Algebra 2H Syllabus
Text: Algebra and Trigonometry: Graphs and Models, 5/E
Marvin L. Bittinger
David J. Ellenbogen
Judith A. Beecher
Judith A. Penna
ISBN-10: 0321783972
ISBN-13: 9780321783974
1st Trimester
Unit 1: Linear Equations
R.5
The Basics of Equation Solving
 zero product property
 linear equations (including clearing the fraction)
 factorable polynomial equations
 solving graphically on TI (Supplement #U1Z)
R.1
The Real-Number System (Supplement #U1A)
 number sets – real, rational, irrational, and integers
 properties of real numbers
1.1
Introduction to Graphing
 ordered pairs
 use of graphing calculator (table and graphing window) (Supplement #U1B)
 skip distance & midpoint formulas and circles
1.3
Linear Functions, Slope and Applications
 slope as average rate of change
 introduce function notation from 1.4
 f ( x ) = mx + b , graphing by hand
 vertical and horizontal lines
1.4
Equations of Lines and Modeling
 point-slope form
 standard form ( Ax + By = C ) with integral coefficients (NOTE: not in text)
 parallel and perpendicular lines
1.5
Linear Equations, Functions, and Models
 solving a formula for a variable (literals) – include factoring a GCF
 solving linear equations
 word problems using linear equations
 zeros of a linear function (algebraically & graphically)
9.1
Systems of Equations in Two Variables
Revised 5/24/12
Page 1 of 5
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9.2
solving graphically, by substitution, and by elimination (supplement #U1C)
skip consistent vs. inconsistent
Systems of Equations in Three Variables
 elimination &/or substitution method, and graphical representation
 special case of no solution & infinitely many solutions, & the graphical representation of
the special cases
 word problems (supplement #U1D)
Unit 2: Quadratics (exponents & radicals)
R.2
Integer Exponents
 properties of exponents including variable exponents
R.6 & R.7
Radical Notation and Rational Exponents
 principal positive root
 operations with square and cube roots (Supplement #U2A)
[TEACHER NOTE: be sure to review FOIL here]
 operations with radicals of higher indices
 need of absolute value for even indices ( x 2 = x )
 rationalizing denominators (conjugates and cube root monomials)
a
 use of rational exponents: x b = b x a (converting, simplifying, writing as a single radical)
 Skip: Pythagorean Theorem
Practice with Basic Algebra Rules & Common Errors (Supplement #U2B)
3.1
The Complex Numbers
 definition of i
 simplifying and operations with radicals of negative numbers (Supplement #U2C)
 operations with imaginary numbers
 complex conjugates
 powers of i
R.4
Factoring
 GCF
 factoring by grouping
 factoring trinomials
 difference of squares
 sum and difference of cubes
 mixed factoring (Supplement #U2D)
3.2
Quadratic Equations, Functions & Models
 solving quadratics by factoring, principle of square roots, completing the square,
quadratic formula
 discriminant
 graphically solving equations and finding zeros of functions (Supplement #U2E)
 Skip: finding the range using TI
Revised 5/24/12
Page 2 of 5
3.3
Analyzing Graphs of Quadratics Functions
 graphing parabolas by hand using h/k form (Supplement #U2G and #U2H)
[TEACHER NOTE: introduce interval notation here when covering realistic values
for the independent variable]
 completing the square
 using -2ba , f -2ba to find the vertex
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3.4
( ( ))
Writing quadratic function given special points (vertex, x-intercepts, etc.) (Supplement #U2J)
math modeling with quadratic word problems (Supplement #U2K)
[TEACHER NOTE: emphasize sketching of quadratic graphs to aid in working
through application problems – when students claim they “don’t know”….]
quadratic min/max word problems (Supplement #U2K)
More Equation Solving
 radical equations including those with extraneous solutions
 identifying & solving equations reducible to quadratic (Supplement #U2F)
2nd & 3rd Trimester
Unit 3: Transformations, Functions and More
R.6
Rational Expressions
 multiplying and dividing
 addition and subtraction
 complex rational expressions
3.4/3.5
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More Equation Solving
rational equations
revisit extraneous solutions
equations with absolute value (including two absolution value terms)
rational literals
1.2
Functions and Graphs
 definition
 independent and dependent variable/ input and output values
 domain and range
 relation vs. function
 function notation
 vertical line test
2.3
The Algebra of Functions
 composite functions and their domains
2.4
Symmetry and Transformations
 graphs of toolkit functions: x , x 2 ,
Revised 5/24/12
x , x 3,
3
x , 1x , x
Page 3 of 5
 transformations of functions (translations, reflections, horiz. & vert. stretches and
compressions); NO combination of horiz. changes f ( b( x - c ))
 symmetry, even/odd
 f x and f ( x)
R.3
Addition, Subtraction, and Multiplication of Polynomials
 polynomial vocabulary (p. 17-18)
 addition, subtraction, multiplication (including variable exponents)
4.1 – 4.3
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4.5
Polynomial Functions
identifying polynomials (and what is not a polynomial)
classifying polynomials in terms of degree and number of terms
end behavior (leading term test)
long division, synthetic division & p/q
graphing polynomial functions – including tangent points & change in concavity
Rational Functions
o holes, asymptotes
o end behavior (horizontal & slant/oblique asymptotes)
Direct & Inverse Variation
2.5
Unit 4: Exponential, Logarithmic and Inverse Functions
5.2
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Exponential Functions and Graphs
definition of exponential functions and basic characteristics
graphs of exponential functions
nt
compound interest formula: A = P (1 + rn )
definition of e
graphs with e
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Solving Exponential Equations
solving exponential equations by getting the same base
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Inverse Functions
inverse relations
one-to-one functions
horizontal line test
finding inverse functions
restricting the domain to create a one-to-one function
graphs of inverse relations
f f -1 ( x) = x and f -1 ( f ( x)) = x
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Logarithmic Equations and Functions
Definition of a logarithm
graphing logarithmic functions
natural logs
5.5
5.1
5.3
(
Revised 5/24/12
)
Page 4 of 5
5.5, 5.6 & 5.2 Applying Logarithms to solve Exponential Equations
 using logarithms to solve exponential equations
 using logs to write an inverse of an exponential function
Unit 5: Statistics Across the Curriculum – (not in text)
One Variable Statistics
 mean, median, mode (advantages & disadvantages of each) (Suppl. #U5A)
 frequency bar graphs (Supplement #U5A)
 descriptions of data (normal-, bimodal, skewed) (Supplement #U5A)
 percentiles (Supplement #U5B)
 standard deviation (Supplement #U5C)
 Z-scores & the Empirical Rule (Supplement #U5D)
Two-Variable Statistics
 linear regression including correlation coefficient (r2), interpolating & extrapolating
(Supplement #U5E)
 Median-median line (Supplement #U5F)
 residuals, residual plots and model choice (Supplement #U5G)
Unit 6: Inequalities
1.6
Solving Linear Inequalities
 compound inequalities - union and intersection (Supplement #U6A)
 absolute value inequalities
4.6
Polynomial Inequalities
 solving polynomial inequalities by hand by sketching a related function & finding the
zeros
 solving related one variable & two variable equations & inequalities (Supplement #U6B)
9.7
Systems of Inequalities and Linear Programming
 inequalities in two variables
 systems of inequalities (Supplement #U6C)
 linear programming (Supplement #U6D)
Unit 7: Combinatorics (Chapter 10)
11.5-11.6
 the fundamental counting principle, combinations and permutations
Revised 5/24/12
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