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Mahomet-Seymour Schools

Curriculum

Mathematics - Algebra II Honors

 

Equations and Systems of Equations

 

The learner will be able to solve linear, absolute value, and quadratic equations.

 

  

 

The learner will be able to solve simple and compound inequalities.

 

  

 

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.

 

  

 

The learner will be able to graph linear, quadratic, and absolute value functions and their inverses.

 

  

 

The learner will be able to distinguish between relations and functions using functional notation.

 

  

 

The learner will be able to write the equation for and give the slope of both vertical and horizontal lines.

 

  

 

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.

 

  

 

The learner will be able to solve systems of inequalities by graphing.

 

  

 

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.

 

  

 

The learner will be able to apply the methods for solving systems of equations to word problems.

 

 

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

 

The learner will be able to state and apply the Laws of Exponents.

 

  

 

The learner will be able to multiply, divide and factor second and third degree polynomials over the Real Numbers.

 

  

 

The learner will be able to solve equations and inequalities by factoring.

 

  

 

The learner will be able to add, subtract, multiply, and divide rational expressions.

 

  

 

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.

 

  

 

The learner will be able to distinguish between Arithmetic and Geometric Sequences and Series.

 

  

 

The learner will be able to find the nth term of an Arithmetic or Geometric Sequence.

 

  

 

The learner will be able to find the arithmetic mean(s) or geometric mean(s).

 

  

 

The learner will be able to find the sum of n terms of an Arithmetic or Geometric Series.

 

  

 

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

 

The learner will be able to simplify real roots of numbers.

 

  

 

The learner will be able to perform the basic four operations on radicals.

 

  

 

The learner will be able to solve equations containing radicals.

 

  

 

The learner will be able to distinguish between real roots of numbers and imaginary roots of numbers.

 

  

 

The learner will be able to simplify radicals containing negative numbers.

 

  

 

The learner will be able to perform the four basic operations on complex numbers.

 

  

 

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.

 

  

 

The learner will be able to graph quadratic functions in the form of y=ax2+bx+c or y=a(x-b)2+k.

 

  

 

The learner will be able to evaluate a polynomial function for a given x value.

 

  

 

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.

 

  

 

The learner will be able to divide polynomials synthetically.

 

  

 

The learner will be able to evaluate terms with rational exponents.

 

  

 

The learner will be able to apply the Laws of Exponents to rational exponents.

 

  

 

The learner will be able to convert terms with rational exponents to radicals and vice versa.

 

  

 

The learner will be able to perform the basic four operations on terms with rational exponents.

 

  

 

The learner will be able to solve equations containing rational exponents.

 

  

 

The learner will be able to convert from exponential form to logarithmic form and vice versa.

 

  

 

The learner will be able to evaluate logarithms without the use of a calculator.

 

  

 

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Logarithms and Trig. Functions

 

The learner will be able to apply the Laws of Logarithms.

 

  

 

The learner will be able to solve equations containing logarithms.

 

  

 

The learner will be able to solve exponential equations using logarithms.

 

The learner will be able to graph exponential functions and logarithms.

 

  

 

The learner will be able to solve exponential growth and decay problems.

 

  

 

The learner will be able to apply the Laws of Logarithms to the Natural Logarithms.

 

  

 

The learner will be able to convert between degree measure and radian measure.

 

  

 

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.

 

  

 

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.

 

  

 

The learner will be able to sketch a right triangle in standard position in each of the four quadrants.

 

  

 

The learner will be able to use the four quadrants to determine the SIGN for special sine and cosine values.

 

  

 

The learner will be able to find the sine and cosine values of special angles in the four quadrants.

 

  

 

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.

 

 

  

 

The learner will be able to find the number of linear and circular permutations of n different elements.

 

  

 

The learner will be able to find the number of both linear and circular permutations with repeated elements.

 

  

 

The learner will be able to distinguish between a permutation and combination.

 

  

 

The learner will be able to find the number of combinations of n elements taken r at a time.

 

  

 

The learner will be able to distinguish between sample space and event.

 

  

 

The learner will be able to find the probability for both independent and dependent events.

 

  

 

The learner will be able to find the probability for events that are mutually exclusive and for events that are not mutually exclusive.

 

  

 

The learner will be able to use the Binomial Theorem to find the probability for tossing coins.

 

  

 

The learner will be able to expand a binomial using either the Binomial Theorem or Pascal's Triangle.

 

  

 

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