Unit 1.
Equations and inequalities (20 hours)
Unit 2.
Linear relations and functions (20 hours)
Unit 3.
Systems of equations and inequalities (20 hours)
Unit 4.
Polynomials: products and factoring: (30 hours)
Unit 5. Roots, irrational numbers, and complex numbers (20
hours)
Unit 6.
Quadratic equations (15 hours)
Unit 7.
Quadratic relations and functions (10 hours)
Unit 8. Polynomial Functions (15 hours)
Unit 9.
Rational polynomial expressions (20 hours)
Unit 10:
Introduction to trigonometry (10hours)
Unit 11: Probability and statistics (optional)
-
Use the order
of operations to evaluate expressions;
-
use formulas
-
determine if
a number belongs to the set of natural numbers, integers, rational; numbers, irrational numbers, or real numbers;
-
use the
propeties of real numbers to simplify expressions;
-
solve
equations using the properties of equalities;
-
translate
word expressions into mathematical expressions;
-
translate
word sentences into equations;
-
use equations
to solve problems.
10A2.1.2. The
student will: ( 8 hours)
-
solve linear
inequalities in the set of real numbers;
-
apply correctly multiplication and division of an inequality by a negative number;
-
relate
concepts: open interval, closed interval, semi-open interval to inequalities;
-
express an
interval in the set of real numbers by using inequality, set notation and graphically on a
number line;
-
solve linear
inequalities in the set of real numbers;
-
identify and
solve compound sentences using and and or;
-
solve
equations containing absolute value;
-
solve linear
inequalities involving absolute value in the set of real numbers and express the solution
as an inequality, using set notation and graphically on the real number line;
10A2.2.1. The
student will: (10 hours)
-
graph a
relation, state its domain and range, and determine if the relation is a function;
-
find the
values of functions for given elements of the domain;
-
identify
equations that are linear and graph them;
-
write linear
equations in standard form;
-
determine the
slope and intercepts of a line
-
use the slope
and intercepts to graph a line
-
determine if
two lines a parallel, perpendicular or neither.
10A2.2.2. The
student will: (10 hours)
-
write the
slope intercept form of an equation given the slope and a point, or two points
-
write the
standard form of an equation given the slope and a point or two points
-
write the
equation of a line that is parallel or perpendicular to the graph of a given equation;
-
draw a
scatter plot and find the prediction equation
-
draw graphs
of inequalities in two vaariables
-
write an
inequality to solve problems
10A2.3.1. The
student will: ( 15 hours)
-
graph a
system of two linear equations with two unknows and find the solution as intercept of two
lines on the graph (GC);
-
solve a
system of two linear equations with two unknowns by using substition method or elimination
method;
-
find the
value of a second order determinant
-
solve a
system of equations using Cramerīs Rule;
-
solve system
of equations in three variables using substitution, elimination or Cramerīs Rule
-
solve
problems involving two or three unknowns.
10A2.3.2. The
student will: (5 hours)
-
find solution
to the system of linear inequalities by graphing (GC);
-
understand
concepts: feasible region, constraints;
-
solve text
problems that recquire use of the system of linear inequalities (GC);
10A2.4.1. The
student will: ( 15 hours)
-
multiply
monomials and powers of monomials
-
divide
monomials
-
add and
subtract polynomials
-
multiply
polynomials: squared binomial, cubed binomial, sum and difference binomial, common term
binomial, binomial times a polynomial and foil.
-
Calculate the
power of a binomial using Pascalīs Triangle.
10A2.4.2. The
student will: (15 hours)
-
factor
polynomials: common factor, difference of
squares, sum or difference of cubes, trinomial with perfect squares, second degree
trinomials (x2 + bx + c and ax2 + bx + c), and polymials in which
first and fourth terms are cubes;
-
divide
polynomials using factoring and long division;
-
divide
polynomials using synthetic division.
10A2.5.1 The
student will: (10 hours)
-
simplify
radicals having various indices
-
simplify
radical expressions using multiplication and division
-
rationalize
the denominator of a fraction containing a radical expression
-
add,
subtract, multiply, and divide radical expressions
-
write
expressions with rational exponents in simplest radical form and vice versa
-
evaluate
expressions in either exponential or radical form
-
simplifly
expressions containing rational exponents
-
solve
equations containing radicals
10A2.5.2 The
student will: ( 10 hours)
-
simplify
radicals containing negative radicands
-
multiply pure
imaginary numbers
-
solved
quadratic equations that have pure imaginary solutions
-
add,
subtract, and multiply complex numbers
-
simplify
rational expressions containing complex numbers in the denominator.
10A2.6.1 The
student will: ( 15 hours)
-
solve
quadratic equations by graphing, factoring, by completing the square and using the
quadratic formula
-
use
discriminant to determine the nature of the roots of a quadratic equation
-
find the sum
and product of the roots of a quadratic equation
-
find all
possible integral roots of a quadratic equation
-
find
quadratic equations to fit a given condition
10A2.7.1 The
student will: (5 hours)
-
write
functions in quadratic form
-
identify the
quadratic term, the linear term, and the constant term of a quadratic function
-
graph
quadratic equations of the form y = (x – h)2 + k, and identify the vertex
and the equations of the axis of symmetry of a parabola
-
graph
equations fo the form y = a (x – h)2
+ k, and identify the vertex, the equation of the axis of symmetry, and the direction of
the opening
10A2.7.2 The
student will: ( 5 hours)
-
determine the
equation of a parabola from given information about the graph
-
solve
problems using quadratic equations
-
graph
quadratic inequalities
-
solve
quadratic inequalities in one variable.
