Prerequisites:
Algebra I, Geometry, and Algebra II with grades of 80 or higher
Grades of 75 or higher on the Geometry, Algebra I, and Algebra II Regents exams and
Teacher recommendation.
Students must meet the prerequisites set forth by OCC in order to enroll in this class.
This is the fourth year of mathematics for students planning to pursue higher education. This course is designed to provide the necessary foundation for a standard calculus course. Topics include absolute value and quadratic inequalities, functions and their equations, exponential and logarithmic functions and their applications, right triangle trigonometry, law of sines and law of cosines, trigonometric functions (circular) and their inverses, trigonometric identities and equations, addition and multiple angle formulas, and binomial theorem. A graphing calculator is required.
Quarter 1
Sep - Nov
Unit or Topic Skills
Chapter 1, 2, and 3:
Linear and Quadratic Functions and Equations; Inequalities
I can:
Know and be able to use the midpoint, distance, center-radius, and standard form of a circle formulas.
Find the domain and range of a function algebraically and graphically.
Know and be able to convert between the various forms of a line.
Solve compound inequalities.
Graph and analyze functions for their key features.
Perform Algebraic operations on functions.
Solve application problems that result in a quadratic.
Find and simplify the difference quotient.
Determine when a function is odd or even.
Solve quadratic equations multiple ways.
Determine the type of roots of a quadratic equation using the discriminant.
Graph quadratic equations using the axis of symmetry and the turning point.
Find the key parts of a quadratic function graph.
Solve absolute-value equations and inequalities.
Quarter 2
Nov - Jan
Unit or Topic Skills
Chapter 4: Polynomial Functions & Rational Functions
I can:
Determine the shape and end behavior of a polynomial graph using the leading term test.
Find the zeros and multiplicities of a polynomial function.
Perform long division of polynomial functions.
Use the Factor and Remainder theorems.
Use synthetic division to find the factors and roots of a polynomial.
Perform operations on rational expressions and solve rational equations.
Graph a rational function, including finding the asymptotes, the x and y intercepts, and any holes.
Solve a polynomial inequality.
Solve a rational inequality.
Chapter 5:
Exponential and Logarithmic Functions
I can:
Simplify expressions using the laws of exponents
Solve exponential equations.
Convert from log to exponential form and vice versa.
Graph exponential functions and their inverses.
Expand and condense logarithmic expressions.
Solve log equations.
Quarter 3
Jan - Apr
Unit or Topic Skills
Chapter 6:
The Trigonometric Functions
I can:
Know the six basic trig ratios.
Know and use the two special right triangles.
Use the two special triangles to find the six trig ratios.
Be able to find the six trig ratios given a ratio and a quadrant.
Be able to use the unit circle to find a trig value for any quadrantal angle or rotational angle that uses one of the special right triangles in degrees and radians.
Convert from radians to degrees and degrees to radians.
Evaluate and graph sine and cosine functions. [Amplitude, frequency, period, phase shift, vertical shift]
Be able to calculate angular and linear velocity.
Chapter 7: Trigonometric Identities, Inverse Functions, and Equations
I can:
Simplify trig expressions.
Use the trig formulas.
Complete trig identity proofs.
Use inverse notation to find the angle.
Solve first degree trig equations.
Solve second degree trig equations including ones with substitution of identities.
Quarter 4
Apr - Jun
Unit or Topic Skills
Chapter 8: Applications of Trigonometry
I can:
Find missing sides and angles using the Law of Sines.
Determine the number of triangles possible using the Law of Sines.
Find the area of a triangle using both the trig area formula and Heron’s formula.
Find missing sides and angles using the Law of Cosines.
Solve application problems that use the Law of Sines and the Law of Cosines.
Chapter 11: Sequences & Series and Binomial Theorem
I can:
Expand and simplify a binomial.
Find a specific term of a binomial expansion.
Find a term of a sequence given an expression.
Find terms of a sequence written in recursive form.
Find the terms of an arithmetic sequence.
Find the partial sum of an arithmetic sequence.
Find the terms of a geometric sequence.
Find the partial sum of a geometric sequence.