MATH B

OLEAN HIGH SCHOOL Course: Name Mathematics B Text: Amsco Mathematics B Other Resources: Review Integrated Math Course 3 Amsco’s Preparing for the Math B Regents Exam Graphing Calculator Grades 10-12 Month

Topic Content Rational Numbers and Polynomial expressions

Skills • • • •

Sept.

Rational Expressions

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Oct.

Real and Complex Numbers

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Concepts

Solving equations and inequalities, Solving abs. Value equations and inequalities, factor polynomials, perform operations with polynomials.

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Operations and solving equations with fractional expressions simplifying complex fractions

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Simplify a radical Perform operations with radicals with same index Rationalize a denominator Use the quad formula Solve radical equation

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Simplify powers of ‘i’ Perform operations with complex numbers

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Major Assessments

Learning Standards

Resource/Text Page

Properties of Rationals and reals equations and inequalities, absolute value, operations and factoring of polynomials

Homework Quizzes Chapter Test

3-2, 3-3, 3-7

Chapter 8 Pages 280 –343

Operations with rational expressions Equations with fractions Problem solving with fractional equations


3-2,3-3,3-7

Chapter 9 Pages 344-378

Roots and radicals Operations with radicals quadratic formula and real roots


3-2, 3-3, 3-7

Chapter 10 Pages 379 - 434

3-3,3-4,


Imaginary and complex #s Operations with

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Oct.

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Relations and Functions

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Nov.

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Transformation Geometry

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Dec.

Exponential Functions

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Solve quadratic equations and inequalities Write a quadratic equation using given conditions

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Identify and graph domain and range Identify relations that are functions Use function notation Relate function to a life situation Apply various types of functions Identify and graph the equation of conic sections Determine the inverse of a function Apply composition of functions Apply basic transformations on figures and functions in the coordinate plane Perform composite transformations Find inverse by reflection

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Evaluate exponential expressions Graph exponential functions Solve exponential equations Solve equations with frac. or negative exponents

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complex # s Equations with imaginary roots Nature of the roots of quad. Equation Quadratic inequalities Relations (Domain & Range) Functions Inverses Compositions Conic Sections


3-4, 3-7


Transformations that provide congruence Direct and opposite isometries Symmetry


3-4, 3-7


Laws of exponents Scientific Notation Fractional exponents Exponential functions Growth & decay Compound Interest


3-4,3-7


Logarithmic Functions

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Jan.

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Geometry of the Circle

Trigonometric Functions

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Apply formulas for circle Apply theorems regarding: tangents and chords; inscribed angles and intersecting chords

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To find measures of angles and lengths of segments formed by intersecting chords, tangents and secants

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Classify angles by quadrant Convert measures radiansÅ ->degrees Express sine and cosine as coordinates Calculate exact values of sin & cos Calculate tangent and reciprocal functions based on sin & cos Find reference angles

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Feb.

Relate logarithmic and exponential functions Graph logarithmic functions Apply the laws of logarithms to solve equations Apply the change of base formula

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Log form Laws of logarithms Common logs Natural logs Log equations Change of base formula

Arcs and angles formed by tangents,chords and secants Measures of chords, tangent and secant segments

Angles as rotations Sine, Cosine and Tangent and reciprocal functions Reference angles Radian measure Exact values of special angles


3-4, 3-7

Chapter 17 Pages 785 – 811


3-1, 3-5



3-5


Trigonometric Graphs

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Mar. •

Trigonometric Applications • • •

Trigonometric Equations and Identities

Apr.

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Identify amplitude, frequency, and period for sine and cosine graphs Graph y = a sin bx + d and y = a cos bx + d Sketch tangent, reciprocal and inverses Generate equations given a trig graph Use sine/cosine graph to solve problems

Find the measures of sides and angles of a triangle by applying the law of sines/ law of cosines To solve application problems including force To find areas trigonometrically Apply basic identities Apply sum, difference, double and half angle identities Solve 1st and 2nd degree trig equations Solve trig equations involving more than one function

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3-5, 3-7


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Trigonometric graphs Inverse trigonometric functions

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Law of sines Law of cosines Area of triangle Ambiguous Case Forces Problem Solving


3-5, 3-7


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Trig Identities Solution of trig equations


3-5, 3-6, 3-7


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Probability and Binomial Theorem

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May

Statistics

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June

• Review

Apply fundamental principles of probability Apply rules for computing permutations and combinations Calculate the probability in a Bernoulli experiment Apply the Binomial Theorem Find the rth term of a binomial expansion

Apply statistical measures of mean and standard deviation Use summation notation Make inferences using the normal distribution To perform linear, logarithmic, exponential and power regressions Interpolate and extrapolate from graphs determined by regressions

Application of above skills to answer regents questions

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Basic probability Permutation & combination Bernoulli experiments Binomial Theorem


3-6


Mean Variance and Standard Deviation Sigma notation Normal Distributions Regressions Linear correlation coefficient Interpolation and extrapolation


3-5, 3-6


Preparation for the regents exam

NYS Math B Regents Exam

3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7

Former Regents Exams