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© 2008 by Mahomet-Seymour Schools.
All Rights Reserved.
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Mahomet-Seymour Schools
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Curriculum
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Mathematics - Algebra II
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Equations and Systems of Equations
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The learner will be able to solve linear, absolute
value, and quadratic equations.
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The learner will be able to solve simple and compound
inequalities.
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The learner will be able to write an equation of a
line given a point on the line and the slope of the line or given two
points on the line.
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The learner will be able to graph linear, quadratic,
and absolute value functions and their inverses.
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The learner will be able to distinguish between
relations and functions using functional notation.
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The learner will be able to write the equation for
and give the slope of both vertical and horizontal lines.
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The learner will be able to solve systems of 2
equations with 2 variables by the graphing method, linear combination
method, substitution method, and Cramer's Rule.
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The learner will be able to solve systems of
inequalities by graphing.
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The learner will be able to solve systems of 3 equations
with 3 variables by either linear combination, Cramer's Rule, substitution
and the use of augmented matrices.
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The learner will be able to apply the methods for
solving systems of equations to word problems.
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The learner
will be able to use the geometric transformations of dilation, translation,
and reflection over lines of symmetry.
The
learner will use be able to use basic matrix manipulations of matrix
multiplication, addition, scalar multiplication.
The
learner will be able to find determinants and use matrices to find
solutions to systems of equations.
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Polynomials and Rational Expressions
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The learner will be able to state and apply the Laws
of Exponents.
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The learner will be able to multiply, divide and
factor second and third degree polynomials over the Real Numbers.
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The learner will be able to solve equations and
inequalities by factoring.
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The learner will be able to add, subtract, multiply,
and divide rational expressions.
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The learner will be able to solve equations containing
rational expressions.
The learner will be able to find points of
discontinuity, vertical asymptotes, and horizontal asymptotes for rational
functions.
The learner will be able to graph all the conics:
parabolas, circles, ellipses, and hyperbolas.
The learner will be able to identify the key
components of all conics, i.e. major and minor axes, vertices, co-vertices,
foci, and asymptotes.
The learner will be able identify all conics while
in standard form.
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The learner will be able to distinguish between
Arithmetic and Geometric Sequences and Series.
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The learner will be able to find the nth term of an
Arithmetic or Geometric Sequence.
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The learner will be able to find the arithmetic
mean(s) or geometric mean(s).
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The learner will be able to find the sum of n terms
of an Arithmetic or Geometric Series.
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The learner will be able to find the sum an infinite,
geometric, convergent series.
The learner will be
able to prove statements by mathematical induction.
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Radicals, Exponents, and Polynomials
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The learner will be able to simplify real roots of numbers.
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The learner will be able to perform the basic four
operations on radicals.
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The learner will be able to solve equations
containing radicals.
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The learner will be able to distinguish between real
roots of numbers and imaginary roots of numbers.
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The learner will be able to simplify radicals
containing negative numbers.
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The learner will be able to perform the four basic
operations on complex numbers.
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The learner will be able to solve quadratic equations
by completing the square and by using the Quadratic Formula.
The learner will
be able to derive the quadratic formula.
The learner will
be able to use sign analysis to graph high order polynomials.
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The learner will be able to graph quadratic functions
in the form of y=ax2+bx+c or y=a(x-b)2+k.
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The learner will be able to evaluate a polynomial
function for a given x value.
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The learner will be able to use Synthetic
Substitution along with the remainder and Factor Theorems to factor and
solve third and fourth degree polynomials.
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The learner will be able to divide polynomials
synthetically.
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The learner will be able to evaluate terms with
rational exponents.
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The learner will be able to apply the Laws of
Exponents to rational exponents.
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The learner will be able to convert terms with rational
exponents to radicals and vice versa.
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The learner will be able to perform the basic four
operations on terms with rational exponents.
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The learner will be able to solve equations
containing rational exponents.
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The learner will be able to convert from exponential
form to logarithmic form and vice versa.
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The learner will be able to evaluate logarithms
without the use of a calculator.
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Logarithms and Trig. Functions
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The learner will be able to apply the Laws of
Logarithms.
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The learner will be able to solve equations containing
logarithms.
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The learner will be able to solve exponential
equations using logarithms.
The learner will
be able to graph exponential functions and logarithms.
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The learner will be able to solve exponential growth and
decay problems.
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The learner will be able to apply the Laws of
Logarithms to the Natural Logarithms.
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The learner will be able to convert between degree
measure and radian measure.
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The learner will be able to use the Pythagorean
Theorem and the 30-60-90 triangle and the 45-45-90 triangle to solve right
triangles.
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The learner will be able to use the Sine and Cosine, Tangent,
Cosecant, Secant and Cotangent Functions to solve for side lengths and
angle measures in a right triangle.
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The learner will be able to sketch a right triangle
in standard position in each of the four quadrants.
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The learner will be able to use the four quadrants to
determine the SIGN for special sine and cosine values.
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The learner will be able to find the sine and cosine
values of special angles in the four quadrants.
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The learner will be able to graph all six
trigonometric functions with appropriate transformation i.e. phase shifts,
vertical shifts, period changes and amplitude changes.
The learner will be able to solve trigonometric
equations.
The learner will be able to solve a triangle by
using the Law of Sines and the Law of Cosines.
The learner will be able to use the trigonometric
identities to verify trigonometric equations.
The learner will be able to use the sum and
difference, double angle, and half-angle identities to solve trigonometric
equations.
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The learner will be able to find the number of linear
and circular permutations of n different elements.
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The learner will be able to find the number of both linear
and circular permutations with repeated elements.
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The learner will be able to distinguish between a
permutation and combination.
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The learner will be able to find the number of
combinations of n elements taken r at a time.
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The learner will be able to distinguish between
sample space and event.
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The learner will be able to find the probability for
both independent and dependent events.
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The learner will be able to find the probability for
events that are mutually exclusive and for events that are not mutually
exclusive.
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The learner will be able to use the Binomial Theorem
to find the probability for tossing coins.
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The learner will be able to expand a binomial using
either the Binomial Theorem or Pascal's Triangle.
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