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SECONDARY MATHEMATICS CURRICULUM GUIDE      

Advanced Topics      

1298310      

Textbook: Blitzer Algebra and Trigonometry 4e    

HILLSBOROUGH COUNTY SCHOOL DISTRICT 2014 – 2015

Last revised 2010-2011      

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ADVANCED TOPICS

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Second semester formulas listed in the curriculum guide will be provided on a formula sheet to be included with the exam.

Calculators through graphing calculators comparable to TI-83+ are recommended for use. Calculations of equation solving capabilities, such as the TI-89 are not permitted. Graphing calculators should be used to reinforce the students understanding of the curriculum and NOT used to introduce the material.

 Springboard activities MAY be supplemented at any time. Access to these activities can be found on www.springboard.collegeboard.com. Springboard activities are NOT required for this course.

 

SEMESTER ONE – Formulas are NOT provided to students first semester.    I. Algebra Fundamentals Part I

A. Simplify expressions involving integral and rational exponents. (Prereq. 2) MA.912.A.4.1, MA.912.A.6.3 B. Scientific Notation (Prereq. 2) MA.912.A.1.1

1. Convert from decimal to scientific notation and vice versa. 2. Solve problems using scientific notation.

C. Simplify expressions involving radicals. (Prereq.3) MA.912.A.6.1 D. Add, Subtract, and Multiply polynomial expressions. (Prereq.4) MA.912.A.4.2

       Time Line:  9 days

 II. Algebra Fundamentals Part II

A. Factor polynomials using the following techniques: (Prereq.5) MA.912.A.4.3 1. GCF 2. Difference of Squares 3. Sum and Difference of Cubes 4. Quadratic Trinomials 5. Grouping

B. Simplify, add, subtract, multiply, and divide rational expressions, not including complex fractions. (Prereq.6) MA.912.A.5.1, MA.912.A.5.2

 9 days  Resource: Springboard Directed Activity 3.2 (Algebra II) to accompany section Prereq. 5  Springboard Directed Activity 5.6 (Algebra II) to accompany section Prereq. 6

ADVANCED TOPICS

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     III. Linear Equations and Inequalities in One Variable

A. Solve linear equations and linear inequalities. (1.2, 1.7) MA.912.A.3.1, MA.912.A.3.4 1. Answers to be given in 3 forms: a graph, a statement, interval notation

B. Solve absolute value equations. (1.6) MA.912.A.3.6 C. Solve absolute value inequalities in one variable and graph the solution. (1.7)

1. Answers to be given in 3 forms: a graph, a statement, interval notation MA.912.A.3.6

 12 days

 IV. Linear Equations and Inequalities in Two Variables

A. Determine the slope of a line given two points a line passes through. (2.3) B. Determine the slope and y-intercept of a line given its equation. (2.3) C. Graph linear equation in two variables. (2.3) MA.912.A.6.3 D. Write the equation of lines, including lines parallel and perpendicular to a given line. (2.3, 2.4)

MA.912.A.3.10 E. Graph linear inequalities in two variables. (8.5) MA.912.A.3.12

 13 days

 End of 1st Quarter

Resource: Springboard Activities and/or Cumulative Teacher Assessment

 4 days

 V. Systems of Linear Equations and Inequalities MA.912.A.3.14

A. Solve systems of linear equations using the following methods: (8.1) 1. linear combination 2. substitution 3. graphing calculator (optional)

B. Solve word problems using systems of equations. (optional, 8.1) C. Graph the solution to the systems of linear inequalities. (8.5)

 8 days

ADVANCED TOPICS

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     VI. Quadratic Functions

A. Add, subtract, multiply, and divide complex numbers. (1.4) MA.912.A.1.6 B. Solve quadratic equations by the following methods: (1.5) MA.912.A.7.2

1. Factoring 2. Quadratic Formula 3. Square Root Method

C. Use the discriminant to determine the nature of the roots. (3.1) MA.912.A.7.4 D. Graph quadratic functions using the following criteria: (3.1) MA.912.A.7.1

1. Vertex of the parabola 2. X-intercepts (roots) and y-intercepts 3. Axis of symmetry

 11 days  Resource: Springboard Guided Activity 3.3 (Algebra II) to accompany section 1.4  Springboard Directed Activity 3.4 (Algebra II) to accompany section 1.5  Springboard Guided Activity 3.6 (Algebra II) to accompany section 3.1

 VII. Polynomial Functions

A. Identify the aspects of polynomial functions. (3.2) MA.912.A.4.6 1. End behavior (even/odd) 2. Multiplicity of roots

B. Graph polynomial functions without a graphing calculator, taking into account the following: (3.2) 1. Leading coefficient test 2. End behavior 3. X-intercepts (roots) and y-intercepts 4. Multiplicity of roots

C. Use synthetic division to divide polynomials. (3.3) MA.912.A.4.4 D. Apply the Factor Theorem and the Remainder Theorem. (3.3) MA.912.A.4.6 E. Use the Rational Root (Zero) Theorem to list all possible zeros. (3.4) MA.912.A.4.6 F. Given a polynomial function, find all roots, including complex conjugates (3.4) MA.912.A.4.7

 11 days  Resource: Springboard Investigative Activity 4.1 (Algebra II) to accompany section 3.2

 Springboard Activities/Exam Review

 7 days

ADVANCED TOPICS

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SEMESTER TWO – 2nd semester formula sheet provided with exam (see attached).    VIII. Exponential and Logarithmic Functions

