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["Mathematics Postsecondary Readiness Competency Code (MPRCC#)","Competency Description"]
["MPRCC1","Understand that to solve certain problems and equations, number systems need to be extended from whole numbers to the set of all integers (positive, negative and zero), from integers to rational numbers, and from rational numbers to real numbers (rational and irrational numbers); define and give examples of each of these types of numbers"]
["MPRCC2*","Know when and how to apply standard algorithms or concepts, and perform them flexibly, accurately and efficiently"]
["MPRCC3","Explain and apply basic number theory concepts such as prime number, factor, divisibility, least common multiple, and greatest common divisor"]
["MPRCC4","Add, subtract, multiply and divide integers, fractions and decimals"]
["MPRCC5","Solve multi-step problems involving fractions and percentages\n(Include situations such as simple interest, tax, markups/markdowns, gratuities and commissions, fees, percent increase or decrease, percent error, expressing rent as a percentage of take-home pay, and so on)"]
["MPRCC6","Locate the position of a number on the number line, know that its distance from the origin is its absolute value, and know that the distance between two numbers on the number line is the absolute value of their difference"]
["MPRCC7","Simplify sums and differences of absolute values"]
["MPRCC8","Use mental strategies to formulate, represent and solve problems"]
["MPRCC9","Use estimation and approximation to solve problems\n(Include evaluating answers for their reasonableness, detecting errors, and giving answers to an appropriate level of precision)"]
["MPRCC10","Use calculators appropriately and make estimations without a calculator regularly to detect potential errors"]
["MPRCC11","Distinguish relevant from irrelevant information, identify missing information, and either find what is needed or make appropriate estimates"]
["MPRCC12","Calculate and apply ratios, proportions, rates and percentages to solve problems"]
["MPRCC13","Recognize proportional relationships and solve problems involving rates and ratios\n(Include being able to express proportional relationships as functions)"]
["MPRCC14","Translate word problems into proportions"]
["MPRCC15","Use and interpret quantities and units correctly in algebraic formulas (Include specifying units when defining variables and attending to units when writing expressions and equations)"]
["MPRCC16","Use the symbols of mathematics correctly and precisely"]
["MPRCC17","Interpret an expression that represents a quantity in terms of the context\n(Include interpreting parts of an expression, such as terms, factors and coefficient)"]
["MPRCC18","Define variables and write an expression to represent a quantity in a problem\n(Include contextual problems)"]
["MPRCC19*","Evaluate algebraic expressions"]
["MPRCC20","Simplify algebraic expressions"]
["MPRCC21*","Apply the order-of-operations to evaluate algebraic expressions, including those with parentheses and exponents"]
["MPRCC22*","Solve linear equations in one variable using manipulations guided by the rules of arithmetic and the properties of equality"]
["MPRCC23","Understand a problem and formulate an equation to solve it\n(Extend to inequalities)"]
["MPRCC24","Use mathematical strategies to formulate a problem in mathematical terms, reach a solution, and interpret the solution in the context of the original problem"]
["MPRCC25","Translate word problems"]
["MPRCC26","Solve word problems"]
["MPRCC27","Recognize and solve problems that can be modeled using a linear equation in one variable, such as time/rate/distance problems, percentage increase or decrease problems, and ratio and proportion problems"]
["MPRCC28*","Solve literal equations for a specified variable"]
["MPRCC29*","Solve linear inequalities in one variable and graph the solution set on a number line"]
["MPRCC30","Identify the intercepts of a linear equation"]
["MPRCC31","Match given linear equations to their graphs, tables, or ordered pairs"]
["MPRCC32","Understand the relationship between the coefficients of a linear equation and the slope and x- and y-intercepts of its graph"]
["MPRCC33","Use the families of linear functions to solve problems (For linear functions f(x) = mx + b, understand b as the intercept or initial value and m as the slope or rate of change)"]
["MPRCC34*","Simplify an expression with integer exponents"]
["MPRCC35","Use scientific notation"]
["MPRCC36","Determine the relative position on the number line of numbers and the relative magnitude of numbers expressed in fractional form, in decimal form, as roots or in scientific notation"]
["MPRCC37","Compare numbers and make sense of their magnitude (Include positive and negative numbers expressed as fractions, decimals, powers, and roots; limit to square and cube roots; include very large and very small numbers and the use of scientific notation)"]
["MPRCC38*","Add, subtract, multiply, and divide polynomials; Divide by monomials and binomials"]
["MPRCC39","Simplify radical expressions"]
["MPRCC40","Add, subtract, or multiply square roots of monomials"]
["MPRCC41*","Factor polynomial expressions"]
["MPRCC42","Manipulate simple expressions\n(Show procedural fluency in the following cases: factoring out common terms; factoring expressions with quadratic structure; writing in standard form sums, differences, and products of polynomials; include rewriting in standard form sums, differences, products, and quotients of simple rational expressions; rewrite expressions with negative exponents and those involving square or cube roots of a single term involving exponents)"]
["MPRCC43*","Solve quadratic equations in one variable by factoring"]
["MPRCC44","Simplify rational expressions (Include operations with rational expressions)"]
["MPRCC45*","Translate fluently between lines in the coordinate plane and their equations\n(Include predicting visual features of lines by inspection of their equations, determining the equation of the line through two given points, and determining the equation of the line with a given slope passing through a given point)"]
["MPRCC46*","Solve systems of equations (Focus on pairs of simultaneous linear equations in two variables; include algebraic techniques, graphical techniques and solving by inspection)"]