Download Math Calculus AP - Morgan County School District Re-3

Morgan County School District Re-3
A.P. Calculus
Month
August
Content and Essential
Questions
What is the language of algebra?
Skills
Assessment
Graphing real numbers. Comparing
and ordering real numbers. Finding
absolute value.
Simplifying expressions.
Homework
Basic properties of real numbers.
Daily quizzes
September
How do you solve one variable
equations?
How do you translate into mathematical
phrases?
How do you solve and graph
inequalities in one variable?
Adding, subtracting, multiplying and
dividing real numbers.
Formal Quizzes after several sections
Solve one variable equations.
Chapter Test
Homework
Translate word problems into
equations and solve.
Formal Quizzes after several sections
Solve one step inequalities with
integers.
Solve multi-step inequalities.
How do you solve and graph absolute
value equations/inequalities in one
variable?
Solve combined inequalities.
How do you prove theorems in algebra?
Solve absolute value equations and
inequalities algebraically and
graphically.
How do you graph linear equations?
How do you write the equation of a
line?
Daily quizzes
Write one variable inequalities to
solve word problems.
Identify and write expressions to
demonstrate properties of equality, real
numbers, order.
Use properties and theorems of real
number and of order, to prove
algebraic
statements.
Chapter Test
Resources
Morgan County School District Re-3
Month
Content and Essential
Questions
A.P. Calculus
Skills
Assessment
Graph lines given the slope and a
point.
Graph linear equations - using both a
chart and slope-intercept form.
Find the slope of a line when given
two points.
October
How do you find the range of a
function?
Writing linear equations when given a
y-intercept and a slope, a point and a
slope, or two points.
Given the domain of a function,
determine the range.
What is the difference between a
function and a relation?
Given a function, determine the
domain and range.
How do you write the equation of a
linear function?
Determine which relations are
functions and which are not. Functions
may be a map, a list, a chart or a
graph.
Homework
Daily quizzes
How do you solve systems of
equations?
How do you solve systems of linear
inequalities?
How do you translate word problems
into linear systems of equations and
into systems of linear functions?
Writing linear functions given a slope
and a y-intercept, a point and a slope
or two points.
Writing linear functions from word
problems.
Writing systems of linear equations
and functions from word problems.
How do you add and subtract
polynomials?
Graph one linear inequality.
How do you use the laws of exponents?
Graph a system of inequalities.
How do you multiply polynomials?
Adding, subtracting, multiplying
integers.
How do you find the LCM and GCF of
Formal Quizzes after several sections
Chapter Test
Resources
Morgan County School District Re-3
Month
A.P. Calculus
Content and Essential
Questions
Skills
algebraic terms?
Identify like terms.
How do you factor polynomials?
Adding and subtracting like terms.
Assessment
Identify exponents.
FOIL
Distributive property.
Find LCM and GCF of numerical
terms.
Order exponents from largest to
smallest.
Multiply polynomials.
Factor out a common factor.
Factor the sum and the difference of
perfect cubes.
Factor the difference of perfect
squares.
November
How do you solve polynomial
equations?
Factor polynomials.
Homework
Solve equations.
Daily quizzes
How do you solve word problems using
polynomial equations?
Identify factors.
Formal Quizzes after several sections
How do you solve polynomial
inequalities?
Write polynomial equations from
word problems.
Chapter Test
How do you divide monomials?
Solve polynomial equations.
How do you use zero and negative
exponents?
Solve conjunction and disjunction
problems.
Resources
Morgan County School District Re-3
Month
Content and Essential
Questions
How do you use scientific notation?
How do you simplify rational
expressions?
A.P. Calculus
Skills
Assessment
Add, subtract, multiply and divide
integers.
Use the laws of exponents.
Counting places.
December
How do you simplify, multiply, divide,
add and subtract rational expressions?
Simplify numerical expressions.
Simplify, multiply, divide, add and
subtract numerical expressions.
Homework
Daily quizzes
How do you simplify complex
fractions?
Factor polynomials.
Formal Quizzes after several sections
Solve polynomial equations.
How do you solve equations with
rational expressions?
Chapter Test
Simplify monomial algebraic
expressions.
Identify a common denominator.
January
How do you find the roots of real
numbers?
Identify perfect squares, perfect cubes.
Homework
Multiply and divide numbers.
Daily quizzes
How do you simplify radical
expressions?
Identify, add and subtract like terms.
Formal Quizzes after several sections
How do you add, subtract, multiply and
divide radical expressions?
Find the root of a perfect square,
perfect cube.
Chapter Test
How do you solve equations with
radical expressions?
Rationalize the denominators of
fractions.
How do you identify rational and
irrational numbers?
Write the conjugate of a binomial.
Multiply conjugates.
How do you convert a fraction to a
decimal?
Identify imaginary numbers.
How do you convert a decimal to a
fraction?
Simplify, add, subtract, multiply and
divide radical expressions.
Resources
Morgan County School District Re-3
Month
Content and Essential
Questions
How do you simplify, add, subtract,
multiply and divide imaginary
numbers?
