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School City of Hobart |
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School City of Hobart Mathematics |
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Mathematics - Pre-Calculus |
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Calculus and Pre-Calculus
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Relations and Functions
The learner will be able to
use polynomial, rational, and algebraic functions to write functions and draw graphs to solve word problems, to find composite and inverse functions, and to analyze functions and graphs. They analyze and graph circles, ellipses, parabolas, and hyperbolas.
| Strand |
Source |
| Applying Calculus Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.1.1
The learner will be able to
recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators.
| Strand |
Source |
| Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.1.2
The learner will be able to
find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions. Use paper and pencil methods and graphing calculators.
| Strand |
Source |
| Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.1.3
The learner will be able to
model and solve word problems using functions and equations.
Example: You are on the committee for planning the prom and need to decide what to charge for tickets. Last year you charged $5.00 and 400 people bought tickets. Earlier experiences suggest that for every 10¢ decrease in price you will sell 50 extra tickets. Use a spreadsheet and write a function to show how the amount of money in ticket sales depends on the number of 10¢ decreases in price. Construct a graph that shows the price and gross receipts. What is the optimum price you should set for the tickets?
.
| Strand |
Source |
| Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.1.4
The learner will be able to
define, find, and check inverse functions.
| Strand |
Source |
| Inverses |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.1.5
The learner will be able to
describe the symmetry of the graph of a function.
| Strand |
Source |
| Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.1.6
The learner will be able to
decide if functions are even or odd.
Example: Is the function tan x even, odd, or neither? Explain your answer.
.
| Strand |
Source |
| Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.1.7
The learner will be able to
apply transformations to functions.
| Strand |
Source |
| Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.1.8
The learner will be able to
understand curves defined parametrically and draw their graphs.
| Strand |
Source |
| Graphing Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.1.9
The learner will be able to
compare relative magnitudes of functions and their rates of change.
| Strand |
Source |
| Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Calculus and Pre-Calculus
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PC.1.10
The learner will be able to
write the equations of conic sections in standard form (completing the square and using translations as necessary), in order to find the type of conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.).
| Strand |
Source |
| Conic Sections |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Logarithmic and Exponential Functions
The learner will be able to
solve word problems involving logarithmic and exponential functions. They draw and analyze graphs, and find inverse functions.
| Strand |
Source |
| Logarithmic Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.2.1
The learner will be able to
solve word problems involving applications of logarithmic and exponential functions.
| Strand |
Source |
| Logarithmic Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.2.2
The learner will be able to
find the domain, range, intercepts, and asymptotes of logarithmic and exponential functions.
Example: For the function L(x) = log10 (x - 4), find its domain, range, x-intercept, and asymptote.
.
| Strand |
Source |
| Logarithmic Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.2.3
The learner will be able to
draw and analyze graphs of logarithmic and exponential functions.
Example: In the last example, draw the graph of L(x).
.
| Strand |
Source |
| Logarithmic Functions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.2.4
The learner will be able to
define, find, and check inverse functions of logarithmic and exponential functions.
| Strand |
Source |
| Inverses |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Trigonometry in Triangles
The learner will be able to
define trigonometric functions using right triangles. They solve word problems and apply the laws of sines and cosines.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.3.1
The learner will be able to
solve word problems involving right and oblique triangles.
Example: You want to find the width of a river that you cannot cross. You decide to use a tall tree on the other bank as a landmark. From a position directly opposite the tree, you measure 50 m along the bank. From that point, the tree is in a direction at 37º to your 50 m line. How wide is the river?
.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.3.2
The learner will be able to
apply the laws of sines and cosines to solving problems.
Example: You want to fix the location of a mountain by taking measurements from two positions 3 miles apart. From the first position, the angle between the mountain and the second position is 78º. From the second position, the angle between the mountain and the first position is 53º. How far is the mountain from each position?
.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.3.3
The learner will be able to
find the area of a triangle given two sides and the angle between them.
Example: Calculate the area of a triangle with sides of length 8 cm and 6 cm enclosing an angle of 60º.
