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Core Content and Skills
Math Algebra 1R
2007-2008
BOE Approved

Real number system  Content   Skills  Mathematical Properties Set Notation   Distinguish between natural, whole, integral, rational, irrational, and real numbers Construct a Venn Diagram to solve verbal problems Identify and apply properties of real numbers (closure, commutative, associative, distributive, identity, and inverse) Perform operations on previous number sets Represent a given situation using a Venn Diagram Find the complement of a subset of a given set Understand finite, infinite, empty/null sets Understand and describe the union and intersection of sets     Algebraic Expressions, Equations, and Inequalities  Content   Skills  Translate a Verbal Phrase to an Algebraic Expression One, Two, and Multi-Step Equations, Fractional Equations, and inequalities Verbal Problems involving one and 2 numbers, consecutive integer, perimeter, motion/distance, coin, age, percent increase/decrease, ratio   Evaluate mathematical expressions using specific values, including exponential and absolute value expressions Simplify expressions using mathematical properties and the order of operations Solve all types of linear equations in one variable using inverse operations and mathematical properties Translate a given verbal sentence to an algebraic expression Create equations to model given situations Identify words and phrases to represent inequalities Solve verbal problems by translating given information into a mathematical inequality and applying inverse operations

Operations With Polynomials  Content   Skills  Combining polynomials Multiplication and division of monomials and polynomials   Add and subtract polynomials in horizontal and vertical form Develop properties of exponents Raise a monomial to a power Multiply monomials Distribute a monomial over a polynomial Distribute a polynomial over another polynomial Square a binomial using binomial expansion Divide a monomial by another monomial Divide a polynomial by a monomial     Factoring and Quadratics  Content   Skills  Finding common factors of monomials Factor polynomials Solving quadratic equations   Factor numbers and monomials Factoring polynomials using the greatest common factor, difference of squares, trinomials where a = 1 or a > 1, perfect square trinomials, and factoring a polynomial completely Solving quadratics by finding square roots Apply the zero property of multiplication to solve a polynomial in its factored form Solving quadratics by using the quadratic formula Translate verbal expressions into quadratic equations Solve quadratic equations derived from verbal expressions using appropriate methods

Rational Expressions and Equations  Content   Skills  Algebraic fractions Proportions and direct variation   Determine when a fraction is undefined Simplify an algebraic fraction by canceling factors Multiply and divide algebraic fractions by canceling factors Adding and subtracting algebraic fractions with monomial or like binomial denominators Solve algebraic proportions     Radical Expressions  Content   Skills  Principal Square Roots Simplifying Radicals   Classify square roots of integers as rational or irrational Define square roots, radicands, and principal roots Determine the square root of integers Determine the square root of real numbers Express radicals in lowest terms Perform operations on radicals

Coordinate Plane and Graphical Analysis  Content   Skills  Linear functions Slope as a rate of change The equations of a line Quadratic functions Absolute value functions Transformations of linear, quadratic, and absolute value functions   Given a linear function in any form, sketch its graph Given 2 points, determine the slope of a line segment using the slope formula Determine the slope of a horizontal and vertical line Given a line, determine the relationship between the slope of the given line and lines parallel to that line Given a quadratic function, sketch its graph Find the vertex and axis of symmetry of a quadratic function from its graph or equation Find the roots of a parabolic function from its graph Given an absolute value function, sketch its graph Investigate how changing the coefficients of a function affects its graph

Systems of Equations and Inequalities  Content   Skills  Systems of Equations: Without and With calculator Systems of Inequalities: Without and with calculator   Graph 2 lines and identify the point of intersection Graph 2 linear inequalities and identify the solution set Solve a system of equations algebraically using the elimination or substitution method Translate a verbal expression into a system of equations Solve a verbal system of equations using a graphical or algebraic method Use the graphing calculator to graph 2 lines and identify the coordinates of the point of intersection Use the graphing calculator to graph 2 linear inequalities and identify the solution set Solve a linear-quadratic system of equations algebraically and graphically

Exponential Equations and Graphs  Content   Skills  Exponential functions Percent increase/decrease   Analyze and solve verbal problems that involve exponential growth and decay. Sketch the graph of an exponential function Determine the percent of increase or decrease of a quantity     Right Triangle  Content   Skills  Pythagorean Theorem Sine, Cosine, and Tangent ratios   Determine the length of a side of a right triangle using the Pythagorean Theorem Determine the length of a side of a right triangle using sine, cosine, and tangent Determine the measure of an acute angle of a right triangle using sine, cosine, and tangent Identify and use Pythagorean triples Identify the legs and hypotenuse of a right triangle. Write and solve a trigonometric equation from a given verbal sentence

Area and Volume  Content   Skills  Area of triangles, circles, and quadrilaterals Perimeter of regular polygons Volume of solids Conversions of units   Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle Calculate volume and surface area of rectangular solids and cylinders Solve problems involving conversions within measurement systems, given the relationship between the units Calculate the relative error in measuring square and cubic units, when there is an error in the linear measure

Probability  Content   Skills  Empirical vs. Theoretical Event probability Probability and the Counting Principle Probability of 2 or more activities With and Without Replacement   Evaluate expressions involving factorials Determine the number of possible events, using counting techniques or the Fundamental Principle of Counting Determine the number of possible arrangements (permutations) of a list of items Determine the number of elements in a sample space and the number of favorable events Calculate the probability of an event and its complement Determine empirical probabilities based on specific sample data Determine, based on calculated probability of a set of events, if some or all are equally likely to occur; one is more likely to occur than another; whether or not an event is certain to happen or not to happen Calculate the probability of: a series of independent events; a series of dependent events; two mutually exclusive events; two events that are not mutually exclusive

Statistics  Content   Skills  Data Representation Measures of Central Tendency Quartiles and other percentiles Lines of best fit   Categorize data as qualitative or quantitative Determine whether the data to be analyzed is univariate or bivariate Determine when collected data or display of data may be biased Compare and contrast the appropriateness of different measures of central tendency for a given data set Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given a set of data Understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a boxand- whisker plot Create a scatter plot of bivariate data Construct manually a reasonable line of best fit for a scatter plot and determine the equation of that line Analyze and interpret a frequency distribution table or histogram, a cumulative frequency distribution table or histogram, or a box-and-whisker plot Evaluate published reports and graphs that are based on data by considering: experimental design, appropriateness of the data analysis, and the soundness of the conclusions Find the percentile rank of an item in a data set and identify the point values for first, second, and third quartiles Identify the relationship between the independent and dependent variables from a scatter plot (positive, negative, or none) Understand the difference between correlation and causation Identify variables that might have a correlation but not a causal relationship Identify and describe sources of bias and its effect, drawing conclusions from data Recognize how linear transformations of one-variable data affect the data’s mean, median, mode, and range Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation

Review  Content   Skills  Review for Regents Examination