A Correlation of. Pearson. Mathematical Ideas. to the. TSI Topics

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1 A Correlation of Pearson 2016 to the

2 A Correlation of 2016 Table of Contents Module M1. Linear Equations, Inequalities, and Systems... 1 Module M2. Algebraic Expressions and Equations (Other Than Linear)... 5 Module M3. Quadratic and Other Polynomial Expressions, Equations, and Functions... 6 Module M4. Expressions, Equations, and Functions Involving Powers, Roots, and Radicals 11 Module M5. Rational and Exponential Expressions, Equations, and Functions Module M6. Plane Geometry Module M7. Transformation and Symmetry Module M8. Measurement (Linear, Area, Three-Dimensional) Module M9. Interpreting Categorical and Quantitative Data Module M10. Statistical Measures Module M11. Probabilistic Reasoning... 21

3 A Correlation of Module M1. Linear Equations, Inequalities, and Systems Topic M1.1: Introduction to Inequalities Use inequality symbols. Reverse inequality symbols. SE/TE: , , Solve word problems involving inequalities. Topic M1.2: Introduction to Equations Decide whether a given number is a solution to an equation. Write sentences as equations. Understand the difference between expressions and equations. Solve modeling word problems. SE/TE: 301, , Topic M1.3: Solving Linear Equations in One Variable Solve linear equations using the addition and multiplication properties of equality. Solve linear equations containing parentheses. Solve linear equations containing fractions. Solve word problems involving solving linear equations in one variable. SE/TE: , 299, , , Topic M1.4: More on Solving Linear Equations in One Variable Understand equations resulting in one solution, infinitely many solutions, or no solution. Solve linear equations resulting in infinitely many solutions. Solve linear equations resulting in no solution. Solve linear equations resulting in one solution, infinitely many solutions, or no solution. Solve word problems involving solving linear equations in one variable. SE/TE: , 299, , , , 457, , 464 1

4 A Correlation of 2016 Topic M1.5: Solving Linear Inequalities Decide whether a given number is a solution to an inequality. Understand the difference between set builder notation and interval notation. Graph inequalities on a number line. Use the addition property of inequality. Use the multiplication property of inequality. Use the addition property and multiplication property of inequality. Write solutions of linear inequalities using different notation. Solve word problems involving linear inequalities. SE/TE: 325, , , Topic M1.6: Set Operations and Compound Inequalities Find and graph the intersection or union of two sets. Solve compound inequalities with the word and. Solve three-part inequalities. Solve compound inequalities with the word or. Solve word problems involving compound inequalities. SE/TE: 61-62, 70, 330, 333, 334 Topic M1.7: Graphing Linear Equations Determine whether ordered pairs are solutions of linear equations. Complete ordered-pair solutions of equations and plot these points. Match linear graphs with their equations. Graph linear equations by plotting points. Solve word problems involving graphing linear equations. SE/TE: 376, 382, 383, ,

5 A Correlation of 2016 Topic M1.8: Intercepts Find x- and y-intercepts. Graph linear equations by plotting x- and y-intercepts. Identify horizontal and vertical lines. Graph horizontal and vertical lines. Solve word problems involving intercepts. SE/TE: 377, 382 Topic M1.9: The Slope of a Line Find slope given two points on a line. Identify slopes and y-intercepts of lines given their equations in slope-intercept form. Find slopes and y-intercepts of lines given their equations in any form. Determine whether the slopes of lines are positive, negative, zero, or undefined. Solve word problems involving slope. SE/TE: , , , 389, Topic M1.10: Parallel and Perpendicular Lines Determine whether lines are parallel, perpendicular, or neither. Use slope-intercept form to determine whether two lines are parallel, perpendicular, or neither. SE/TE: 380, 383, 388, 391 Topic M1.11: Equations of Lines Write an equation of a line given its slope and y-intercept. Write an equation of a line given its slope and a point on the line. Write an equation of a line given two points on the line. Write an equation of a line given its graph. Solve word problems involving the equations of lines. SE/TE: ,