10A2.8.1 The
student will: ( 15 hours)
-
evaluate
polynomial functions
-
identify
general shapes of the graphs of polynomial functions
-
find factors
of polynomials using the factor theorem and synthetic division
-
find the
number of positive real zeros, negative real zeros, and complex zeros for a polynomial
function
-
identify all
posible rational zeros of a polynomial function using the Rational Zero Theorem
-
find zeros of
a polynomial function
-
graph
polynomial functions to find significant points
-
find the
composition of functions
-
determine the
inverse of a function or relation
-
graph a
function and its inverse.
10A2.9.1 The
student will: (20 hours)
-
solve
problems involving direct, inverse, and joint variation
-
simplify
rational expressions
-
simplify
complex fractions
-
find the
least common denominator of two or more
algebraic expressions
-
add and
subtract rational expressions
-
solve
rational equations
-
use rational
expressions to solve problems
10A2.10.1 The student will: (10 hours)
-
change radian
measure to degree measure and vice versa
-
identify
coterminal angles
-
find the
least possible angle that is coterminal to a given angle
-
find the
values of expressions involving sine, cosine, and tangent
-
use a
calculator to find values of trigonometric functions
-
use right
triangles to find trigonometric values
-
solve
problems involving right triangles using right triangle trigonometry
10A2.11.1 The
student will: (10 hours)
- represent data using line plots and
stem-and-leaf plots
-
read and
interpret data from line plots and stem-and-leaf plots
-
find the
median, mode, and mean of sets of data
-
use the
median, mode, and mean to interpret data
-
find the
range and interquartile range for a set of data
-
determine if
any values in a set of data are outliers
-
represent
data using box-and-whiskers plots
-
find the
standard deviation for a set of data
-
solve
problems involving normally distributed data
10A2.11.2 The
student will: (10 hours)
-
solve
problems using the Basic Counting Principle
-
solve
problems involving permutations
-
solve
problems involving circular permutations
-
solve
problems involving combinations
-
find the
probability of an event and determine the odds of a success or failure
-
find the
probability of two or more independent or dependent events
-
find the
probability of mutually exclusive events or inclusive events
-
use
simulation to solve various probability problems
-
use binomial
experiments to find probabilities.
AII/T.1. The
student will identify field properties, axioms of equality and inequality, and properties
of order that are valid for the set of real numbers and its subsets, and complex numbers.
AII/T.2. The student will add, subtract, multiply, divide, and simplify rational expressions, including complex fractions.
AII/T.3. The student will
·
Add,
subtract, multiply, divide, and simplify radical expressions containing positive rational
numbers and variables and expressions containing rational exponents; and
· Write radical expressions as expressions containing rational exponents and vice versa.
AII/T.4 The student will solve absolute value equations and inequalities graphically. Graphing calculators will be used both as a primary method of solution and to verify algebraic solutions.
AII/T.5 The
student will identify and factor completely polynomials representing the difference of
squares, perfect square trinomials, the sum and difference of cubes, and general
trinomials.
AII/T.6. The student will select, justify, and apply a
technique to solve a quadratic equation over the set of complex numbers. Graphing calculators will be used for solving and
confirming algebraic solutions.
AII/T.7. The student will solve equations containing
rational expressions and equations containing radical expressions algebraically and
graphically. Graphing calculators will be
used both as a primary tool for solving and confirming algebraic solutions.
AII/T.8. The student will recognize multiple
representations of functions (linear, quadratic, and absolute value) and convert between a
graph, a table, and symbolic form.
AII/T.9. The student will find the domain, range, zeros,
and inverse of a function the value of a function for a given element in its domain; and
the composition of multiple functions. Functions
will include those that have domains and ranges that are limited and/or discontinuous
AII/T.10 The student will investigate and describe
the relationships between the solution of an equation, zero of a function, x-intercept of
a graph, and factors of a polynomial expression through the use of graphs.
AII/T.13 The student will solve a system of linear
inequalities with and without the use of a graphing calculator.
AII/T.15. The student will recognize the general shape of
polynomial functions, locate the zeros, sketch the graphs, and verify graphical solutions
algebraically. The graphing calculator will be used as a tool to
investigate the shape and behavior of polynomial functions.
AII/T.17. The student will perform operations on complex
numbers and express the results in simplest form. Simplifying
results will involve using patterns of the powers of i.
AII/T.20. The student will solve practical problems
involving a combination of direct and inverse variations.
AII/T.22. The student, given the value of one trigonometric
function, will find the values of the other trigonometric functions. Properties of the unit circle and definitions of
circular functions will be applied.
AII/T.23. The student will find the values of the
trigonometric functions of the special angles and their related angles as found in the
unit circle without the aid of a calculating utility.
This will include converting radians to degrees and vice versa.
MA.4
The sudent will expand binomials having positive integral exponents through the use
of the Binomial Theorem and Pascalīs Triangle.