How do you solve quadratic equations
by completing the square, using the
quadratic formula and using the
graphing calculator?
February
How do you use the discriminate to
determine what type of roots a
quadratic equation will produce?
How do you graph a quadratic
equation?
How do you find the axis of symmetry,
the vertex, the x and y intercepts, the
range and the domain of parabola's
(quadratic equations)?
How do you write a quadratic equation
when you have been given the roots of
the equation?
A.P. Calculus
Skills
Assessment
Factor quadratics.
Solve quadratics by completing the
square.
Solve quadratics using the quadratic
formula.
Determine what the discriminate is.
Homework
Determine if the discriminate is
positive, negative or equal to zero.
Daily quizzes
Formal Quizzes after several sections
Complete the square of a quadratic
equation.
Chapter Test
Find the vertex of a parabola from the
equation.
Find the axis of symmetry of a
parabola from the equation.
Find the x and y-intercepts of a
parabola from the equation.
Find the range and the domain of a
parabola from the graph and from the
equation.
Solve quadratic equations by factoring.
Write quadratic equations when given
the roots of the equation.
March
How do you divide one polynomial by
another polynomial?
Add, subtract and multiply
polynomial equations.
Homework
Daily quizzes
Resources
Morgan County School District Re-3
Month
Content and Essential
Questions
How do you find factors of polynomials
and solve polynomials using the
remainder and factor theorems?
How do you determine the number, the
nature and the roots of a polynomial
equation?
A.P. Calculus
Skills
Divide polynomial equations using
long division.
Divide polynomial equations using
synthetic division.
Assessment
Formal Quizzes after several sections
Chapter Test
Find the factors of polynomials using
the remainder and factor theorems.
end of chapter 8
Solve polynomials using the remainder
and factor theorems.
Determine the number of roots in a
polynomial equation.
Given one imaginary root, find the
other (conjugate) root.
April
How do you find the distance between
two points? How do you find the
midpoint?
What is the relationship between the
center and radius of a circle and the
equation of the circle?
Find the number of positive and
negative roots.
Simplify radical expressions.
Homework
Average coordinates.
Daily quizzes
Identify the center of a circle from the
equation.
Formal Quizzes after several sections
Chapter Test
Complete the square.
What is the relationship between the
focus, directrix, vertex, and axis of a
parabola and the equation of the
parabola?
Work in the coordinate plane.
Write and graph linear equations.
What is the relationship between the
center, foci, and intercepts of an ellipse
and the equation of the ellipse?
Using intercepts.
What is the relationship between the
foci, intercepts, and asymptotes of a
hyperbola and the equation of the
Find the foci of ellipses, parabola and
hyperbola.
Understand asymptotes.
Resources
Morgan County School District Re-3
Month
Content and Essential
Questions
A.P. Calculus
Skills
Assessment
hyperbola?
How do you use graphs to determine
the number of real solutions of a
quadratic system?
Use the distance formula to create the
equations of conic sections based on
their definitions.
Graph conic sections.
How do you use algebraic methods to
find the solutions to a quadratic system?
How do you solve systems of linear
equations in three variables?
end of chapter 9
Substitution method for systems of
equations.
Understand that the solution to a
system of an equation is the point of
intersection.
end of chapter 9
May
How do you extend the meaning of
exponents to include rational numbers?
How do you extend the meaning of
exponents to include irrational numbers
and to define exponential functions?
How do you find the composite of two
given functions and find the inverse of
a function?
How do you define logarithmic
functions and to learn how they are
related to exponential functions?
How do you apply the basic properties
of logarithms?
Use laws of exponents.
Homework
Solve equations.
Daily quizzes
Define logarithms.
Formal Quizzes after several sections
Convert rational exponents to radical
form.
Chapter Test
Convert radical form to rational
exponents.
Use logarithms to solve for an
exponent.
Evaluate using function notation.
Find the inverse of a function.
How do you use common logarithms to
Resources
Morgan County School District Re-3
Month
Content and Essential
Questions
solve equations involving powers and
to evaluate logarithms with any given
base?
How do you use exponential and
logarithmic functions to solve growth
and decay problems?
A.P. Calculus
Skills
Convert from logarithmic form to
exponential form.
Convert from exponential form to
logarithmic form.
Use the laws of exponents to evaluate
expressions.
Use the law of exponents to solve
equations.
How do you use degrees to measure
angles?
Measure angles using degrees.
How do you define trigonometric
functions of acute angles?
Convert from degree, minutes and
seconds to decimal form.
How do you define trigonometric
functions of general angles?
Convert form decimal form, to
degrees, minutes and seconds.
How do you use a calculator or
trigonometric tables to find values of
trigonometric functions?
Identify the values of the six trig
functions when given a right triangle
or an angle.
How do you the fin side and angles of a
right triangle?
Use trig functions to solve for an
unknown.
Find the reference angle.
Use trig to solve for the missing parts
of a right angle.
Assessment
Resources