Download Algebra II - Lisle CUSD 202

MATHEMATICS PHILOSOPHY
Mathematics is the language used to identify and describe patterns enabling us to make predictions. The study of mathematics includes numbers and
shapes as well as operations and relationships. It includes arithmetic, measurement, algebra, geometry, trigonometry, probability and statistics.
The Mathematics Department of Lisle District 202 will ensure that all students in their study of mathematics have opportunities to become proficient with
algorithms and acquire an understanding of concepts which enable them to apply their knowledge to new situations. This will be done by investigating,
reasoning, visualizing, and problem solving. Students will communicate their findings both verbally and in written form.
MATHEMATICS
Applied Math
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Use order of operations and work with powers and square roots
Explore and solve one-step equations
Perform operations using positive and negative integers
Solve multi-step equations
Explore data and graphs
Develop skills needed to factor and simplify variable expressions
Solve problems using fractions, percents and decimals
Develop proportional reasoning
Explore linear equations, data, and polynomials
Solve problems by finding patterns
Compute the amount needed to finance a new car
Identify different types of automobile insurance
Solve problems by using a map
Determine the cost of a trip, including gasoline or car rental,
meals, and hotels
Solve problems by projecting estimates
Determine the dimensions of a scale drawing
Estimate quotients, using compatible numbers
Applied Geometry
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Measure and classify angles
Do basic constructions with a compass and a straightedge
Understand and write basic geometric proofs
Name congruent triangles and their corresponding parts
Use congruent triangles to justify constructions
Classify polygons
Use the properties of parallelograms, rectangles, rhombuses, and squares
Find the area of a rectangle, a square, a parallelogram, a triangle, and a trapezoid
Find the circumference and the area of a circle
Solve problems using proportions
Make maps and scale drawings
Find the lateral area, total area, and volume of a right prism, cylinder, regular pyramid, right circular cone, and a sphere.
Use right triangles to solve problems involving pyramids
and cones
Use the tangent, sine, and cosine ratios of an acute angleof a right triangle
Find the distance between two points in the coordinate plane
Find the slope of a line
Explorations in Geometry
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Use the software, Geometry Sketchpad, to make geometric conjectures.
Use inductive and deductive reasoning skills.
Define and construct paragraph and formal proofs.
Perform transformations including translations, reflections, and rotations.
Solve problems involving perpendicular and parallel lines in the coordinate plane.
Prove triangles congruent and their use in solving real-life problems.
Explore properties of polygons.
Use properties of proportion with similar polygons.
Study right triangles and trigonometric ratios.
Explore segments and angles as they relate to circles.
Solve problems using area, volume, and surface area.
Algebra I Part I
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Use graphs to display data relationships
Use variables to model relationships
Organize data in matrices
Analyze data using scatter plots
Model and solve two-step equations
Use probability and logical reasoning
Solve proportions and inequalities using addition, subtraction, multiplication and division
Solve multi-step and compound inequalities
Understand slope and its applications
Understand rates of change
Write the equation of a line in standard form
Solve systems by graphing, substitution, and elimination methods
Algebra I Part II
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Graph systems of linear equations and inequalities
Solve linear equations using substitution and linear combinations
Solve problems using multiplication and division of exponents
Use zero and negative exponents to solve problems
Use scientific notation to solve problems
Solve problems using exponential growth and decay
Use square roots to solve problems
Simplify radicals
Solve quadratic equations by graphing and quadratic formula
Graph quadratic inequalities
Add, subtract, and multiply polynomials
Factor polynomials
Use rules to solve special products of polynomials
Solve problems using proportions
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Solve problems using direct and inverse variation
Add, subtract, multiply, and divide rational expressions
Solve rational expressions
Solve radical expressions and equations
Use the Pythagorean Theorem and its converse
Solve problems using the distance and midpoint formulas
Algebra I
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Make an algebraic model and solve simple real-life problems
Use tables to organize data and graphs to model data visually
Organize data in a matrix
Solve linear equations
Solve literal equations
Sketch a scatter plot of a data collection and use a scatter
plot to recognize patterns
Interpret slope as a constant or average rate of change
Approximate solutions of real-life problems by using a graph
Model a real-life situation using the slope intercept model,
and the point-slope model
Find a linear equation that approximates a set of data points
Find a best-fitting line for a collection of data points
Solve and graph simple linear inequalities
Solve a system of linear equations by graphing, substitution and linear combinations
Use models for exponential growth and decay to solve real-life problems
Use the Pythagorean Theorem to solve problems
Use quadratic models in real-life problems
Solve proportions
Solve rational equations
Geometry
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Use inductive and deductive reasoning skills
Perform transformations including translations, reflections, and rotations
Define and construct informal proofs
Define formal proof and link steps of geometric proofs
Define and use reflectional and rotational symmetry
Prove theorems using postulates and properties
Solve problems involving perpendicular and parallel lines in the coordinate plane
Solve problems using area formulas
Solve problems using the formulas for circumference and area of a circle
Develop an understanding of volume and surface area
Develop an understanding for the concept of maximizing volume while minimizing surface area
Use scale factor to enlarge or reduce a figure
Use properties of proportion with similar polygons
Explore properties of triangles, quadrilaterals and other polygons
Explore segments and angles as they relate to circles
Algebra II with Trigonometry
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Solve and graph linear equations
Use problem-solving strategies to solve real-life problems
Use equations to solve problems
Fit a line to a set data
Graph, solve, and use a system of linear equations
Use linear programming to answer questions
Solve a system of linear equations in three variables
Solve any quadratic equation
Identify a relation and a function
Use translations and reflections to sketch the graph of a function
