TSI Mathematics & Statistics Test - Elementary Algebra

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1 TSI Mathematics & Statistics Test - Elementary Algebra Querium Lesson Titles Adult Education Standards Aligned TEKS Aligned CCRS Solving Equations Using the Distributive Property Solving Equations by Combining Like Terms Performs operations with Real Numbers & algebraic expressions Employing correct order of operations Formulates & solves linear equations & inequalities Linear systems with 2 & 3 variables and variation Graphs & translates functions on a rectangular coordinate system The Distributive Property Operations with Integers Operations with Fractions Translating Words to Algebra to Solve Word Problems Combining Like Terms The Order of Operations Rules of the Order of Operations Exponents and Parenthesis in Operations Equations with One Variablte Inequalities with One Variable Evaluating Expressions using Substitution LInear Equations as Tables, Graphs, and Words Graphing Inequalities Solving a System of Linear Equations Using Substitution in Word Problems Solving a System of Linear Equations by Elimination in Word Problems Shifting a Function on a Coordinate Plane Linear Translation Rules Linear Translation Tables Finding the Slope of a Linear Function Level D (+6, 7-8): Apply & extend previous understandings of numbers to the system of rational numbers; Apply & extend previous understandings of operations with fractions to add, subtract, mult & divide rational numbers; Know that there are numbers that are not rational, and approx them by rational numbers; Use properties of operations to generate equivalent expressions Level D (+6,7-8): Analyze and solve linear equations and pairs of simultaneous linear equations. Level D (+6, 7-8): Analyze and solve linear equations and pairs of simultaneous linear equations. (7.3A) add, subtract, multiply, and divide rational numbers fluently; and (7.3B) apply and extend previous understandings of operations to solve using addition, subtraction, multiplication, and division of rational numbers. (7.10A) write one-variable, two-step equations and inequalities to represent constraints or conditions within ; (7.10B) represent solutions for one-variable, two-step equations and inequalities on number lines; (7.10C) write a corresponding real-world problem given a one-variable, two-step equation or inequality; (7.11A) model and solve one-variable, two-step equations and inequalities; (7.11B) determine if the given value(s) make(s) one-variable, twostep equations and inequalities true; (8.5A) represent linear proportional situations with tables, graphs, and equations in the form of y = kx; (8.5B) represent linear nonproportional situations with tables, graphs, and equations in the form of y = mx + b,where b 0; (8.5E) solve involving direct variation; (8.5I) write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations; Level E (High School): Represent and (8.5G) identify functions using sets of ordered solve equations and inequalities graphically pairs, tables, mappings, and graphs; (II.B.1) Recognize and use algebraic properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions; (I.B.1) Perform computations with real and complex numbers (II.C.1) Recognize and use algebraic properties, concepts, procedures, and algorithms to solve equations, inequalities, and systems of linear equations; (II.C.2) Explain the difference between the solution set of an equation and the solution set of an inequality; (VII.A.2) Recognize and distinguish between different types of functions; (VII.B.1) Understand and analyze features of a function; (VII.C.1) Apply known function models; (VII.C.2) Develop a function to model a situation; (VIII.A.3) determine a solution (II.D.1) Interpret multiple representations of equations and relationships; (II.D.2) Translate among multiple representations of equations and relationships Identifying the X and Y intercepts Identifies characteristics of linear functions Finding the Slope of a Linear Function from a Graph Finding the X and Y Intercepts on a Graph Calculating Slope from a Graph Level D (+6, 7-8): Use functions to model relationships between two quantities (7.7) represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b; (8.5G) identify functions using sets of ordered pairs, tables, mappings, and graphs; (VII.B.1) Understand and analyze features of a function Slope Intercept Form Substituing Zero to Find the Intercept 1

