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 The ACT and the New Missouri Learning Standards for Mathematics (6-12)Introduction and Observations:Overall, the new standards represent a lot of hard work by both educators and parents and are well written. The process seemed to be transparent, with many comments from the public. I do, however, want to make the following observations I would probably refer to them as goals instead of standards. Since there are few math teachers who would claim to be proficient with every topic identified, it’s unrealistic to say that this is what every student needs to know to be ready for college or work.The role of calculators is not addressed. My assumption is that students will be able to use their calculator on the whole test (Like the ACT) but that may not be true.While the use of words such as explain, prove and derive are useful when writing goals or standards, they make writing a test to assess these goals or standards more difficult to write and even more difficult to grade objectively. Multiple choice tests, such as the ACT, put the higher level thinking into the “Front end” of the question through reading. Asking students to explain or prove (E.g., prove the Pythagorean Identity) puts the higher level thinking on the “Back end”. This makes writing the questions easier, but grading much more difficult.The standards are actually written for grades 6-11. They identify some topics for a math course after Algebra 2, but are not specific about which topics are necessary or most important.The ACT and the Missouri Learning Standards for Mathematics (6-12) Purpose:This guide identifies the topics from traditional high school math courses that are addressed by the ACT, the new Missouri Learning Standards for Math (6-12) or both.Overview:This guide (Divided into 4 sections: Algebra 1 and 2, Geometry and Pre-calculus) is based on the content of the most widely used textbooks and form a “generic” table of contents for each course. For the ACT, the 3 released tests from the previous 10 years (2006-2015) were examined. With the Missouri Learning Standards, only the topics for ALL students were included. Optional Topics are identified with a * (E.g., the topics for any course after Algebra 2 are identified as 12*). Topics that are implied, but not mentioned specifically are identified by ** (E.g., knowing how to apply the “discriminant” is implied, but that term is not included).Legend:Topics in black are included both the ACT and the Missouri Learning Standards. Unless noted, all other topics appeared on an ACT at least twice. Topics in blue were found on the ACT, but not included on the Missouri learning ics in green are included on the Missouri Learning Standards, but have not appeared on a released ACT within the last ten ics in red are not included on the Missouri Learning Standards and have not appeared on a released form of the ACT within the last 10 years.Following the 4 sections is a list of other topics that have appeared on the ACT within the last ten years and other topics addressed by the Missouri Learning Standards. Topics that are addressed by the Missouri Learning Standards for grades 6-8 are identified, but this guide only specifies topics for grades 9-12.Copyright Dr. Gary Moss Focus on Learning Center July 2016Algebra 11.1Exponents and Powers (NQ A1)1.2 Making a Table (6-8)1.3Order of Operations (6-8)1.4Finding Patterns (6-8)1.5Equations and Inequalities (CED A1)1.6Exploring Problem Solving (CED A1)1.7Problem Solving Plan Using Models (CEDC A1)1.8Tables and Graphs (IF B1)1.9An Introduction to Functions (6-8)2.1The Real Number Line (6-8)2.2Modeling Addition of Integers (6-8)2.3Addition of Real Numbers (6-8)2.4Modeling Subtractions of Integers (6-8)2.5Subtraction of Real Numbers (6-8)2.6Adding