Find the mean, median, mode, and quartiles of a set of numbers
Solve equations that have radicals and rational exponents
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Graph exponential functions and evaluate exponential expressions
Solve exponential equations
Find the rational zeros of a polynomial function
Find the range and standard deviation of a collection of numbers
Solve equations that contain rational expressions
Use trigonometric relationships to evaluate
the trigonometric functions of acute angles
Algebra II
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Solve linear equations
Define a function and find the domain and range
Define a one-to-one function and find the inverse of a function
Find all the roots and zeros of polynomials
Decompose rational expressions into partial fractions
Graph exponential functions
Solve exponential and logarithmic equations
Solve systems by graphing, substitution, elimination, and augmented matrix methods
Solve non-linear equations
Evaluate linear programming problems
Solve linear equations using matrices
Find a certain number of terms for sequences and series
Interpret mathematical induction
Find and graph the equation of a parabola, ellipse, and hyperbola
Choose a sample space, and find the probabilities for simple events
Distinguish between theoretical and empirical probability as well as statistics versus probability theory
Explorations in Algebra II
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Review and expand on basic problem solving strategies in algebra
Evaluate matrix addition, subtraction, and multiplication
Solve systems using matrices
Explore determinants and inverse matrices
Write and graph equations of lines
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Fit a line or curve of best fit to real life data
Factor quadratic and cubic functions
Work with the complex number system
Graph polynomial, rational, logarithmic, and exponential functions
Solve problems involving logarithmic and exponential functions
Understand trigonometric ratios and functions
Solve equations using inverse trigonometric functions
Work with trigonometric identities
Pre-calculus
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Find composite functions
Solve systems of equations graphically and algebraically
Solve systems of equations by using inverses of matrices
Solve systems of equations by using matrices
Use linear programming procedure to solve problems
Determine the inverse of a relation or function
Graph a function and its inverse
Graph rational functions
Find the critical points of the graph of a polynomial function and determine if each is a minimum, maximum, or point of inflection
Determine continuity or discontinuity of functions
Identify the end behavior of graphs
Determine roots of polynomial equations
Graph quadratic equations and inequalities
Approximate the real zeros of a polynomial function
Solve rational equations and inequalities
Solve radical equations and inequalities
Find exact values for the six trigonometric functions of special angles
Solve right triangles
Solve triangles by using the law of sines and law of cosines
Evaluate inverse trigonometric functions
Graph inverses of trigonometric functions
Use the basic trigonometric identities to verify other identities
Solve trigonometric equations
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Use the standard and general forms of the equations of a circle, parabola, hyperbola, and ellipse
Graph and solve systems of second-degree equations and inequalities
Graph exponential functions and inequalities
Explorations In Pre-calculus
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Find exact values for the six trigonometric functions of special angles
Solve right triangles
Solve triangles by using the law of sines and law of cosines
Evaluate inverse trigonometric functions
Graph trigonometric functions and their inverses
Use the basic trigonometric identities to verify other identities
Solve trigonometric equations
Use the standard and general forms of the equations of a circle, parabola, hyperbola, and ellipse
Find the nth term of an arithmetic or geometric sequence
Find the sum of n terms of an arithmetic or geometric series
Find the limit of the terms of an infinite sequence
Find the sum of an infinite geometric series
Use sigma notation to write, expand, and solve problems
Graph polar numbers and equations
Write complex numbers in polar form
Find powers and roots of complex numbers in polar form using DeMoivre’s Theorem
Probability and Statistics
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Display, describe and interpret distributions
Compute the equation of the regression line
Explain the difference between observational and experimental study
Identify the properties of normal distribution
Use the central limit theorem to solve problems
Find the mean, variance, and standard deviation of a binomial experiment
Find the confidence intervals for the mean
Use chi-square distributions to calculate confidence distribution
Calculus
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Find limits graphically, numerically, and analytically
Use limits to solve application problems
Find the derivative of a function using the limit definition
Analytically find the first and second derivatives of various functions
Use derivatives in real life application problems
Find equations of tangent lines
Describe and find critical numbers and points of inflection of a function
Use optimization techniques in application problems
Use the Fundamental Theorem of Calculus to find the value of definite integrals
Find derivatives and integrals of expressions involving transcendental functions
Use substitution to integrate functions
Use techniques of integration to find areas under curves & volumes of solids of revolutions
Use techniques of integration to solve application problems involving arc lengths, surfaces of revolution, work, fluid pressure and fluid force
VISION STATEMENT
LISLE COMMUNITY SCHOOL
DISTRICT # 202
believes that we must provide an educational environment which grants each student access to the highest quality and richest variety of integrated
educational experiences, within our means. This environment will be created with the assistance of student’s family, local businesses, educational
agencies, and community and support groups. Our goal is continuous, measurable improvement, and excellence in the education of our students.
The Mission of
School District 202
The Mission of School District 202 is to promote excellence in the Lisle Community Unit School District #202 Schools by providing a challenging,
comprehensive, and viable educational program for all students, that will lead to the attainment of knowledge, competencies and skills, which, upon
completion, will enable our students to be successful life-long learners, and productive members of society.
Board of Education
Adminstration
Pam Ahlmann, President
Janna Sampson, Vice-Pres.
Kari Altpeter, Secretary
Amy Narot
Robert Tarasewicz
Pat Sarb
Joan Costin
Dr. Patricia Wernet, Superintendent
Keith Filipiak, Assistant Supt For Business Affairs
Dr. Christine A. Messina, Director of Curriculum
Karen Gordon, Director of PPS
Pete Sullivan, Principal
Mark Cunningham, Assistant Principal
Department Head – Grade 6 –12 – Mike Coit