining these conic sections separately, students will find the points of intersection of pairs of conics by using algebraic, geometric and technological methods. The student will write equations from graphs and will be able to predict the type of conic from the given equation. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 7 Trigonometric Functions |
The student will expand his knowledge of the use of trigonometry. Students will convert between degree and radian measures of angle. He will find arc lengths and areas of sectors of circles. The student will examine the six trigonometric functions using the coordinates of the point where the terminal ray of an angle in standard position intersects a circle centered at the origin; the student will then evaluate and graph the trigonometric functions. The student will learn about and evaluate inverse trigonometric functions. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 8 Trigonometric Equations and Applications |
The student will solve trigonometric equations and gain an appreciation of the applications of periodic functions in a wide variety of fields. Students start by solving simple trigonometric equations and apply them to problems from analytic geometry. The student will explore changes in the sine and cosine curves, including period and amplitude changes and horizontal and vertical translations. The student will then use such changes to develop models of real-world periodic phenomena from physics, astronomy, meteorology, and oceanography. The student will prove a variety of trigonometric identities and use them to simplify and solve more difficult trigonometric expression and equations. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 9 Triangle Trigonometry |
The student will use trigonometry to find the unknown sides or angles of a triangle. He will solve application problems such as finding angles of elevation and depression. The student will learn and use the formula for the area of a triangle using the sine of one of the angles. The student will investigate and use the Law of Sines and the law of cosines. The student will apply his knowledge of triangle trigonometry to solve problems from navigation and surveying. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 10 Trigonometric Addition Formulas |
The student will derive the difference formula for cosine and apply this knowledge to the formulas for cos (" + $) and sin (" ± $). The student will go through the process of deriving the formulas for tan (" ± $), sin 2", cos 2", tan 2", sin "/2, cos "/2, and tan "/2. Students will use the formulas to find exact values for functions of angles and to solve trigonometric equations algebraically or geometrically (using technology). |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 11 Polar Coordinates and Complex Numbers |
The student will learn a new way of locating points in a plane. The student will convert from polar coordinates to rectangular coordinates and vice versa. The will graph in both systems and use polar coordinates to study powers and roots of complex numbers. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 12 Vectors and Determinants |
Vectors in two and three dimensions are represented geometrically and algebraically. Students learn how to perform basic operations on vectors, including addition, scalar multiplication, finding dot product, and finding the cross product. Students will solve physics and navigation problems involving vectors in two dimensions. Determinants are used to find the intersection of lines in a plane or in space. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 13 Sequences and Series |
The student will study finite and infinite sequences and series. The student will be able to distinguish between and arithmetic sequence and a geometric sequence. The student will be able to find specific terms, number of terms of finite sequences, and ratio/difference of the terms of the sequence. The student will be able to find the sum of finite and infinite series. The student will also be able to interpret and use sigma notation to represent a series. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |
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Chapter 14 Matrices |
The student will be introduced to the fundamentals of matrix arithmetic and the application to matrices to a wide variety of fields. The student will learn to perform matrix addition, scalar multiplication, and matrix multiplication. The student will also use matrices to solve systems of equations. |
Homework class discussions group discussions demonstrations presentations quizzes Chapter Test |