6 A Correlation of 2016 Topic M1.12: Graphing Linear Equations Using Slope Graph a line given its slope and a point on the line. Graph a line given its equation in slopeintercept form. Graph a line given its equation in any form. Solve word problems involving graphing linear equations. Topic M1.13: Graphing Linear Inequalities in Two Variables Determine whether ordered pairs are solutions of linear inequalities in two variables. Graph linear inequalities in two variables. Solve word problems involving graphing linear inequalities. Topic M1.14: Systems of Linear Equations by Graphing Decide whether an ordered pair is a solution to a system of linear equations. Solve linear systems by graphing. Describe systems of linear equations. Solve word problems by graphing systems of linear equations. Topic M1.15: Systems of Linear Equations by Substitution Solve linear systems using the substitution method. Solve word problems involving systems of linear equations. SE/TE: , , , SE/TE: , 437, 438 SE/TE: , , , SE/TE: 422, 424, 425, Topic M1.16: Systems of Linear Equations by Elimination Solve linear systems using the elimination method when multiplication is not necessary. Solve linear systems using the elimination method when multiplication is necessary. Solve word problems involving systems of linear equations. SE/TE: , 425,

7 A Correlation of 2016 Topic M1.17: Systems of Linear Equations by Any Method Solve linear systems using any method. Solve word problems involving mixtures. Solve word problems involving unknown numbers. Solve word problems involving prices or investments. Solve word problems involving wind or currents. Topic M1.18: Systems of Linear Inequalities Understand the solution sets of systems of linear equations and systems of linear inequalities. Decide whether an ordered pair is a solution to a system of linear inequalities. Graph systems of linear inequalities. Solve word problems involving systems of linear inequalities. SE/TE: , , , SE/TE: , , , 438 Module M2. Algebraic Expressions and Equations (Other Than Linear) Topic M2.1: Introduction to Expressions Review the order of operations. Identify coefficients, constants, and variables in an expression. SE/TE: , 240, , 297, 301, 309, 347 Evaluate algebraic expressions. Rewrite phrases as algebraic expressions. Topic M2.2: Simplifying Expressions Understand the difference between terms and factors. Identify terms as like or unlike. Combine like terms. Simplify expressions. SE/TE: , 232, , 303, 347 Topic M2.3: Review of Expressions Simplify expressions. Translate phrases into expressions. Translate sentences into equations. SE/TE: 301, ,

8 A Correlation of 2016 Module M3. Quadratic and Other Polynomial Expressions, Equations, and Functions Topic M3.1: Introduction to Polynomials Identify polynomials. Identify terms of a polynomial. Determine the coefficient and degree of each term. Combine like terms. SE/TE: 344, Classify polynomials as monomials, binomials, or trinomials. Find the degree of a polynomial. Write polynomials in descending order. Evaluate polynomials and polynomial functions. Topic M3.2: Adding and Subtracting Polynomials Add polynomials. Subtract polynomials. Add or subtract polynomial functions. Solve perimeter word problems involving the addition or subtraction of polynomials. Solve word problems involving the addition or subtraction of polynomials. SE/TE: 345, 350 Topic M3.3: The Product Rule and Power Rules for Exponents Identify exponents and bases. Write repeated factors using exponential notation. Evaluate an exponential expression. Use the product rule for exponents. Use the power rule for exponents. Use the power of a product rule for exponents. Use more than one rule for exponents. Solve word problems involving the product rule and power rules for exponents. SE/TE: 4, , , 343 6

