Download INTRODUCTION - Warrior Run School District

WARRIOR RUN SCHOOL DISTRICT
WARRIOR RUN HIGH SCHOOL
MATH CURRICULUM
ALGEBRA II
PREPARED BY:
MATH TEACHERS
SUBMITTED:
JUNE 2007
INTRODUCTION
The early units of Algebra II review the topics of elementary algebra stressing those
concepts and skills necessary for success in the remainder of the course. New material is
introduced while continuing to build and strengthen basic concepts and skills. The later units
contain such concepts as relations, functions, sequences and series, infinite geometric series and
basic concepts of probability and statistics.
EXPECTED LEVELS OF ACHIEVEMENT
Most students taking this course are college-bound juniors. A grade of 80% overall is
expected. Past experience indicates that students able to maintain 80% or better are prepared to
succeed in Trigonometry or Probability and Statistics and on the SAT examination. A list of
expectations follows:
1) Students are expected to attain an average grade of 80% on all tests and quizzes.
2) Students are expected to complete all homework assignments. Homework will be
part of each nine weeks’ average.
3) Students will be able to master 80% of all written objectives as outlined in each unit
of instruction.
4) Students will have a working knowledge of algebraic concepts which can be applied
in both the academic setting and in practical application in daily living situations.
PROCEDURES FOR EVALUATION
Students will be evaluated using a variety of measurements. Grades will be determined
on a percentage basis as outlined in the teacher’s course description. Evaluation will be based on
the following:
1)
2)
3)
4)
Tests
Quizzes, announced and unannounced
Homework
Class participation
2
REFERENCES
Textbook: Intermediate Algebra 7th Ed.
(Gustafson/Frisk)
TIMELINE
Unit 1
A Review of Basic Algebra
6.5 weeks
Unit 2
Graphs, Equations of Lines, and Functions
4 weeks
Unit 3
Systems of Equations
2.5 weeks
Unit 4
Inequalities
3 weeks
Unit 5
Polynomials and Polynomial Functions
4.5 weeks
Unit 6
Rational Expressions
4 weeks
Unit 7
Radicals and Rational Exponents
4 weeks
Unit 8
Quadratic Functions
1 week
Unit 9
Circles and Parabolas
1 week
Unit 10
Arithmetic and Geometric Sequences
1 week
Unit 11
Probability and Statistics
2.5 weeks
TOTAL:
34 weeks
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UNIT 1
A REVIEW OF BASIC ALGEBRA
OBJECTIVES
Students will be able to:
1) simplify/evaluate expressions involving positive and negative exponents, roots,
and/or absolute value. Std. 2.1.11A
2) simplify/evaluate expressions involving multiplying with exponents, powers of
powers, and powers of products. Std.2.1.11A
3) simplify/evaluate expressions using the order of operations to solve problems.
Std. 2.2.8A
4) express numbers and/or simplify expressions using scientific notation.
2.1.11A
5) write, solve and/or apply a linear equation.
Std.
Std. 2.8.11.N and 2.8.11.D
6) name the basic sets of numbers, assign a number to the most restrictive set, and
correctly label one set as a subset of another. Std. 2.8.8.A
7) identify the properties of the real numbers and apply them to algebraic expressions.
Std. 2.2.11.A
CONTENT
1) The Real Number System (Obj. 1 and 6)
2) Arithmetic and Properties of Real Numbers (Obj. 1, 2, and 7)
3) Exponents (Obj. 1, 2, and 3)
4) Scientific Notation (Obj. 4)
5) Solving Equations (Obj. 5)
6) Using Equations to Solve Problems (Obj. 5)
7) More Applications of Equations (Obj. 5)
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UNIT 2
GRAPHS, EQUATIONS OF LINES, AND FUNCTIONS
OBJECTIVES
Students will be able to:
1) identify or graph functions, linear equations or linear inequalities on a
coordinate plane. Stds. 2.8.11.J and 2.9.11.G
2) calculate the distance and/or midpoint between 2 points on a number line or
on a coordinate plane. Stds. 2.8.11.J and 2.9.11.G
3) compute the slope and/or y-intercept represented by a linear equation or
graph. Stds. 2.8.11.J and 2.9.11.G
4) relate slope to perpendicularity and/or parallelism. Stds. 2.8.11.J and
2.9.11.G
5) apply the formula for the slope of a line to solve problems.