and Subtracting Matrices (12*)2.7Multiplication of real Numbers (6-8)2.8Modeling the Distributive Properties (6-8)2.9The Distributive Property (6-8)2.10Division of Real Numbers (6-8)2.11Probability and Odds (6-8**)3.1Modeling One Step Equations (NQ A1)3.2Solving Equations Using Addition & Subtraction (NQ A1)3.3Solving Equations Using Multiplication (NQ A1)3.4Solving Multi-Step Equations (NQ A1)3.5Modeling Equations with Variables on Both Sides (NQ A1)3.6Solving Equations with Variables on Both Sides (NQ A1)3.7Linear Equations and Problem Solving (NQ A1)3.8Solving Decimal Equations (NQ A1)3.9Formulas and Functions (IF A1 and SSE A1)3.10Rates, Ratios and Percent (6-8)3.11Inductive and Deductive Reasoning (CO C1 and C2)4.1Coordinates and Scatter Plots (6-8)4.2Graphing a Scatter Plot (6-8)4.3Graphing Linear Equations (REI C1)4.4Quick Graphs Using Intercepts (REI C1)4.5Investigating Slope (DS A6)4.6The Slope of a Line (DS A6)4.7Direct Variation (6-8)4.8Graphing Families of Linear Equations (CED A1)4.9Quick Graphs Using Slope-Intercept Form (CED A1)4.10Graphing Linear Equation (CED A1)4.11Solving Linear Equations Using Graphs (CED A1)4.12Functions and relations (IF A1)5.1Writing Linear Equations in Slope-Intercept Form (CED A2)5.2Writing Linear Equations Given the Slope and a Point (CED A2)5.3Writing Linear Equations Given Two Points (CED A2)5.4Fitting a Line to Data (LQE A1)5.5Best Fit Lines (LQE A1)5.6Point Slope Form of a Linear Equation (LQE A1)5.7Investigation of the Standard Form of a Linear Equation (LQE A1)5.8The Standard Form of a Linear Equation (LQE A1)5.9Investigating Linear Modeling (LQE A1)5.10Predicting with Linear Models (LQE A1)6.1Investigating Inequalities (CED A1)6.2Solving One-Step Inequalities (CED A1)6.3Solving Multi-Step Inequalities (CED A1)6.4Solving Compound Inequalities (CED A1)6.5Solving Compound Inequalities (CED A1)6.6Solving Absolute-Value Equations (CED A1)6.7Graphing Absolute-Value Equations (CED A1)6.8Graphing Linear Inequalities in Two Variables (CED A1)6.9Graphing Inequalities (CED A1)6.10Histograms and Mean, Median & Mode (6-8)6.11Box-and-Whisker Plots (6-8)7.1Investigating graphs of Linear Systems (CED A3)7.2Solving Linear Systems by Graphing (CED A3)7.3Solving Linear Systems by Substitution (CED A3)7.4Solving Linear Systems by Linear Combinations (REI B3)7.5Applications of Linear Systems (REI B3)7.6Investigating Special Types of Linear Systems (REI B3)7.7Special Types of Linear Systems (REI C3)7.8Solving Systems of Linear Inequalities (REI C3)8.1Multiplication Properties of Exponents (NQ A1)8.2Zero and Negative Exponents (NQ A1)8.3Graphing Exponential Functions (CED A2)8.4Division Properties of Exponents (NQ A1)8.5Scientific Notation (6-8)8.6Linear and exponential Growth Models (CED A2)8.7Exponential Growth Functions (CED A2)8.8Investigating Exponential Decay (CED A2)8.9Exponential Decay Functions (CED A2)8.10Fitting Exponential Models (CED A2)9.1Solving Quadratic Equations by Finding Square Root (SSE A3)9.2Simplifying Radicals (NQ A2)9.3Investigation Graphs and Quadratic Functions (CED A2)9.4Graphing Quadratic Functions (CED A2)9.5Graphing Quadratic Curves of Best Fit (CED A2)9.6Solving Quadratic Equations by Graphing (CED A2)9.7Approximating Solutions by Graphing (REI A2)9.8Solving Quadratic Equations by the Quadratic Formula (REI A2)9.9Investigating the Applications of the Discriminate (REI A2**)9.10Applications of the Discriminate (REI A2**)9.11Graphing Quadratic Inequalities (REI B1)9.12Comparing Linear, Exponential and Quadratic Models (CED A2)10.1Adding and Subtracting of polynomials (SSE A2)10.2Graphing polynomial Functions (SSE A2)10.3Multiplying Polynomials (SSE A2)10.4Special Products of Polynomials (SSE A2)10.5Solving Polynomial Equations in Factored Form (SSE A3)10.6Modeling the Factorization