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Precalculus
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6-8 Science
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SELECT SUBJECT
All Precalculus
A.
Functions
B.
Quadratic, Polynomial, and Exponential Functions
C.
Exponential and Logarithmic Functions
D.
Trigonometric Functions
E.
Analytic Trigonometry
F.
Polar Coordinates and Vectors
G.
Systems of Equations and Inequalities
H.
Matrices and Determinants
I.
Sequences, Series, and Probability
J.
Analytic Geometry
Precalculus
»
I.
Sequences, Series, and Probability
I.1.
Sequences and Series
I.1.M.
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I.1.Q.
Unit Challenge
I.1.1.
Sequences
I.1.1.O.
Overview
I.1.1.1.
Write out the first five terms of a sequence
I.1.1.2.
Write out the first five terms of a sequence whose terms alternate in sign
I.1.1.3.
Find the nth term of a sequence
I.1.1.4.
Write an expression for the nth term of the sequence
I.1.1.5.
Write the first five terms of the sequence defined recursively
I.1.1.6.
Write the terms of a sequence involving factorials
I.1.1.7.
Word Problems – Compound Interest
I.1.1.8.
Word Problems – Population
I.1.2.
Series
I.1.2.O.
Overview
I.1.2.1.
Find the sum using summation notation
I.1.2.2.
Use sigma notation to write the sum
I.1.2.3.
Find the partial sum of a series
I.1.2.4.
Find the sum of the infinite series
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I.2.
Arithmetic Sequences and Partial Sums
I.2.M.
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I.2.Q.
Unit Challenge
I.2.1.
Arithmetic Sequences
I.2.1.O.
Overview
I.2.1.1.
Determine whether the sequence is arithmetic
I.2.1.2.
Find the common difference of the arithmetic sequence
I.2.1.3.
Write the first five terms of an arithmetic sequence given an equation
I.2.1.4.
Write a formula for the sequence given the initial term and common difference
I.2.1.5.
Write a formula for the sequence given any two terms
I.2.1.6.
Write the first five terms of the arithmetic sequence given the initial term and common difference
I.2.1.7.
Write the first five terms of the arithmetic sequence given any two terms
I.2.1.8.
Find the nth term of an arithmetic sequence given an equation
I.2.1.9.
Find the nth term of the arithmetic sequence given any two terms
I.2.2.
Arithmetic Sums
I.2.2.O.
Overview
I.2.2.1.
Find the nth term of the arithmetic sequence given any two terms
I.2.2.2.
Find the nth partial sum of the arithmetic sequence given a sequence
I.2.2.3.
Find the partial sum given a sequence in sigma notation
I.2.2.4.
Word Problems – find the total prize money
I.2.2.5.
Word Problems – find the total sales
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I.3.
Geometric Sequences and Series
I.3.M.
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I.3.Q.
Unit Challenge
I.3.1.
Geometric Sequences
I.3.1.O.
Overview
I.3.1.1.
Determine whether the sequence is geometric
I.3.1.2.
Find the common ratio of the geometric sequence
I.3.1.3.
Write the first five terms of the geometric sequence given the initial term and common ratio
I.3.1.4.
Write the first five terms of the geometric sequence given the initial term and equation
I.3.1.5.
Write the expression for the nth term in the sequence given the initial term and common ratio
I.3.1.6.
Find the nth term of the geometric sequence given three terms in the sequence
I.3.1.7.
Find the nth term of the geometric sequence given any two terms
I.3.2.
Sums of Geometric Sequences and Series
I.3.2.O.
Overview
I.3.2.1.
Find the sum of the finite geometric sequence
I.3.2.2.
Use summation notation to write the sum of the sequence
I.3.2.3.
Find the sum of the infinite geometric series
I.3.2.4.
Word Problems – Increasing Annuities
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I.4.
Mathematical Induction
I.4.M.
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I.4.Q.
Unit Challenge
I.4.1.
Using Mathematical Induction
I.4.1.O.
Overview
I.4.1.1.
Find the statement P
_{k+1 }
for each given statement P
_{k }
I.4.1.2.
Find the formula for the sum of the first n terms of the sequence
I.4.2.
Sum of Powers of Integers
I.4.2.O.
Overview
I.4.2.1.
Find the sum using the formulas for the sums of powers of integers
I.4.3.
Finite Differences
I.4.3.1.
State whether the sequence has a linear model, quadratic model, or neither given a
_{1}
and a
_{n}
I.4.3.2.
Find a quadratic model for the sequence with the indicated terms
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I.5.
The Binomial Theorem
I.5.M.
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I.5.Q.
Unit Challenge
I.5.1.
Binomial Coefficients and Expansions
I.5.1.O.
Overview
I.5.1.1.
Find the binomial coefficient using The Binomial Theorem
I.5.1.2.
Find the binomial coefficient using Pascal’s triangle
I.5.1.3.
Use the binomial theorem to expand and simplify the expression
I.5.1.4.
Expand binomials representing differences rather than sums
I.5.1.5.
Find the nth term in a binomial expansion
I.5.1.6.
Find the coefficient of a term in an expansion
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I.6.
Counting Principles
I.6.M.
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I.6.Q.
Unit Challenge
I.6.1.
The Fundamental Counting Principle
I.6.1.O.
Overview
I.6.1.1.
Word Problems – Selecting pairs of numbers at random
I.6.1.2.
Word Problems – Using the fundamental counting principle
I.6.2.
Permutations
I.6.2.O.
Overview
I.6.2.1.
Word Problems – Find the number of permutations of n Elements
I.6.2.2.
Word Problems – Find the number of permutations of n Elements taken r at a time
I.6.2.3.
Word Problems – Find the number of distinguishable permutations of n objects
I.6.3.
Combinations
I.6.3.O.
Overview
I.6.3.1.
Word Problems – Find the number of combinations of n elements taken r at a time
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I.7.
Probability
I.7.M.
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I.7.Q.
Unit Challenge
I.7.1.
Probability of an Event
I.7.1.O.
Overview
I.7.1.1.
Find the sample space
I.7.1.2.
Find the probability of an event
I.7.1.3.
Find the probability of an event using combinations – Lottery Word Problems
I.7.2.
Mutually Exclusive, Independent, and Complementary Events
I.7.2.O.
Overview
I.7.2.1.
Find the probability of a union of events
I.7.2.2.
Find the probability of mutually exclusive events
I.7.2.3.
Find the probability of independent events
I.7.2.4.
Find the probability of the complement of an event
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