2 Formulates & solves word and applications Understands characteristics of functions Factors polynomial expressions by GCF, grouping, difference of squares, trinomials Integrated throughout lessons Level D (+6, 7-8): Solve real-life mathematical using numerical and algebraic expressions and equations; Level E(High School): Create equations that describe numbers or relationships (7.10A) write one-variable, two-step equations and inequalities to represent constraints or conditions within ; (7.10C) write a corresponding real-world problem given a onevariable, two-step equation or inequality. TSI Mathematics & Statistics Test - Intermediate Algebra Determine the Slope from a Real World Equation Determine the Slope from Real World Graph Find the X and Y Intercepts from a Real World Equation Find the X and Y Intercepts from a Real World Graph Finding Domain and Range Domain and Range in the Real World Factoring out the GCF in Polynomial Expressions Factoring Polynomial Expressions by Grouping Factoring Polynomial Expressions by the Difference of Squares Factoring Polynomial Expressions by Trinomials Level D (+6, 7-8): Define, evaluate & compare functions; Use functions to model relationships between quantities; Level E (High School): Understand the concept of a function and use function notation; Interpret functions that arise in applications in terms of the ; Analyze functions using different representations; Build a function that models a relationship between two quantities; Construct and compare linear, quadratic and exponential models and solve ; interpret expressions for functions in terms of the situation they model; Level E (High School): Perform arithmetic operations on polynomials; Level E (High School): Interpret the structure of expressions; Write expressions in equivalent forms to solve ; Perform arithmetic operations on polynomials; Write expressions in equivalent forms to solve (8.2A) determine the domain and range of a linear function in mathematical, determine reasonable domain and range values for real-world situations, both continuous and discrete, and represent domain and range using inequalities; (A.2A) determine the domain and range of a linear function in mathematical, determine reasonable domain and range values for real-world situations, both continuous and discrete, and represent domain and range using inequalities (II.D.1) Interpret multiple representations of equations and relationships; (II.D.2) Translate among multiple representations of equations and relationships; (VIII.A.1) Analyze given information; (VIII.A.2) Formulate a plan or strategy; (VIII.A.3) Determine a solution; (VIII.C.1) Formulate a solution to a real world situation; (IX.A.1) Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem; (IX.A.2) Use mathematical language to represent and communicate the mathematical concepts in a problem; (IX.A.3) Use mathematics as a language for reasoning, making connections, and generalizing (VII.C.1) Apply known function models; (VII.C.2) Develop a function to model a situation; (VIII.C) Use a function to model a real world situation; (III.C.1) Apply known function models (A.10E) factor, if possible, trinomials with real factors in the form ax2 + bx + c, including (II.B.1) Recognize and use algebraic (field) properties, perfect square trinomials of degree two; (A.10F) concepts, procedures, and algorithms to combine, decide if a binomial can be written as the transform, and evaluate expressions (e.g., polynomials, difference of two squares and, if possible, use radicals, rational expressions); the structure of a difference of two squares to rewrite the binomial Solves quadratic equations by factoring and by using the quadratic formula Solves equations using the square root property Simplifies square roots with numerical values Solves simple radical and rational equations Factoring out GCF Solving Quadratic Equations by Factoring Solving Quadratic Equations using the Quadratic Formula Using the Zero Product Property to Solve Quadratic Equations The Quadratic Formula Solving Equations with Square Roots Solving Equations with One Variable Evaluating Square Roots Simplifying Square Roots Estimating Irrational Numbers Solving Simple Radical Equations Solving Equations with Variables in the Denominators Solving Simple Radicals Level E (High School): Solve equations and inequaltiies in one equation; Construct & compare linear, quadratic, and exponential models and solve Level E (High School): Extend the properties of exponents to rational exponents; Interpret the structure of expressions; Write expressions in equivalent forms to solve ; Level D (+6, 7-8): Work with radicals and integer exponents; (A.10E) factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two (A2.4F) solve quadratic and square root equations (8.2B) approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line; (A2.4F) solve quadratic and square root equations (II.A.1) Explain and differentiate between expressions and equations using words such as solve, evaluate and simplify ; (II.C.1) Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to solve equations, inequalities, and systems of linear equations; (IX.A.1) Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem; (VIII.A.3) Determine a solution (I.B.1) Perform computations with real and complex numbers; (VIII.A.3) Determine a solution (II.B.1) Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions (e.g, polynomials, radicals, rational expressions) (I.A.1) Compare real numbers (VIII.A.3) Determine a solution;(ii.c.1) Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to solve equations, inequalities, and systems of linear equations 2