of x2 +bx + c (SSE A3)10.7Factoring x2 +bx + c (SSE A3) Common on ACT10.8Modeling the Factorization of ax2 +bx + c (SSE A3) Rare on ACT10.9Factoring ax2 +bx + c (SSE A3) Rare on ACT10.10Modeling the Factorization of ax2 + 2abx +b2 (SSE A3) Rare on ACT 10.11Factoring Special Products (SSE A3)10.12Factoring Using the Distributive Property (SSEA3)11.1Ratio and Proportion (6-8)11.2Percent (6-8)11.3Direct and Inverse Variation (6-8)11.4Modeling Inverse Variation (CED A1**)11.5Simplifying Rational Expressions (SSE A2)11.6Multiplying and Dividing Rational Expressions (SSEA 2)11.7Adding and Subtracting Rational Expressions (SSE A2)11.8Modeling Polynomial Division (APR A2)11.9Dividing Polynomials (APR A2)11.10Rational Equations and Functions (IF C1)11.11Graphing Rational Functions (IF C1)12.1Functions Involving Square Roots (NQ A2)12.2Operations with Radical Expressions (NQ A2)12.3Solving Radical Equations (NQ A2)12.4Modeling Completing the Square (SSE A3 and REI A2)12.5Completing the Square (SSE A3 and REI A2)12.6Investigating the Pythagorean Theorem (CO C2)12.7The Pythagorean Theorem and Its Converse (CO C2)12.8The Distance and Midpoint Formulas (CO C2)12.9Investigating Special Triangles (SRT C1)12.10Trigonometric Ratios (SRT C1)12.11Logical Reasoning: Proof (CO C1, C2 and C3)ALGEBRA 21.1 Apply Properties of Real Numbers (6-8)1.2Evaluate and Simplify Algebraic Expressions (6-8)1.3Solve Linear Equations (CED A1)1.4Rewrite Formulas and Equations (CED A1)1.5Use Problem Solving Strategies and Models (CED A1)1.6Solve Linear Inequalities (CED A1)1.7Solve Absolute Value Equations and Inequalities (REI A1)2.1Represent Relations and Functions (CED A1)2.2Represent Relations and Functions (CED A1)2.3Graph Equations of Lines (CED A1)2.4Write Equations of Lines (CED A1)2.5Model Direct Variation (CED A1)2.6Draw Scatter Plots (6-8) and Best-Fitting Lines (LQE A1)2.7Use Absolute Value Functions and Transformations (REI A1)2.8Graph Linear Inequalities in Two Variables (REI C2)3.1Solve Linear Systems by Graphing (REI B1)3.2Solve Linear Systems Algebraically (REI B1)3.3Graph Systems of Linear Inequalities (REI C3)3.4Solve Systems of Linear Equations in Three Variables3.5Perform Basic Matrix Operations (12*)3.6Multiply Matrices (12*)3.7Evaluate Determinants and Apply Cramer's Rule (12*)3.8Use Inverse Matrices to Solve Linear Systems (12*)4.1Graph Quadratic Functions in Standard Form (REI A2)4.2Graph Quadratic Functions in Vertex or Intercept Form (REI A2)4.3Solve x2 + bx + c = 0 by Factoring (REI A2) Common on ACT4.4Solve ax2 + bx + c = 0 by Factoring (REI A2) Rare on ACT4.5Solve Quadratic Equations by Finding Square Roots (REI A2)4.6Perform Operations with Complex Numbers (NQ B1)4.7Complete the Square (REI A2)4.8Use the Quadratic Formula (REI A2) and the Discriminant (REI A2**)4.9Graph and Solve Quadratic Inequalities (REI B1)4.10Write Quadratic Functions and Models (REI A2)5.1Use Properties of Polynomials (APR A1)5.2Evaluate and Graph Polynomials (APR A1)5.3Add, Subtract, and Multiply Polynomials (APR A1)5.4Factor and Solve Polynomial Equations (APR A1)5.5Apply the Remainder and Factor Theorems (APR A2)5.6Find Rational Zeros (APR A5)5.7Apply the Fundamental Theorem of Algebra (NQ B3*)5.8Write Polynomial Functions and Models (APR A5)6.1Evaluate nth Roots and Use Rational Exponents (NQ A1)6.2Apply Properties of Rational Exponents (NQ A1)6.3Perform Function Operations and Composition (BF A1)6.4Use Inverse Functions (SSE A2)6.5Graph Square Root and Cube Root Functions (NQ A1)6.6Solve Radical Equations (NQ A3, NQ A4, REI A2)7.1Graph Exponential Growth Functions (FM A1)7.2Graph Exponential Decay Functions (FM A2)7.3Use Functions Involving e (SSE A2**)7.4Evaluate Logarithms and Graph Logarithmic Functions (SSE A3)7.5Apply Properties of Logarithms (SSE A3)7.6Solve