2.8.11.L
Std.
6) given the graph of the line, 2 points on the line, or the slope and a point on a
line, write or identify the linear equation in point-slope, standard and/or slopeintercept form. Std. 2.8.11.L
7) determine if a relation is a function given a set of points or a graph. Std.
2.8.11.O
8) identify the domain and domain of a relation. Std. 2.8.11.O
CONTENT
1) Graphing Linear Equations (Obj. 1 and 2)
2) Slope of a Nonvertical Line (Obj. 3 and 4)
3) Writing Equations of Lines (Obj. 5 and 6)
4) Introduction to Functions (Obj. 7 and 8)
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UNIT 3
SYSTEMS OF EQUATIONS
OBJECTIVES
Students will be able to:
1) write and/or solve systems of equations using graphing, substitution and/or
elimination. Stds. 2.8.11.F and 2.8.11.H
2) solve systems of 3 equations in 3 variables using elimination.
2.8.11.H
Std.
CONTENT
1) Solution by Graphing (Obj. 1)
2) Solution by Elimination (Obj. 1)
3) Solutions of Three Equations in Three Variables (Obj. 2)
UNIT 4
INEQUALITIES
OBJECTIVES
Students will be able to:
1) solve compound inequalities and/or graph their solution sets on a number line
including absolute value inequalities. Std. 2.8.11.H and 2.8.11J
2) identify or graph functions, linear equation or linear inequalities on a coordinate
plane. Stds. 2.8.11.H and 2.8.11.J
CONTENT
1) Linear Inequalities
(Obj. 1 and 2)
2) Equations and Inequalities with Absolute Value (Obj. 1 and 2)
3) Linear Inequalities in Two Variables (Obj. 2)
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4) Systems of Inequalities (Obj. 2)
UNIT 5
POLYNOMIALS AND POLYNOMIAL FUNCTIONS
OBJECTIVES
Students will be able to:
1) describe a given polynomial with respect to type, degree and identification of
coefficient and variable. Std. 2.8.11.S
2) add, subtract and/or multiply polynomial expressions, expressing answers in
simplest form. Std. 2.8.11.S
3) factor algebraic expressions, including difference of squares and trinomials.
Std. 2.8.11.S
4) solve quadratic equations using factoring. Std. 2.8.11.N
5) evaluate polynomial functions. Std. 2.8.11.S
CONTENT
1) Polynomials and Polynomial Functions (Obj. 1 and 5)
2) Adding and Subtracting Polynomials (Obj. 2)
3) Multiplying Polynomials (Obj. 2)
4) The Greatest Common Factor and Factoring by Grouping (Obj. 3)
5) The Difference of Two Squares; the Sum and Difference of Two Cubes
(Obj. 3)
6) Factoring Trinomials (Obj. 3)
7) Summary of Factoring Techniques (Obj. 3)
8) Solving Equations by Factoring (Obj. 4)
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UNIT 6
RATIONAL EXPRESSIONS
OBJECTIVES
Students will be able to:
1) simplify a given rational expression. Std. 2.8.11.S
2) solve problems involving proportions. Std. 2.8.11.P
3) solve variation problems (direct, inverse, joint, and combined).
2.8.11.P
4) multiply and divide rational expressions. Std. 2.8.11.S
5) simplify complex fractions. Std. 2.8.11.S
6) solve a rational equation. Std. 2.8.11.N
7) solve applied problems using similar triangles. Std. 2.8.11.P
CONTENT
1) Rational Functions and Simplifying Rational Expressions (Obj. 1)
2) Proportion and Variation (Obj. 2, 3, and 7)
3) Multiplying and Dividing Rational Expressions (Obj. 4)
4) Complex Fractions (Obj. 5)
5) Equations Containing Rational Expressions (Obj. 6)
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Std.
UNIT 7
RADICALS AND RATIONAL EXPONENTS
OBJECTIVES
Students will be able to:
1) write radical expressions in simplest form. Std. 2.1.11.A
2) simplify square roots where the radicand is any real number.
2.1.11.A
Std.