.
| Strand |
Source |
| Triangles |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Trigonometric Functions
The learner will be able to
define trigonometric functions using the unit circle and use degrees and radians. They draw and analyze graphs, find inverse functions, and solve word problems.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.1
The learner will be able to
define sine and cosine using the unit circle.
Example: Find the acute angle A for which sin 150º = sin A.
.
| Strand |
Source |
| Unit Circle |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.2
The learner will be able to
convert between degree and radian measures.
Example: Convert 90º, 45º, and 30º to radians.
.
| Strand |
Source |
| Radians/Angles |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.3
The learner will be able to
learn exact sine, cosine, and tangent values for 0, ~/2, ~/3, ~/4, ~/6, and multiples of ~. Use those values to find other trigonometric values.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.4
The learner will be able to
solve word problems involving applications of trigonometric functions.
Example: In Indiana, the day length in hours varies through the year in a sine wave. The longest day of 14 hours is on Day 175 and the shortest day of 10 hours is on Day 355. Sketch a graph of this function and find its formula. Which other day has the same length as July 4?
.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.5
The learner will be able to
define and graph trigonometric functions (i.e., sine, cosine, tangent, cosecant, secant, cotangent).
Example: Graph y = sin x and y = cos x, and compare their graphs.
.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.6
The learner will be able to
find domain, range, intercepts, periods, amplitudes, and asymptotes of trigonometric functions.
Example: Find the asymptotes of tan x and find its domain.
.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.7
The learner will be able to
draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.8
The learner will be able to
define and graph inverse trigonometric functions.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.9
The learner will be able to
find values of trigonometric and inverse trigonometric functions.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.10
The learner will be able to
know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line.
Example: Use a right triangle to show that the slope of a line at 135º to the x-axis is -1.
.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.4.11
The learner will be able to
make connections between right triangle ratios, trigonometric functions, and circular functions.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Trigonometric Identities and Equations
The learner will be able to
prove trigonometric identities, solve trigonometric equations, and solve word problems.
| Strand |
Source |
| Trigonometric Identities |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.5.1
The learner will be able to
know the basic trigonometric identity cos2x + sin2x = 1 and prove that it is equivalent to the Pythagorean Theorem.
| Strand |
Source |
| Trigonometric Identities |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.5.2
The learner will be able to
use basic trigonometric identities to verify other identities and simplify expressions.
| Strand |
Source |
| Trigonometric Identities |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.5.3
The learner will be able to
understand and use the addition formulas for sines, cosines, and tangents.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.5.4
The learner will be able to
understand and use the half-angle and double-angle formulas for sines, cosines, and tangents.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.5.5
The learner will be able to
solve trigonometric equations.
| Strand |
Source |
| Trigonometric Equations |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.5.6
The learner will be able to
solve word problems involving applications of trigonometric equations.
Example: In the example about day length in Standard 4, for how long in winter is there less than 11 hours of daylight?
.
| Strand |
Source |
| Trigonometric Equations |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Polar Coordinates and Complex Numbers
The learner will be able to
define polar coordinates and complex numbers and understand their connection with trigonometric functions.
| Strand |
Source |
| Polar Forms/Equations/Graphs |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.6.1
The learner will be able to
define polar coordinates and relate polar coordinates to Cartesian coordinates.
| Strand |
Source |
| Polar Forms/Equations/Graphs |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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PC.6.2
The learner will be able to
represent equations given in rectangular coordinates in terms of polar coordinates.
| Strand |
Source |
| Polar Forms/Equations/Graphs |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.6.3
The learner will be able to
graph equations in the polar coordinate plane.
| Strand |
Source |
| Polar Forms/Equations/Graphs |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.6.4
The learner will be able to
define complex numbers, convert complex numbers to trigonometric form, and multiply complex numbers in trigonometric form.
Example: Write 3 + 3i and 2 - 4i in trigonometric form and then multiply the results.
