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1 Algebra I Algebra II Geometry Pre Calculus U1: translate between words and algebra add and subtract real numbers multiply and divide real numbers evaluate containing exponents evaluate containing U1: Classify and order real numbers  Identify and use real number properties  Simplify, add, subtract, multiply and divide square roots  Simplify and evaluate algebraic U1: Recall Algebra I skills useful for Geometry   solve several types of   combine like terms by adding and subtracting   solve using FOIL square roots and classify numbers   factor and solve quadratic within the real number system  Simplify involving use order of operations to exponents   converting measurements simplify  Identify the domain and range of   simplifying ratios use the Commutative, relations and   solving simple absolute value Associative, and Distributive  Write using function Properties to simplify understand basics of graphing on a coordinate axis system notation, evaluate and graph  Apply transformations to points and sets of points U2: solve onestep using addition or subtraction solve onestep using multiplication and subtraction solve in one variable that contain more than one operation solve in one variable that contain variable terms on both sides solve in two or more variables for one variable write ratios and write and solve proportions use proportions to solve word problems solve problems containing percents, fractions and decimals U2: Solve linear and linear  Apply proportional relationships to rates, similarity and scale  Identify linear, find the slope of a linear function and graph linear  Write linear in slope/intercept form  Graph linear on the coordinate plane  Simplify compound  Write and solve absolute value and  Graph and transform absolute value U2:   Understand basic terms of geometry   Understand basic postulates of geometry   Identify segments and rays   Recognize parallel lines   Find the lengths of segments   Find the measures of angles   Identify special angle pairs   Find the distance between two points in the coordinate plane   Find the coordinates of the midpoint of a segment in the coordinate plane   Find perimeters of rectangles and squares, and circumference of circles U3:   Recognize conditional statements   Write converses of conditional statements Review unit:  real numbers and their properties  exponents and radicals  polynomials and factoring  rational  solving  linear in one variable  errors and the algebra of calculus U1: Functions and graphs  rectangular coordinates  graphs of  linear in two variables   analyzing graphs and  transforming  composite  inverse  Mathematical modeling and variation U2: Polynomials and rational  quadratic and models  polynomial of higher degree  polynomial and synthetic division  complex numbers
2 solve word problems containing percents finding percent of increase or decrease U3: review inequality symbols and graph in one variable  solve one step using addition and subtraction  solve one step using multiplication and division  solve that contain more than one operation  solve that contain variables on both sides  solve and graph compound  solve in one variable involving absolute value U4: graph relationships and identify discrete and continuous graph find domain and range of a relation and identify a relation which is a function use function notation graph recognize and extend arithmetic sequences recognize and extend geometric sequences U3: Solve systems of by graphing  Solve systems of linear by substitution and elimination  Solve systems of linear  Graph points in three dimensions and state solutions of linear in three dimensions  Solve systems of three in three dimensions  Solve parametric, graph parametric and write the function represented by parametric U4: Use matrices to display mathematical and real world data  Use matrix addition, subtraction, multiplication by a scalar and matrix multiplication  Use graphing calculators to perform matrix operations  Find the determinant of matrices up to dimensions of 3X3  Find the inverse of a 2X2 matrix  Solve systems of by writing and solving a matrix equation  Solve systems of by using Cramer s Rule   Write bi conditionals   Recognize good definitions   Use the Law of Detachment   Use the Law of Syllogism   Connect reasoning in algebra and geometry   Prove and apply theorems about angles U4:  identify angles formed by two lines and a transversal  prove and use properties of parallel lines  use a transversal in proving lines parallel  relate parallel and perpendicular lines  classify and find the measures of their angles  classify polygons  find the sums of the measures of the interior and exterior angles of polygons  graph lines given their  write of lines  relate slope and parallel lines  relate slope and perpendicular lines U5:  To recognize congruent figures and their corresponding parts  prove two congruent using the SSS and SAS postulate  prove two congruent  zeros of polynomial  rational  nonlinear U3: Exponential and logarithmic  exponential and their graphs  logarithmic and their graphs  properties of logarithms  exponential and logarithmic  exponential and logarithmic models U4: Trigonometry  radian and degree measure  trigonometric : the unit circle  right angle trigonometry  trigonometric of any angle  graphs of sine and cosine  graphs of other trigonometric  inverse trigonometric  applications and models U5: Analytic Trigonometry  using fundamental identities  verifying trigonometric identities  solving trigonometric
3 U5: identify and graph linear use x and yintercepts to graph lines find the slope of a line from its equation find the slope of a line by using the slope formula solve problems which contain direct variation of variables write the equation of a line in slopeintercept form given a point and slope or given two points U6: solve a system of two using the graphing method using the substitution method using the elimination method using the elimination method with multiplication of graph linear in two variables in two variables U7: evaluate containing zero and integer exponents evaluate powers of ten and U5: Graph and transform quadratic  Identify the vertex, maximum and minimum points, direction of opening, axis of symmetry and y intercept of a quadratic function  Find zeros of a quadratic function from a graph and solve quadratic by factoring  Factor in the form of cubed term plus cubed term and cubed term minus cubed term  Solve quadratic by taking square root  Solve quadratic by completing the square  Solve quadratic by using the quadratic formula U6: Define and use imaginary and complex numbers  Use the quadratic formula to solve quadratic with complex roots  Solve quadratic using tables and graphs and by using algebra  Perform operations with complex