9 A Correlation of 2016 Topic M3.4: Multiplying a Monomial and a Polynomial Multiply a monomial and a polynomial using the rectangular method. Multiply a monomial and a polynomial using the distributive property. Solve word problems involving multiplying a monomial and a polynomial. Topic M3.5: Multiplying Binomials Multiply two binomials using the rectangular method. Multiply two binomials using the distributive property. Multiply two binomials using the FOIL method. Identify the mistakes in finding the product. Solve area word problems involving multiplying binomials. Topic M3.6: Multiplying Polynomials Multiply two polynomials. Multiply polynomial functions. Identify the mistakes in finding the product. Solve geometry word problems involving multiplying polynomials. For related content, see: SE/TE: 346 SE/TE: , 350 SE/TE: , 350 Topic M3.7: Special Products Square binomials. Find the product of a sum and difference of two terms. Find higher powers of binomials. Solve geometry word problems involving special products. Topic M3.8: Factoring the Greatest Common Factor Review finding the greatest common factor of a list of numbers. Find the greatest common factor of a list of terms. Factor out the greatest common factor. Factor by grouping. SE/TE: , 350 SE/TE: , 206, , 350 7

10 A Correlation of 2016 Topic M3.9: Factoring Trinomials of the Form x^2+bx+c Factor trinomials of the form x^2+bx+c, where b>0 and c>0. Factor trinomials of the form x^2+bx+c, where b<0 and c>0. Factor trinomials of the form x^2+bx+c, where c<0. Factor out the greatest common factor and then factor trinomials of the form x^2+bx+c. Topic M3.10: Factoring Trinomials of the Form ax^2+bx+c Factor trinomials of the form ax^2+bx+c, where ac is positive. Factor trinomials of the form ax^2+bx+c, where ac is negative. Factor out the greatest common factor and then factor trinomials of the form ax^2+bx+c. Factor by grouping. Factor by substitution. Topic M3.11: Factoring Special Cases Factor perfect square trinomials. Factor a difference of two squares. Factor the sum or difference of two cubes. Identify the mistake in factoring a polynomial. Topic M3.12: Solving Quadratic Equations by Factoring Solve quadratic equations by factoring. Solve higher-degree polynomial equations by factoring. Solve geometry word problems involving quadratic equations. Solve word problems involving consecutive integers. Solve word problems involving quadratic models. SE/TE: 350 SE/TE: , 350 SE/TE: 348, 349, 350 SE/TE: 351, , , 470, 475 8

11 A Correlation of 2016 Topic M3.13: Using the Square Root Property to Solve Quadratic Equations Solve equations of the form x^2=k. Solve equations of the form (ax+b)^2=k. Use formulas involving squared variables. Solve word problems using the square root property. SE/TE: , , Topic M3.14: Completing the Square to Solve Quadratic Equations Complete the square. Solve by completing the square when the coefficient of the squared term is one. Solve by completing the square when the coefficient of the squared term is not one. Simplify before solving. Solve word problems by completing the square. For related content, see: SE/TE: 352 Topic M3.15: Using the Quadratic Formula to Solve Quadratic Equations Identify the values of a, b, and c for quadratic equations. Use the quadratic formula to solve equations. Use the discriminant to determine the number of real solutions. Approximate solutions from the quadratic formula using a calculator. Solve word problems using the quadratic formula. SE/TE: , Topic M3.16: Introduction to Complex Numbers Identify the real and imaginary parts of a complex number. Write complex numbers using i notation. Plot complex numbers and find their absolute value. Add and subtract complex numbers. 9

12 A Correlation of 2016 Topic M3.17: Using Complex Numbers Multiply complex numbers. Find complex conjugates. Divide complex numbers. Perform operations with square roots of negative numbers. Solve word problems involving complex numbers. Topic M3.18: Solving Quadratic Equations with Complex Solutions Solve quadratic equations by the square root property. Solve quadratic equations by completing the square. Write quadratic equations given complex roots. Topic M3.19: Using the Quadratic Formula (with Complex Solutions) Solve quadratic equations using the quadratic formula. Use the discriminant to determine the number and types of solutions. Determine the most efficient method to use when solving a quadratic equation. Solve word problems modeled by quadratic equations. Topic M3.20: Quadratic Functions Evaluate quadratic functions. Convert between f(x)=ax^2+bx+c and standard form f(x)=a(x-h)^2+k. Recognize characteristics of parabolas from functions written in vertex form. Write an equation for a parabola given its graph. Solve word problems involving quadratic functions. For related content, see: SE/TE: 352, 355 SE/TE: , SE/TE: , ,

