La Habra High School
Mathematics Department

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Integrated Algebra 2 Standards

ALGEBRAIC PRINCIPLES & EQUATIONS

• solve absolute value equations & inequalities.
• graph solution sets of absolute value equations and inequalities.
• find the solution for a system of linear equations or inequalities.
• add, subtract, multiply, and divide polynomials.
• identify and factor polynomials involving the difference of squares, perfect square trinomials, trinomials, and the sum and difference of cubes.
• compute sums, differences, products, and quotients of rational expressions.
• simplify rational expressions.
• simplify rational expressions with negative exponents.
• solve quadratic equations by factoring, completing the square, or using the quadratic formula.
• graph quadratic equations.
• apply knowledge of quadratic equations to solve word problems.
• investigate the effect of the coefficients on the graph of a quadratic function.
• write the equations of motion given the velocity, angle of elevation, and initial height.
• graph exponential and logarithmic functions.
• demonstrate knowledge of the relationship between exponents and logarithms.
• solve problems involving logarithms and exponents.
• identify the proper use of the properties of real numbers, exponents, and logarithms.
• state and apply the laws of exponents in solving problems involving growth and decay.
• convert logarithms from one base to another.
• simplify logarithms.
• express a logarithm in exponential form.
• solve logarithmic equations.
• write a general quadratic equation in graphing form and recognize the particular conic section from a quadratic equation.
• draw the graph of a general quadratic equation in standard form.
• write proofs about properties of positive integers.
• calculate the general or specific term in an arithmetic or geometric sequence.
• find the sum of terms in an arithmetic and/or geometric series.
• find the summation formulas for arithmetic series and finite and infinite geometric series.
• given a polynomial of nth degree, determine the number of roots.
• apply the Factor Theorem, Remainder Theorem, and Descarte's Rule of Signs to determine whether a binomial is a factor of a given polynomial of higher degree.

FUNCTIONS

• find the domain and range of functions.
• graph a function knowing its restrictions.
• graph rational functions and their asymptotes.
• graph rectangular hyperbolas.
• write an equation of the horizontal and/or vertical asymptotes.
• graph quadratic functions.
• identify maximum or minimum values.
• find the zeros of a quadratic function.
• find the sum, difference, product, quotient, and composition of two or more functions.
• find the inverse of a polynomial, exponential, or logarithmic function.

TRIGONOMETRIC FUNCTIONS

• state the definition of sine and cosine as coordinates on the unit circle.
• graph the sine and cosine functions.
• state the Pythagorean Identity for trigonometric functions.
• demonstrate the relationship between the Pythagorean Identity and the Pythagorean Theorem.
• determine unknown measures in acute or obtuse triangles using the Laws of Sines or the Law of Cosines.
• find polar coordinates of a point given in rectangular coordinates, and vice versa.
• given polar coordinates, graph a vector.
• compute the sum of vectors.
• find the product of vectors and a scalar.
• sketch the sum of vectors using the parallelogram method.
• express angles using radian measurement.
• convert angle measurements between degrees and radians.
• give exact values of trigonometric functions of angles in radian measure.

PROBABILITY & STATISTICS

• analyze a problem situation and apply the fundamental counting principle.
• apply combinations and permutations to solve problems.
• state the definition of conditional probability.
• solve conditional probability problems.
• solve probability problems involving discrete outcomes.
• find probabilities using geometric relationships.
• sketch the graph of a normal distribution.
• find probabilities using the standard normal distribution percentages.
• compute probabilities using the graph of a binomial distribution.
• use the graphing calculator to find the line of best fit for a data set.

GEOMETRIC PRINCIPLES

• construct an indirect proof of a geometric property.
• state the Triangle Inequality Theorem.
• determine if three given lengths form a triangle.
• prove theorems about inscribed angles, chords, and intercepted arcs.
• compute measures of angles and arcs.
• find the measure of interior and exterior angles of an n-gon.
• find the length of a side of a regular polygon given the radius of the inscribed circle.
• identify type of polygon by its number of sides.