numbers U7: Identify, evaluate, add and subtract polynomial  Multiply polynomials and using the ASA and AAS postulates  use triangle congruence and CPCTC to prove that parts of two are congruent  use and apply properties of isosceles  identify congruent overlapping  prove two congruent by first proving two other congruent U6:  use properties of mid segments to solve problems  use properties of perpendicular bisectors and angle bisectors  identify properties of perpendicular bisectors and angle bisectors  identify properties of medians and altitudes of a triangle  define and classify special types of quadrilaterals  use relationships among sides and among angles of parallelograms  use relationships involving diagonals of parallelograms or transversals  determine whether a quadrilateral is a parallelogram  use properties of diagonals of rhombuses and rectangles  determine whether a  sum and difference formulas  multiple angle and product to sum formulas U6: Additional topics in trigonometry  law of sines  law of cosines  vectors in the plane  vectors and dot products  trigonometric form of a complex number U7: Systems and and  linear and nonlinear systems of  two variable linear systems  multivariable linear systems  partial fractions  systems of  linear programming U8: Matrices and determinants  matrices and systems of  operations with matrices  the inverse of a square matrix  determinant of a square matrix  applications of matrices and determinants U9: Sequences, series, and probability
4 convert between standard notation and scientific notation use multiplication properties of exponents to evaluate and simplify use division properties of exponents to evaluate and simplify classify polynomials and write polynomials in standard form add and subtract polynomials multiply polynomials find special binomial products U8: write the prime factorization of numbers and find the GCF of monomials factor polynomials by using the greatest common factor factor quadratic polynomials in which the coefficient of the squared term is one factor fourterm polynomials which can be factored by grouping two and two factor quadratic polynomials in which the coefficient of the squared term is greater than one factor perfectsquare trinomials and difference of two squares choose the appropriate factoring method and combine methods to factor a polynomial U9: identify quadratic and determine whether they binomial expansion using Pascal s triangle  Dividing polynomials using polynomial long division and synthetic division  Using synthetic division to evaluate a function for a given value and to determine factors of a polynomial function  Identifying the multiplicity of roots and finding possible rational roots of a polynomial function  Solving third and fourth degree polynomials using solution hints  Writing polynomial from given roots  Using the Fundamental Theorem of Algebra and the Complex Conjugate Root Theorem U8: Solve problems using direct variation,  Solve problems using inverse and joint variation,  Multiply and divide rational  Add and subtract rational  Name zeros and of vertical asymptotes of rational  Solve rational and parallelogram is a rhombus or a rectangle  verify and use properties of trapezoids and kites U7:  write ratios and solve proportions  identify similar polygons  apply similar polygons  use AA, SAS, and SSS similarity statements  apply AA, SAS and SSS similarity statements  Solve by simplifying square roots  Solve by multiplying square roots  Solve by dividing square roots  Solve by adding and subtracting square roots  find and use relationships in similar right  use the Side Splitter Theorem  use the Triangle Angle Bisector Theorem U8:  use the Pythagorean Theorem  use the converse of the Pythagorean Theorem  use the properties of use the properties of use tangent ratios to determine side lengths in  sequences and series  arithmetic sequences and partial sums  geometric sequences and series  mathematical induction  the binomial theorem  counting principles  probability U10: Topics in analytic geometry  the three dimensional coordinate system  vectors in space  the cross product of two vectors  lines and planes in space U11: Analytic geometry in three dimensions  the three dimensional coordinate system  vectors in space  the cross product of two vectors  lines and planes in space U12: Limits and an introduction to calculus  introduction to limits  techniques for evaluation limits  the tangent line problem  limits at infinity and limits of sequences
5 have a maximum or minimum value  find zeros, axis of symmetry and vertex of a graphed quadratic function  solve quadratic by factoring  solve quadratic by using square roots  solve quadratic by completing the square  solve quadratic by using the Quadratic Formula U10: review direct variation and solve problems with direct variation  learn about inverse variation and solve problems with inverse variation  identify excluded values of rational  simplify rational  multiply and divide rational  add and subtract rational with like denominators  add and subtract rational with unlike denominators  divide a polynomial by a monomial or binomials  solve rational U9: Simplify and evaluate radical and containing rational exponents  Convert from radical form to exponential and from exponential form to radical form  Graph radical and transform radical by changing parameters  Solve radical and U10: Learn the process of linear interpolation  Evaluate, write and graph piecewise  Add, subtract, multiply and divide and use the composition of  Find the inverse of a function and graph both the function and its inverse on the same coordinate plane  use sine and cosine to determine side lengths in  use angles of elevation and depression to solve problems U9:  find the area of a parallelogram  Find the area: triangle, trapezoid, rhombus or kite, regular polygon, regular polygon using trigonometry, triangle using trigonometry  find the measures of central angles and arcs  find circumference and arc length  find the areas of circles, sectors, and segments of circles U10:  find the surface area of a prism, cylinder, pyramid, cone, prism  find the volume of a cylinder, pyramid, cone  find the surface area and volume of a sphere U11:  Use the relationship between a radius and a tangent  use the relationship between two tangents from one point  use congruent chords, arcs, and central angles  recognize properties of lines through the center of a circle  the area problem
6  find the measure of an inscribed angle  find the measure of an angle formed by a tangent and a chord  find the measures of angles formed by chords, secants, and tangents  find the lengths of segments associated with circles  write an equation of a circle  find the center and radius of a circle
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