Last Updated February 17, 2001
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Platte Canyon High School Mathematics and Science |
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Algebra 2 I.
Introduction
A.
Numbers and Variables
1.
Identify number properties such as commutative, associative,
distributive, and inverse and identity elements for addition and multiplication.
2.
Distinguish and use the appropriate notation for natural number,
whole number, integer, rational and real number systems. 3.
Distinguish between exact values and estimated values of numbers.
(i.e.. √2 and 1.41)
4.
Scientific Notation a.
Recognize and convert between decimals and scientific notation. b.
Multiply and divide numbers expressed in scientific notation.
5.
Rules of Exponents
a.
Add and subtract expressions containing exponents.
b.
Multiply and divide expressions containing exponents.
c.
Raise expression containing exponents to powers.
6.
Use formulas to find missing values.
B.
Finance
1.
Checking Accounts a.
Write checks, deposit slips and keep an accurate check register.
b.
Reconcile a checking account from a bank statement.
2.
Credit and Financing Loans a.
Use the simple interest formula to find the interest on a given amount of
money. b.
Use the TI-83 calculator to find the missing value ( number of payments,
interest, payment, present value, future value) for a given loan or saving
situation. c.
Compute the amount of interest paid on a loan and compare consumer
situations. II.
One Variable Statistics A.
Find the mean, median, and mode of a given data set and explain which
best represents the data sat.
B.
Draw a box plot by hand and find the five summary values.
C.
Find the interquartile range and describe the outliers mathematically.
D.
Display and organize data in a histogram, box plot, circle graph, and
stem and leaf. III.
Two Variable Statistics and Data Analysis
A.
Use variables in situations and experiments
1.
Experiments
a.
Design and conduct an experiment.
b.
Collect and analyze the data.
c.
Graph the data and find the graph of best fit. 2.
Collect and record data to the appropriate number of digits based on the
measuring instrument.
3.
Distinguish between accuracy and precision.
B.
Distinguish between functions and relations.
C.
Consider guideline and criteria for a best-fit line.
D.
Draw a best-fit line from data that is approximately linear data.
E.
Find the slope of a line when given two points, the equation, or a graph.
F.
Find the point-slope form of a linear equation given two points.
G.
Write the equation of a line when given its graph or sufficient
information
about its graph.
H.
Analyze data pairs and determine which are independent values and which
are dependent values.
I.
Interpolate and extrapolate with a linear model and identify
inherent
difficulties involved. J.
Provide real-world meanings for values and variables of a linear model
and for answers obtained with the model.
K.
Learn the median-median best-fit procedure. L.
Calculate the median-median line as a model for a given data set without
using the built-in calculator routine. M.
Calculate and use standard deviation of one variable data by hand and
using the calculator to describe variability of data.
N.
Calculate and use standard error and residuals of two variable data to
describe variability of data.
IV.
Linear Functions
A.
Equations - y = mx + b and Ax + By = C
1.
Analyze linear functions by equations, tables, graphs, and
situations.
2.
Solve linear equations algebraically.
3.
Analyze and explain the behaviors, transformations, and general
properties of linear functions from an algebraic, graphic,
and tabular approach. (y =
mx + b and Ax + By = C)
B.
Find the slope and intercepts of any linear function given any of
the
four representations.
C.
Experiment with and discover relationships involving mid-points, parallel
lines, perpendicular lines and slopes. V.
Absolute Value
A.
Equation y = a|x - h| + k
1.
Analyze absolute value functions by equations, tables, graphs,
and situations.
2.
Solve absolute value equations algebraically.
3.
Analyze and explain the behaviors, transformations, and general
properties of absolute value functions from an algebraic,
graphic, and tabular approach (y
= a|x - h| + k).
B.
Find the slopes, intercepts and vertex of any absolute value function
given any of the four representations. VI.
Quadratic
A.
Equations y = (x - r1)(x - r2) ; y
= ax2 +bx + c and y = a(x - h)2 + k
1.
Analyze quadratic functions by equations, tables, graphs, and
situations.
2.
Solve quadratic equations algebraically.
3.
Analyze and explain the behaviors, transformations, and general
properties of quadratic functions from an algebraic, graphic, and
tabular approach (y = (x - r1)(x -
r2); y = ax2 +bx + c
and y = a(x - h)2 + k).
B.
Find the intercepts, vertex (maximum or minimum) and the axis of
symmetry of any quadratic function given any of the four representations.
C.
Determine the nature of the roots using the discriminant.
D.
Imaginary Numbers
1.
Discuss how imaginary numbers fit into our number system.
2.
Find imaginary roots for quadratic functions and discuss the
way they appear on a real number graph of a quadratic
function. VI.
Root Functions
A.
Equation y = a(x - h)(1/n) + k
1.
Analyze root functions by equations, tables, graphs, and
situations.
2.
Solve root equations algebraically.
3.
Analyze and explain the behaviors, transformations, and general
properties of root functions from an algebraic, graphic,
and tabular approach (y =
a(x - h)(1/n) + k)
B.
Find the intercepts and endpoint of any root function given any of the
four representations.
C.
Use function notation to find values of root functions.
D.
Recognize and convert root functions from fractional exponents and
root notation. E.