.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.6.5
The learner will be able to
state, prove, and use De Moivre's Theorem.
| Strand |
Source |
| Trigonometric Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
Sequences and Series
The learner will be able to
define and use arithmetic and geometric sequences and series, understand the concept of a limit, and solve word problems.
| Strand |
Source |
| Sequences/Series |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.7.1
The learner will be able to
understand and use summation notation.
| Strand |
Source |
| Sequences/Series |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.7.2
The learner will be able to
find sums of infinite geometric series.
| Strand |
Source |
| Series |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.7.3
The learner will be able to
prove and use the sum formulas for arithmetic series and for finite and infinite geometric series.
| Strand |
Source |
| Series |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.7.4
The learner will be able to
use recursion to describe a sequence.
| Strand |
Source |
| Sequences |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.7.5
The learner will be able to
understand and use the concept of limit of a sequence or function as the independent variable approaches infinity or a number. Decide whether simple sequences converge or diverge.
| Strand |
Source |
| Sequences |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.7.6
The learner will be able to
solve word problems involving applications of sequences and series.
Example: You put $100 in your bank account today, and then each day put half the amount of the previous day (always rounding to the nearest cent). Will you ever have $250 in your account?
.
| Strand |
Source |
| Sequences/Series |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
Data Analysis
The learner will be able to
model data with linear and non-linear functions.
| Strand |
Source |
| Data Collection and Classification |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.8.1
The learner will be able to
find linear models using the median fit and least squares regression methods. Decide which model gives a better fit.
Example: Measure the wrist and neck size of each person in your class and make a scatter plot. Find the median fit line and the least squares regression line. Which line is a better fit? Explain your reasoning.
.
| Strand |
Source |
| Scatterplots |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.8.2
The learner will be able to
calculate and interpret the correlation coefficient. Use the correlation coefficient and residuals to evaluate a "best-fit" line.
Example: Calculate and interpret the correlation coefficient for the linear regression model in the last example. Graph the residuals and evaluate the fit of the linear equation.
.
| Strand |
Source |
| Scatterplots |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.8.3
The learner will be able to
find a quadratic, exponential, logarithmic, power, or sinusoidal function to model a data set and explain the parameters of the model.
Example: Drop a ball and record the height of each bounce. Make a graph of the height (vertical axis) versus the bounce number (horizontal axis). Find an exponential function of the form y = a.bx that fits the data and explain the implications of the parameters a and b in this experiment.
.
| Strand |
Source |
| Data Collection and Classification |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
Mathematical Reasoning, Problem Solving
The learner will be able to
use a variety of strategies to solve problems.
| Strand |
Source |
| Strategies |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.9.1
The learner will be able to
use a variety of problem-solving strategies, such as drawing a diagram, guess-and-check, solving a simpler problem, examining simpler problems, and working backwards.
Example: The half-life of carbon-14 is 5,730 years. The original concentration of carbon-14 in a living organism was 500 grams. How might you find the age of a fossil of that living organism with a carbon-14 concentration of 140 grams?
.
| Strand |
Source |
| Strategies |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.9.2
The learner will be able to
decide whether a solution is reasonable in the context of the original situation.
Example: John says the answer to the problem in the first example is about 10,000 years. Is his answer reasonable? Why or why not?
.
| Strand |
Source |
| Evaluating Solutions |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.9.3
The learner will be able to
decide if a given algebraic statement is true always, sometimes, or never (statements involving rational or radical expressions, trigonometric, logarithmic or exponential functions).
Example: Is the statement sin 2x = 2 sinx cosx true always, sometimes, or never? Explain your answer.
.
| Strand |
Source |
| Analyzing Problems |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.9.4
The learner will be able to
use the properties of number systems and order of operations to justify the steps of simplifying functions and solving equations.
| Strand |
Source |
| Strategies |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.9.5
The learner will be able to
understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.
| Strand |
Source |
| Analyzing Problems |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
PC.9.6
The learner will be able to
define and use the mathematical induction method of proof.
Example: Prove De Moivre's Theorem using mathematical induction.
.
| Strand |
Source |
| Analyzing Problems |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Pre-Calculus, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
|