Exponential and Logarithmic Equations (SSE A3)7.7Write and Apply Exponential (SSE A3) and Power Functions8.1Model Inverse and Joint Variation (CED A1**)8.2Graph Simple Rational Functions (APR A4**)8.3Graph General Rational Functions (APR A4**)8.4Multiply and Divide Rational Expressions (APR A4)8.5Add and Subtract Rational Expressions (APR A4)8.6Solve Rational Equations (APR A4)9.1Apply the Distance and Midpoint Formulas (6-8)9.2Graph and Write Equations of Parabolas (GPE A2)9.3Graph and Write Equations of Circles (GPE A1)9.4Graph and Write Equations of Ellipses9.5Graph and Write Equations of Hyperbolas9.6Translate and Classify Conic Sections9.7Solve Quadratic Systems (REI B1)10.1Apply the Counting Principle and Permutations (12**)10.2Use Combinations (12*) and the Binomial Theorem 10.3Define and Use Probability (6-8)10.4Find Probabilities of Disjoint and Overlapping Event (CP A1)10.5Find Probabilities of Independent and Dependent Events (CP A2)10.6Construct and Interpret Binomial Distributions11.1Find Measures of Central Tendency and Dispersion (6-8)11.2Apply Transformations to Data (BF A3**)11.3Use Normal Distributions (DS B1)11.4Select and Draw Conclusions from Samples (DS A4)11.5Choose the Best Model for Two-Variable Data (DS A2)12.1 Define and Use Sequences and Series (LQE B1)12.2Analyze Arithmetic Sequences and Series (LQE B1)12.3Analyze Geometric Sequences and Series (LQE B1)12.4Find Sums of Infinite Geometric Series (LQE B1)12.5Use Recursive Rules with Sequences and Functions (LQE B2 and LQE B3)13.1Use Trigonometry with Right Triangles (SRT C1)13.2Define General Angles and Use Radian Measure (12*)13.3Evaluate Trigonometric Functions of Any Angle (12*)13.4Evaluate Inverse Trigonometric Functions (12*)13.5Evaluate Inverse Trigonometric Functions (12*)13.6Apply the Law of Cosines (12*)14.1Graph Sine, Cosine, and Tangent Functions (!2*)14.2Translate and Reflect Trigonometric Graphs (12*)14.3Verify Trigonometric Identities--Only basic (12*)14.4Solve Trigonometric Equations (!2*)14.5Write Trigonometric Functions and Models (!2*)14.6Apply Sum and Difference Formulas14.7Apply Double-Angle and Half-Angle Formulas (12*) Rare on ACTGEOMETRY1.1Identify Points, Lines, and Plane (6-8)1.2Use Segments and Congruence (6-8)1.3Use Midpoint and Distance Formulas (6-8)1.4Measure and Classify Angles (6-8)1.5Describe Angle Pair Relationships (6-8)1.6Classify Polygons (6-8)1.7Find Perimeter, Circumference, and Area (6-8)2.1Use Inductive Reasoning2.2Analyze Conditional Statements (CO C1, C2 and C3)2.3Apply Deductive Reasoning (CO A1)2.4Use Postulates and Assumptions (CO A1)2.5Reason Using Properties from Algebra (CO A1)2.6(Prove) Statements about Segments and Angles (CO A1)2.7(Prove) Angle Pair Relationships (CO A1)3.1Identify Pairs of Lines and Angles (CO A1)3.2Use Parallel Lines and Transversals (CO A1)3.3(Prove) Lines are Parallel (CO C1)3.4Find and Use Slopes of Lines (DS A6)3.5Write and Graph Equations of Lines (LQ E3)3.6(Prove) Theorems about Perpendicular Lines (CO C1)4.1Apply Triangle Sum Properties (CO C2)4.2Apply Congruence and Triangles (CO C2)4.3(Prove) Triangles Congruent by SSS (CO B2)4.4(Prove) Triangles Congruent by SAS and HL (CO B2)4.5Prove Triangles Congruent by ASA and AAS (CO B2)4.6Use Congruent Triangles (CO B2)4.7Use Isosceles and Equilateral Triangles (CO B2)4.8Perform Congruence Transformations (CO B1)5.1Midsegment Theorem (GPE B3) and Coordinate Proof (GPE B1)5.2Use Perpendicular Bisectors (CO A1)5.3Use Angle Bisectors of Triangles (CO C1)5.4Use Medians and Altitudes (CO C2)5.5Use Inequalities in a Triangle5.6Inequalities in Two Triangles and Indirect Proof6.1Ratios, Proportions, and the Geometric Mean (SRT A2)6.2Use Proportions to Solve Geometry Problems (SRT A2)6.3Use Similar Polygons (SRT A2)6.4(Prove) Triangles Similar by AA (SRT