Distinguish between exact values and estimated values of numbers.
(i.e..
√2 and 1.41) VII.
Inequalities and Systems of Equations A.
Solve one variable linear and absolute value inequalities with
conjunctions and disjunctions.
B.
Solve one variable quadratic inequalities with sign graphs.
C.
Solve two variable systems of equalities graphically and algebraically.
1.
Linear-linear
2.
Linear-quadratic
3.
Quadratic-quadratic
D.
Solve two variable systems of inequalities graphically
1.
Linear-linear
2.
Linear programming
3.
Linear-quadratic
4.
Quadratic-quadratic
VIII.
Cubic and Power Functions A.
Use real world examples, patterns, and finite differences (tables) to
identify cubic and power functions.
B.
Graphs, Tables, and Rules
1.
Graph cubic and power functions by paper-and-pencil, calculator,
and/or computer.
2.
Solve problems involving cubic and power situations.
3.
Experiments (problem solving)
a.
Design and conduct an experiment.
b.
Collect and analyze the data.
c.
Graph the data and find the curve of best fit.
C.
Slope, Intercepts, Points of Inflection, and Symmetry
1.
Discuss slope and rate of change for cubic and power functions.
2.
Using graphs and tables, find the intercepts of cubic and power
functions.
3.
Find the local minimum and/or local maximum and the point of
inflection for a given cubic and/or power function; discuss the significance. 4.
Discuss symmetry around the point of inflection and/or the line of
symmetry for cubic and power functions.
5.
Discuss odd and even symmetry.
D.
Cubic and Power Equations and Functions
1.
Derive cubic functions from graphs and tables.
2.
Analyze cubic functions from equations, tables and graphs.
3.
Find the zeros graphically and the roots algebraically.
E.
Analyze and explain the behaviors, transformations, and general properties
of cubic and power functions from an algebraic, graphic, and
tabular approach. F.
Compare and contrast cubic and power functions with the previously
learned functions. G.
Find and recognize the relationship between a power function and its
inverse; find the composition of a power function and its inverse. IX.
Rational Functions
A.
Use real world examples and patterns to identify rational functions.
B.
Graphs, Tables, and Rules
1.
Graph rational functions by paper-and-pencil, calculator,
and/or computer.
2.
Solve problems involving rational situations.
3.
Experiments (problem solving)
a.
Design and conduct an experiment.
b.
Collect and analyze the data.
c.
Graph the data and find the curve of best fit.
4.
Discuss exponent rules, complex fractions and clearing fractions.
C.
Slope, Intercepts, Asymptotes, and Symmetry
1.
Discuss slope and rate of change for rational functions.
2.
Using graphs and tables, find the intercepts of rational functions.
3.
Discuss symmetry for rational functions. 4.
Discuss asymptotes and limits and their impact on domain and range.
D.
Rational Equations and Functions
1.
Derive rational functions from graphs, tables, and situations.
2.
Analyze rational functions from equations, graphs, tables, and
situations.
3.
Find the zeros graphically and the roots algebraically.
4.
Identify rational equations as inverse variations.
5.
Recognize the different forms (proper and improper) of rational
equations and convert (long divide or multiply) between them.
E.
Analyze and explain the behaviors, transformations, and general properties
of rational functions from algebraic, graphic, and tabular
approach.
F.
Systems of equations
1.
Linear and Rational
a.
Solve systems of linear and rational equations graphically. b.
Solve systems of linear and rational equations algebraically.
2.
Quadratic and Rational a.
Solve systems of quadratic and rational equations graphically. b.
Solve systems of quadratic and rational equations algebraically. G.
Compare and contrast rational functions with previously learned
functions. X.
Exponential and Logarithmic Functions
A.
Use real world examples, patterns, and finite differences (tables) to
identify exponential and logarithmic functions.
B.
Graphs, Tables, and Rules 1.
Graph exponential and logarithmic functions by paper-and-pencil,
calculator, and/or computer.
2.
Solve problems involving exponential and logarithmic situations.
3.
Experiments (problem solving)
a.
Design and conduct an experiment.
b.
Collect and analyze the data.
c.
Graph the data and find the curve of best fit. 4.
Develop tables for exponential functions and discuss the meaning of
negative exponents and exponent rules for operations.
5.
Investigate the rules for logarithms.
C.
Slope, Intercepts and Symmetry
1.
Discuss slope and rate of change for exponential and logarithmic
functions.
2.
Using graphs and tables, find the intercepts of exponential and
logarithmic functions. 4.
Discuss symmetry around the
line y = x for inverse functions. (i.e.
for exponential and logarithmic functions)
5.
Discuss asymptotes and limits.
D.
Exponential and Logarithmic Equations 1.
Derive exponential and logarithmic equations from graphs, tables, and
situations. 2.
Analyze exponential and logarithmic functions from equations, graphs,
tables, and situations.
3.
Find the zeros graphically. E.
Analyze and explain the behaviors, transformations, and general
properties of exponential and logarithmic functions from a symbolic, graphic,
and tabular approach.
F.
Systems of equations
G.
Compare and contrast exponential and rational functions with
previously
learned functions.
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Last Updated February 17, 2001
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