A. Graph exponential functions of the form y = bx and logarithmic functions of the form y = log x . (4.1 , 4.2)

1. Vertical and horizontal translations, and reflections MA.912.A.8.3 B. Introduce base e and natural logarithms. (4.2) C. Write exponential equations as logarithmic equations and vice versa. (4.2) MA.912.A.8.1 D. Evaluate logarithmic expressions without the aid of a calculator (4.2) MA.912.A.8.2 E. Use the product rule, quotient rule, and power rule to expand and condense logarithmic

expressions (4.3) MA.912.A.8.2 F. Apply the change of base property (4.3) MA.912.A.8.6 G. Solve exponential and logarithmic equations (4.4) MA.912.A.8.6

Time Line: 15 days  Resource: Springboard Investigative Activity 2.3 (Algebra II) to accompany section 4.1  Springboard Investigative Activity 2.6 (Pre-Calculus) to accompany section 4.1  Springboard Investigative Activity 2.4 (Algebra II) to accompany section 4.3  Springboard Directed Activity 2.7 (Pre- Calculus) to accompany sections 4.1 – 4.4

 IX. Trigonometric Functions

A. Convert angle measures from degrees to radians and vice versa. (5.1) MA.912.T.1.1 B. Find coterminal angles. (5.1) C. Define sine, cosine, and tangent values for special angles: 0 30 45 60 90 ,180 and 270 . (5.2)

MA.912.T.1.3 D. Use reference angles to find the sine, cosine, and tangent values of other angles. (5.3) MA.912.T.1.3 E. Graph y = sin x and y = cos x including: MA.912.T.1.6

1. Changes in amplitude 2. Changes in period 3. Vertical shift (NO phase shift)

 13 days  Resource: Springboard Guided Activity 3.1 (Pre-Calculus) to accompany section 5.2

 

               

b                                                      

ADVANCED TOPICS

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     X. Trigonometric Identities

A. Simplify trigonometric expressions. (6.1) MA.912.T.3.2 B. Verify basic trigonometric identities. (6.1) MA.912.T.3.2

1. Note: suggested problems p.614 #1-18 C. Solve linear and quadratic trigonometric equations involving sine, cosine, and tangent only, for

0 ≤ θ < 360 and 0 ≤ θ < 2π . Do not include equations with double angles, half-angles or multiple angles. (6.5) MA.912.T.3.4

 11 days  Resource: Springboard Directed Activity 4.1 (Pre- Calculus) to accompany section 6.1

 End of 3rd Quarter

Resource: Springboard Activities and/or Cumulative Teacher Assessment

 2 days

 XI. Triangle Trigonometry

A. Use Pythagorean Theorem. (5.2) B. Define sine, cosine, and tangent as ratios of sides of a right triangle. (5.2) MA.912.T.2.1 C. Use trigonometry to solve:

1. Missing measures in a right triangle. (5.2, 5.8) MA.912.T.2.1 2. Word problems involving angles of elevation and angles of depression. (5.2, 5.8) MA.912.T.2.2

D. Use Law of Sines to solve oblique triangles. Do NOT include ambiguous case. (7.1) MA.912.T.2.3 sin A sin B sin C

1. Formula given: = = a b c

E. Find the area of a triangle given SAS. (7.1) MA.912.T.2.4 1

1. Formula given: k = bc sin A 2

F. Use the Law of Cosines to solve oblique triangles. (7.2) MA.912.T.2.3 1. Formula given: c2 = a2 + b2 − 2ab cos C

G. Find the area of triangles to solve oblique triangles with Heron’s formula (7.2) MA.912.T.2.4

1. Formula given: k = s ( s − a ) ( s − b) ( s − c ) where s = a + b + c 2

 16 days  Resource: Springboard Investigative Activity 4.5 (Pre-Calculus) to accompany section 7.2

ADVANCED TOPICS

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   XII. Sequence and Series

A. Find particular terms of a sequence from the general term. (11.1) MA.912.D.11.1 B. Use recursion formulas, factorial notation, and summation notation. (11.1) MA.912.D.11.4 C. Find the common difference for an arithmetic sequence. (11.2) MA.912.D.11.1 D. Write the terms of an arithmetic sequence. (11.2) MA.912.D.11.3 E. Use the formula for the general term of an arithmetic sequence. (11.2) MA.912.D.11.3

1. Formula given: an = a1 + (n −1) d F. Use the formula for the sum of the first n terms of an arithmetic sequence. (11.2) MA.912.D.11.4

n 1. Formula given: Sn = (a1 + an ) 2

G. Find the common ratio of a geometric sequence. (11.3) MA.912.D.11.1 H. Write the terms of a geometric sequence. (11.3) MA.912.D.11.3 I. Use the formula for the general term of a geometric sequence. (11.3) MA.912.D.11.3

1. Formula given: a = a r n−1 n 1

J. Use the formula for the sum of the first n terms of a geometric sequence. (11.3) MA.912.D.11.4 a1 (1 − r ) n

1. Formula given: Sn = 1 − r

K. Use the formula for the sum of an infinite geometric sequence. (11.3) MA.912.D.11.4

1. Formula given: S = a1 ∞ 1 − r

 12 days  Resource: Springboard Guided Activity 2.1 (Algebra II) to accompany section 11.2  Springboard Guided Activity 2.2 (Algebra II) to accompany section 11.3

 XIII. Probability

A. Use the fundamental counting principle to determine the number of possible outcomes of an event. (11.6) MA.912.P.1.1

B. Distinguish between a permutation and a combination. (11.6) C. Solve problems using the counting principle, permutations and combinations. (11.6) MA.912.P.1.2

n! n! 1. Formulas given: n Pr =

( n − r )! and n Cr =

r !(n − r )! D. Determine the probability that an event will occur for independent and dependent events. (11.7)

MA.912.P.2.1

 12 days

Springboard Activities / Exam Review 7 days