13 A Correlation of 2016 Topic M3.21: Graphs of Quadratic Functions Graph a parabola given its equation in vertex form. Graph a parabola using its roots. Identify the domain, range, and intercepts of a quadratic function from its graph. Use graphs to locate maxima or minima values. Solve word problems involving graphs of quadratic functions. SE/TE: , 406, Module M4. Expressions, Equations, and Functions Involving Powers, Roots, and Radicals Topic M4.1: Integer Exponents and the Quotient Rule Simplify expressions with a zero exponent. Understand the negative exponent rule. Simplify expressions containing negative SE/TE: , exponents. Use the quotient rule for exponents. Use more than one rule for exponents. Solve word problems involving the quotient rule of exponents. Topic M4.2: Dividing a Polynomial by a Monomial Divide a polynomial by a monomial. Solve geometry word problems involving the division of a polynomial by a monomial. Solve word problems involving the division of a polynomial by a monomial. Topic M4.3: Dividing a Polynomial by a Polynomial Divide using long division of polynomials. Divide using synthetic division. Identify the mistakes in finding the quotient. Solve geometry word problems involving the division of polynomials. Solve word problems involving the division of polynomials. 11

15 A Correlation of 2016 Topic M4.8: More Simplifying and Operations with Radicals Simplify expressions containing radicals. Write radical expressions with quotients in lowest terms. \ Topic M4.9: Solving Equations Containing Radicals Solve radical equations with one radical term. Solve radical equations with two isolated radical terms. Solve radical equations with two radical terms. Identify extraneous solutions. Solve word problems involving solving radical equations. Topic M4.10: Square Root and Cube Root Functions Evaluate square root and cube root functions. Identify the domain and range for square root and cube root functions. Find the intercepts of square root and cube root functions. Solve word problems involving square root and cube root functions. Topic M4.11: Graphing Square Root and Cube Root Functions Graph square root and cube root functions. Identify intervals on which square and cube root functions are increasing, decreasing, or constant. Identify the domain, range, and intercepts of square and cube root functions given their graphs. SE/TE: 261,

16 A Correlation of 2016 Module M5. Rational and Exponential Expressions, Equations, and Functions Topic M5.1: The Fundamental Property of Rational Expressions Evaluate rational expressions. Identify values for which a rational expression is undefined. Write rational expressions in lowest terms. Recognize equivalent forms of rational expressions. Solve word problems involving rational expressions. Topic M5.2: Multiplying and Dividing Rational Expressions Multiply rational expressions. Find reciprocals. Divide rational expressions. Solve word problems involving the multiplication or division of rational expressions. Topic M5.3: Adding and Subtracting Rational Expressions Add or subtract rational expressions having the same denominator. Find the least common denominator for a group of rational expressions. Rewrite rational expressions with given denominators. Add or subtract rational expressions having different denominators. Solve word problems involving the addition or subtraction of rational expressions. Topic M5.4: Simplify Complex Fractions Use the method of first simplifying the numerator and denominator separately. Use the method of multiplying the numerator and denominator of all fractions by the LCD. 14

17 A Correlation of 2016 Topic M5.5: Solving Rational Equations. Evaluate rational functions Solve rational equations. Solve rational equations with variables in denominators. Solve formulas for specified variables. Topic M5.6: Rational Functions Find the domain and range of rational functions. Solve word problems involving unknown numbers. Solve word problems involving distance, rate, and time. Solve word problems about work. Topic M5.7: Graphing Rational Functions Graph rational functions. Identify intervals on which rational functions are increasing, decreasing, or constant. Analyze graphs of rational functions. Solve word problems involving graphing rational functions. Topic M5.8: Variation Understand the difference between direct and inverse variation. Solve problems about direct variation. Solve problems about inverse variation. Solve word problems involving direct and inverse variation. Module M6. Plane Geometry Topic M6.1: Lines and Angles Name lines, line segments, rays, and angles using different notations. Classify angles. Identify and calculate measures of complementary and supplementary angles. Identify and calculate measures of congruent angles. Identify and calculate measures of angles using properties of parallel lines. SE/TE: , SE/TE: , , 454, 455, ,