A3)6.5(Prove) Triangles Similar by SSS and SAS (CO C2)6.6Use Proportionality Theorems (SRT A2)6.7Perform Similarity Transformations (CO A2)7.1Apply the Pythagorean Theorem (6-8)7.2Use the Converse of the Pythagorean Theorem (6-8)7.3Use Similar Right Triangles (SRT A2)7.4Special Right Triangles Apply the Tangent Ratio (SRT C1)7.5Apply the Sine and Cosine Ratios (SRT C1)7.6Solve Right Triangles (SRT C1)8.1Find Angle Measures in Polygons (CO C3)8.2Use Properties of Parallelograms (CO C3)8.3Show that a Quadrilateral is a Parallelogram (CO C3)8.4Properties of Rhombuses, Rectangles, and Squares (CO C3)8.5Use Properties of Trapezoids and Kites8.6Identify Special Quadrilaterals (CO C3**)9.1Translate Figures and Use Vectors (CO A2)9.2Use Properties of Matrices (CO A2**)9.3Perform Reflections (CO A4)9.4Perform Rotations (CO A3)9.5Apply Compositions of Transformations (CO A5)9.6Identify Symmetry (CO A3)10.1Use Properties of Tangents (C B1)10.2Find Arc Measures (C B1)10.3Apply Properties of Chords (C B1)10.4Use Inscribed Angles and Polygons (CO C3)10.5Apply Other Angle Relationships in Circles (C A2)10.6Find Segment Lengths in Circles (C A2)10.7Write and Graph Equations of Circles (GPE A1)11.1Areas of Triangles and Parallelograms (GPE B4)11.2Areas of Trapezoids, Rhombuses (GPE B4) and Kites11.3Perimeter and Area of Similar Figures (SRT A2)11.4Circumference and Arc Length (C B1)11.5Areas of Circles and Sectors (C B2)11.6Areas of any Regular Polygon (A = ? ap)11.7Geometric Probability (6-8**)12.1Explore Solids (GMD A1)12.2Surface Area of Prisms and Cylinders (GPE B4**)12.3Surface Area of Pyramids and Cones (GPE B4**)12.4Volume of Prisms and Cylinders (GMD A1)12.5Volume of Pyramids and Cones (GMD A1)12.6Surface Area and Volume of Spheres (GMD A1** and SRT A1**)12.7Explore Similar Solids (SRT A1)PRE-CALCULUS1.1Relations and Functions (IF A1)1.2Composition of Functions (BF A1)1.3Graphing Linear Equations (CED A2)1.4Writing Linear Equations (CED A2)1.5Writing Equations of Parallel and Perpendicular Lines (CED A2**)1.6Modeling Real-World Data with Linear Functions (CED A1)1.7Piecewise Functions1.8Graphing Linear Inequalities (REI C2)2.1Solving Systems of Equations in Two Variables (REI B1)2.2Solving Systems of Equations in Three Variables (12*)2.3Modeling Real-World Data with Matrices (12*)2.4Modeling Motion with Matrices (12*)2.5Determinants and Multiplicative Inverses of Matrices (12*)2.6Solving Systems of Linear Inequalities (REI C3)2.7Linear Programming (CED A1)3.1Symmetry and Coordinate Graphs (CO A3)3.2Families of Graphs (BF A1)3.3Graphs of Nonlinear Inequalities (REI B1)3.4Inverse Functions and Relations (BF A2)3.5Continuity and End Behavior (12*)3.6Critical Points and Extrema (12*)3.7Graphs of Rational Functions (REI A2)3.8Direct, Inverse, and Joint Variation (CED A1**)4.1Polynomial Functions (SSE A2)4.2Quadratic Equations (SSE A3)4.3The Remainder and Factor Theorems (APR A2)4.4The Rational Root Theorem 4.5Locating Zeros of a Polynomial Function (APR A5)4.6Rational Equations and Partial Fractions (12*)4.7Radical Equations and Inequalities (NQ A4)4.8Modeling Real-World Data with Polynomial Functions (SSE A2)5.1Angles and Degree Measure (CO A1)5.2Trigonometric Ratios in Right Triangles (SRT C3)5.3Trigonometric Functions on the Unit Circle (12*)5.4Applying Trigonometric Functions (12*)5.5Solving Right Triangles (SRT C3)5.6The Law of Sines (12*)5.7The Ambiguous Case for the Law of Sines5.8The Law of Cosines (12*)6.1Angles and Radian Measure (12*)6.2Linear and Angular Velocity (12*)6.3Graphing Sine and Cosine Functions (12*)6.4Amplitude and Period of Sine and (12*)6.5Translations of Sine and Cosine (12*)6.6Modeling Real-World Data with Sinusoidal (12*)6.7Graphing Other Trigonometric Functions (12*)6.8Trigonometric Inverses and Their Graphs (12*)7.1Basic