3) solve problems dealing with Pythagorean Theorem and/or distance formula
(radicals involved). Std. 2.1.11.A
4) convert from rational exponent notation to radical notation and vice versa.
Std. 2.1.11.A
5) add and subtract radical expressions. Std. 2.8.11.S
6) multiply and divide radical expressions. Std. 2.8.11.S
7) solve radical equations. Std. 2.8.11.N
8) write complex numbers in simplified a + bi form. Std. 2.8.11.S
CONTENT
1) Radical Expressions (Obj. 1 and 2)
2) Applications of Radicals (Obj. 3)
3) Rational Exponents (Obj. 4)
4) Simplifying and Combining Radical Expressions (Obj. 1 and 5)
5) Multiplying and Dividing Radical Expressions (Obj. 6)
6) Radical Equations (Obj. 7)
7) Complex Numbers (Obj. 8)
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UNIT 8
QUADRATIC FUNCTIONS
OBJECTIVES
Students will be able to:
1) solve quadratic equations by factoring. Std. 2.8.11.N
2) solve quadratic equations by completing the square. Std. 2.8.11.N
3) solve quadratic equations by using the quadratic formula.
2.8.11.N
Std.
CONTENT
1) Quadratic Equations (Obj. 1, 2, and 3)
UNIT 9
CIRCLES AND PARABOLAS
OBJECTIVES
Students will be able to:
1) recognize a circle or parabola by looking at the form of the equation.
2.9.11.G
2) determine the direction which a parabola opens, given the equation of
the parabola. Std. 2.9.11.G
3) complete the square to find the vertex of the parabola y = ax2 + bx + c.
Std. 2.9.11.G
4) determine the center and radius of a circle, given equation of the circle.
Std. 2.9.11.G
5) graph a circle by finding the center and radius. Std. 2.9.11.G
6) graph a parabola by finding the vertex and plotting points.
Std. 2.9.11.G
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Std.
CONTENT
1) Equations of Circles and Parabolas (Obj. 1, 2, 3, and 4)
2) Graphing Circles (Obj. 5)
3) Graphing Parabolas (Obj. 6)
UNIT 10
ARITHMETIC AND GEOMETRIC SEQUENCES
OBJECTIVES
Students will be able to:
1) identify a sequence as being arithmetic and determine its common difference.
Std. 2.11.11D
2) find a specific term of an arithmetic sequence. Std. 2.11.11.D
3) find the sum of n terms of an arithmetic sequence.
Std. 2.11.11.D
4) identify a sequence as being geometric and determine its common ratio.
Std. 2.11.11.D
5) find a specific term of a geometric sequence. Std. 2.11.11.D
6) find the sum of n terms in a geometric sequence. Std. 2.11.11.D
CONTENT
1) Arithmetic Sequences (Obj. 1, 2, and 3)
2) Geometric Sequences (Obj. 4, 5, and 6)
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UNIT 11
PROBABILITY AND STATISTICS
OBJECTIVES
Students will be able to:
1) determine the number of permutations and/or combinations or apply the fundamental
counting principle. Std. 2.7.8.A
2) find probabilities for independent, dependent or compound events and represent as a
fraction, decimal or percent. Std. 2.7.11.E
3) find, convert and/or compare the probability and/or odds of a simple event.
2.7.11.A
Std.
4) calculate or select the appropriate measure of central tendency(mean, median or mode) of
a set of data given as a list of data or presented as a stem-and-leaf plot. Std. 2.6.8.A
5) appropriately display and/or use data in problem-solving settings. Std. 2.6.8.E
6) create and/or use appropriate graphical representations of data, including box-andwhisker plots, stem-and-leaf plots or scatter plots. Std. 2.6.8.E
7) analyze data and/or answer questions based on displayed data (box-and whisker plots,
stem-and-leaf plots or scatter plots). Std. 2.6.8.E
CONTENT
1) Fundamental Rule of Counting (Obj. 1)
2) Permutations and Combinations (Obj. 1)
3) Probability of Independent and Dependent Events (Obj. 2)
4) Odds (Obj. 3)
5) Measures of Central Tendency (Obj. 4)
6) Data Display and Analysis (Obj. 5, 6, and 7)
a- Frequency Tables and Histograms
b- Stem-and-Leaf Plots
c- Box-and-Whisker Plots
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