3 Applies unit conversions in word Formulates algebraic expressions & equations to solve word Applies rules of exponents Analyzes models involving 2-D and 3-D representations and applies ratios and proportions to solve geometric Applies Pythagorean Theorem in concrete and abstract Employs algebra in geometric applications Word with mixed units of measurement Converting Measurements Using Proportions Distance/Rate/Time Problems Simple Interest Problems Using Systems of Equations to Model Age Problems Using Systems of Equations to Model Cost/Value Problems Simplifying Rational Exponents Integer Exponents Rational Exponents as Radicals Level E (High School): Reason quantitatively and use units to solve. Level E (High School): Write expressions in equivalent forms to solve ; Level D(+6,7-8): Solve real-life & mathematical using numerical and algebraic expressions and equations Level E (High School): Extend the properties of exponents to rational exponents No specific TEK on "applies" (7.D) solve involving ratios, rates, and percents, including multi-step involving percent increase and percent decrease, and financial literacy (7.E) convert between measurement systems, including the use of proportions and the use of unit rates (8.C) model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world using rational number coefficients and constants; TSI Mathematics & Statistics Test - Geometry & Measurement (IV.B.2) Convert within a single measurement system; (VIII.A.1) analyze given information; (VIII.A.2) Formulate a plan or strategy; (VIII.A.3) Determine a solution;(viii.a.4) Justify the solution; (VIII.A.5) Evaluate the olving process; (IX.A.1) Use mathematical symbols, generalizing (II.A.1) Explain and differentiate between expressions and equations using words such as solve, evaluate and simplify ; (II.B.1) Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions; (III.A.3) Recognize and apply right triangle relationships including basic trigonometry; (IX.A.1) Use mathematical symbols, generalizing; (VIII.A.1) analyze given information; (VIII.A. 2) Formulate a plan or strategy; (VIII.A.3) Determine a solution;(viii.a.4) Justify the solution; (VIII.A.5) Evaluate the problem-solving process (A.11B) simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents; (A. (IV.B.4) Describe patterns and departure from patterns in 9B) interpret the meaning of the values of a and a set of data. b in exponential functions of the form f(x) = abx in real-world Finding Missing Measurements of Similar Figures Using Proportions Similar Figures Solving a Problem with a Visual Using the Pythagorean Theorem Using the Pythagorean Theorem on a Coordinate Plane Finding Missing Sides Using the Pythagorean Theorem The Pythagorean Theorem Finding Side Lengths of Parallelograms Using Algebra Finding Angles in a Triangle Using Algebra Writing an Equation to Solve a Geometry Problem Level D (+6, 7-8): Draw, construct, and describe geometrical figures and describe the relationships between them Level D (+6, 7-8): Understand and apply the Pythagorean Theorem Level D (+6, 7-8): Solve real-life and mathematical involving angle, measure, area, surface area, and volume (7.9A) solve involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids; (7.9D) solve involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape's net. (8.7C) use the Pythagorean Theorem and its converse to solve (8.8B) model the relationship between the volume of a cylinder and a cone having both congruent bases and heightsand connect that relationship to the formulas; (8.7B) use previous knowledge of surface area to make connections to the formulas for lateral and total surface areaand determine solutions for involving rectangular prisms, triangular prisms, and cylinders; (III.A.1) Identify and represent the features of plan and space figures; (III.A.2) Make, test, and use conjectures about one-, two-, and three-dimensional figures and their properties; (IV.C.3) Determine indirect measurements of figures using scale drawings, similar figures, the Pythagorean Theorem and basic trigonometry; (IX.A.1) Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem; (IX.A.2) Use mathematical language to represent and communicate the mathematical concepts in a problem (III.C.1) Make connections between geometry and algebra; (III.D.1) Make and validate geometric conjectures (IX.A.1) Use mathematical symbols, generalizing 3