Trigonometric Identities--Only Sin2 X + Cos2 X not provided (12*)7.2Verifying Trigonometric Identities--Only basic (12*)7.3Sum and Difference Identities (12*)7.4Double-Angle and Half-Angle Identities (12*) Rare on ACT7.5Solving Trigonometric Equations (12*)7.6Normal Form of a Linear Equation (12*)7.7Distance From a Point to a Line (12*)8.1Geometric Vectors (12*)8.2Algebraic Vectors (12*)8.3Vectors in Three-Dimensional Space (12*)8.4Perpendicular Vectors (12*)8.5Applications with Vectors (12*)8.6Vectors and Parametric Equations (12*)8.7Modeling Motion Using Parametric Equations (12*)8.8 Transformational Matrices in Three-Dimensional Space (12*)9.1Polar Coordinates (12*)9.2Graphs of Polar Equations (12*)9.3Polar and Rectangular Coordinates (12*)9.4Polar Form of a Linear Equation (12*)9.5Simplifying Complex Numbers (NQ B2)9.6The Complex Plane and Polar Form of Complex Numbers (12*) 9.7Products and Quotients of Complex Numbers in Polar Form (12*)9.8Powers and Roots of Complex Numbers (12*)10.1Introduction to Analytic Geometry (12*)10.2Circles (GPE A1)10.3Ellipses (12*)10.4Hyperbolas (12*)10.5Parabolas (GPE A2)10.6Rectangular and Parametric Forms of Conic Sections (12*)10.7Transformations of Conies (12*)10.8Systems of Second-Degree Equations and Inequalities (12*)11.1Real Exponents (NQ A1)11.2Exponential Functions (FM A1)11.3The Number e (12*)11.4Logarithmic Functions (SSE A3)11.5Common Logarithms (SSE A3)11.6Natural Logarithms (12*)12.1Arithmetic Sequences and Series (LQE B1)12.2Geometric Sequences and Series (LQE B1)12.3Infinite Sequences and Series (LQE B1)12.4Convergent and Divergent Series (12*)12.5Sigma Notation and the nth Term (12*)12.6The Binomial Theorem (12*)12.7Special Sequences and Series (12*)12.8Sequences and Iteration (12*)12.9Mathematical Induction (12*)13.1Permutations and Combinations (12*)13.2Permutations with Repetitions (12*)13.3Probability and Odds (6-8**)13.4Probabilities of Compound Events (CP A1, CP A2 and CP A6)13.5Conditional Probability (CP A4 and CP A5) 13.6The Binomial Theorem and Probability14.1The Frequency Distribution (CP A4)14.2Measures of Central Tendency (6-8)14.3Measures of Variability (DS B1)14.4The Normal Distribution (DS B1 and DS B2)14.5 The “Empirical Rule--67%-95%-99.7% rule for the Normal Distribution (DS B1)Other Topics on the ACT, but not a Missouri Math StandardLogic (Converse, inverse and contrapositive)Step Functions Stem-Leaf plotsOther Topics identified by the Missouri Standards, but not addressed by the ACT The inverse relationship between exponents and Logarithms to solve exponential and logarithmic equations.Logarithmic scales (Addressed by the ACT science test)Analyze how random sampling could be used to make inferences about population parameters.Describe and explain the purposes, relationship to randomization ad differences among sample surveys, experiments and observational studies.Use data from sample to estimate characteristics of the population and recognize the meaning of the margin of error in these estimates.Describe and explain how the relative sizes of a sample and the population affect the margin of error of predictions.Fit a data set to a distribution using its mean and standard deviation to determine whether the data is approximately normally distributed.Construct geometric figures using various tools and methods.Prove all circles are similar using similarity transformations Derive the equation of a parabola given a focus and a directrix. Use geometric shapes, their measures and their properties to describe objects. Apply the concept of density on area and volume in modeling situations. Apply geometric methods to solve design mathematical modeling problems. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. ................
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