4 Uses coordinate geometry to solve involving slopes, distances, and equations of lines Solving Problems Involving Slope Using Coordinate Geometry Finding the Distance between Two Points Using Coordinate Geometry Finding Equations of Lines Using Coordinate Geometry Finding the Distance between Two Points Writing a Rule for a Linear Equation Creating a Table of Values for a Linear Function Level D (+6, 7-8): Understand the connections between proportional relationships, lines and linear equations; Analyze and solve linear equations and pairs of simultaneous linear equations (8.7D) determine the distance between two points on a coordinate plane using the Pythagorean Theorem; (8.4A) use similar right triangles to develop an understanding that slope, m, given as the rate comparing the changein y-values to the change in x-values, (y2 - y1) / (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) onthe same line; (8.4B) graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; (III.C.1) Make connections between geometry and algebra; (IX.A.1) Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem; (IX.A.2) Use mathematical language to represent and communicate the mathematical concepts in a problem Parallelograms, Rectangles, Triangles, and Squares Finding Missing Measurements of Dilated Figures Uses transformations, reflections and lines of symmetry Finding New Vertices of of a Translated Shape Rotating Geometric Shapes Dilations Level D (+6, 7-8): Understand congruence and similarity using physical models, transparencies, or geometry software (8.10A) generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane; (8.10B) differentiate between transformations that preserve congruence and those that do not (III.B.1) Identify and apply transformations to figures; (III. B.2) Identify the symmetries of a plane figure; (III.B.3) Use congruence transformations and dilations to investigate congruence, similarity, and symmetries of plane figures Converts measures, including in the metric system Uses rational and irrational values within a geometric Calculates & interprets measures of center (mean, median, mode) and variability (range) Makes predictions using statistics Translations, Rotations, and Reflections Converting Measurements within the Customary System Converting Measurements within the Metric System Finding Missing Lengths in a Scale Drawing Writing Proportions Solving Proportions Level D (+6, 7-8): Understand ratio concepts and use ratio reasoning to solve Level D (+6, 7-8): Apply and extend previous understandings of numbers to the system of rational numbers (7.4E) convert between measurement systems, including the use of proportions and the use of unit rates (8.3C) use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation; (7.5C) solve mathematical and real-world involving similar shape and scale drawings. TSI Mathematics & Statistics Test - Data, Statistics, & Probability Calculating and Choosing the Best Measure of Central Tendency Mean Median Mode Range Effect of Extreme Values in Mean, Median, and Mode Making Predictions from a Given Frequency Distribution Making Predictions from a Circle Graph Interpreting a Frequency Distribution Table Interpreting a Circle Graph Level D (+6, 7-8): Summarize and describe distributions; Use random sampling to draw inferences about a population; Draw informal comparative inferences about two populations; Investigate chance processes and develop, use, and evaluate probability models (6.12B) use the graphical representation of numeric data to describe the center, spread, and shape of the data distribution; (6.12C) summarize numeric data with numerical summaries, including the mean and median (measures of center) and the range and interquartile range (IQR) (measures of spread), and use these summaries to describe the center, spread, and shape of the data distribution; (6.12D) summarize categorical data with numerical and graphical summaries, including the mode, the percent of values in each category (relative frequency table), and the percent bar graph, and use these summaries to describe the data distribution. (7.6C) make predictions and determine solutions using experimental data for simple and compound events; (7.6D) make predictions and determine solutions using theoretical probability for simple and compound events. (IV.A.1) Select or use the appropriate type of unit for the attribute being measured; (IV.B.1) Convert from one measurement system to another; (IV.B.2) Convert within a single measurement system (III.C.1) Make connections between geometry and algebra (III.A.3) Recognize and apply right triangle relationships including basic trigonometry. (IV.D.1) Compute and use measures of center and spread to describe data; (X.B.1) Use multiple representations to demonstrate links between mathematical and real world situation; (X.B.2) Understand and use appropriate mathematical models in the natural, physical, and social sciences (IV.D.2) Apply probabilistic measures to practical situations to make an informed decision; (IX.B.2) Summarize and interpret mathematical information provided orally, visually, or in written form within the given Matching Data with the Appropriate Graph 4

5 Using Theoretical Probability to Make a Prediction Calculates probabilities and Using Experimental Probability to Make a uses theoretical probabilties Prediction and experimental results to make predictions and decisions Probability of a Simple Event Uses variability (range) and selects the appropriate measure of central tendency to describe data Analyzes trends in frequency distributions, dot plots, line graphs, circle graphs, and bar graphs Probability of Independent Events Calculating and Choosing the Best Measure of Central Tendency Making Predictions from a Given Frequency Distribution Making Predictions from a Circle Graph Making Predictions from a Bar Graph Interpreting a Frequency Distribution Table Interpreting a Circle Graph Level C (4th, 5th, 6th +): Summarize and describe distributions; Represent and interpret data; (7.6E) find the probabilities of a simple event and its complement and describe the relationship between the two;simple experiments; (7.6F) use data from a random sample to make inferences about a population; (7.10A) construct sample spaces for simple or composite experiments - new TEKS and language; (7.6I) determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces. (7.12A) compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads; (8.11A) construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariatedata; (V.B.1) Compute and interpret the probability of an event and its complement; (V.B.2) Compute and interpret the probability of conditional and compound events (VI.B.1) Determine types of data; (VI.B.2) Select and apply appropriate visual representations of data; (VI.B.3) Compute and describe summary statistics of data; (VI.B. 4) Describe patterns and departure from patterns in a set of data (VI.C.1) Make predictions and draw inferences using summary statistics; (VI.C.2) Analyze data sets using graphs and summary statistics; (VI.C.3) Analyze relationships between paired data using spreadsheets, graphing calculators or statistical software; (IX.B.2) Summarize and interpret mathematical information provided orally, visually, or in written form within the given Applies counting principles Matching Data with the Appropriate Graph Calculating the Number of Outcomes Fundamental Counting Principal Level C (4th, 5th, 6th +): Compute fluently with multi-digit numbers and find common factors and multiples; Use the four operations with whole numbers to solve (7.6A) represent sample spaces for simple and compound events using lists and tree diagrams; (V.A.1) Determine the nature and the number of elements (7.6B) select and use different simulations to in a finite sample space represent simple and compound events with and without technology 5

MIDLAND ISD ADVANCED PLACEMENT CURRICULUM STANDARDS. ALGEBRA l

MIDLAND ISD ADVANCED PLACEMENT CURRICULUM STANDARDS. ALGEBRA l (1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The (A) describe independent and dependent