18 A Correlation of 2016 Topic M6.2: Plane Figures Identify different types of triangles. Use the sum of the angles in a triangle to find unknown angle measures. Identify different types of quadrilaterals. Use properties of quadrilaterals to find unknown angle measures. Recognize other polygons, including regular polygons. Topic M6.3: Perimeter and Area Find the perimeter of triangles Find the perimeter of quadrilaterals or other polygons. Find the perimeter of composite figures. Find the area of triangles. Find the area of rectangles and squares. Find the area of parallelograms and trapezoids. Find the area of composite figures. Solve perimeter or area word problems. Topic M6.4: Circles Find the radius and diameter of a circle. Find the circumference and area of a circle. Solve word problems involving circles. Topic M6.5: Working with Perimeter, Circumference, and Area Find the missing dimension of a figure given its perimeter, circumference, or area. Find the perimeter or circumference of a figure given its area. Find the area of a figure given its perimeter or circumference. Solve word problems involving perimeter, circumference, or area. SE/TE: 458, 459, , 463, 464 SE/TE: , 479, , , 486, SE/TE: , , 488 SE/TE: ,

19 A Correlation of 2016 Topic M6.6: The Pythagorean Theorem Review square roots. Use the Pythagorean Theorem to find the hypotenuse. Use the Pythagorean Theorem to find unknown side lengths. Determine if lists of numbers are Pythagorean triples. Solve word problems involving the Pythagorean Theorem. Topic M6.7: Congruent and Similar Figures Understand the difference between similarity and congruency. Use properties of congruence to find measures of angles and sides. Use proportions to find measures of unknown sides in similar figures. Solve word problems involving congruent and similar figures. Topic M6.8: Congruent and Similar Triangles Use angle and side relationships to prove congruency. Use properties of congruence to find measures of angles and sides. Use proportions to find measures of unknown sides in similar triangles. Solve word problems involving congruent and similar triangles. Module M7. Transformation and Symmetry Topic M7.1: Reflections Reflect a point across a line. Transform figures using reflections. Solve word problems involving reflections. Topic M7.2: Rotations Transform figures using rotations. Identify rotation images of figures. Find the angle of rotation. Solve word problems involving rotations. SE/TE: 22, 213, 259, , 475 SE/TE: , 470, SE/TE: , , 472, SE/TE: , SE/TE: , 505,

20 A Correlation of 2016 Topic M7.3: Symmetry Identify types of symmetry in plane figures. Identify types of symmetry in space figures. Solve word problems involving symmetry. Topic M7.4: Dilations Find scale factors in dilations. Transform figures using dilation. Use scale factors to find lengths. Solve word problems involving dilations. SE/TE: 499 SE/TE: 502, Module M8. Measurement (Linear, Area, Three-Dimensional) Topic M8.1: U.S. Customary Units Learn units for time. Learn U.S. customary units for length. Learn U.S. customary units for capacity and weight. SE/TE: 474, 475, 476, , 482, 485 (#21-24), Convert measurements by multiplying or dividing. 486, 487 (#63, 66), 488, 493, 494 Convert measurements using unit fractions. Solve word problems involving U.S. customary units. Topic M8.2: The Metric System: Length Learn the basic metric units of length. Determine the correct unit. Convert among metric units. Solve word problems involving metric units of length. SE/TE: 474, 475, , 484 (#7-16), , 487 Topic M8.3: The Metric System: Capacity and Mass Learn the basic metric units of capacity and mass. Determine the correct unit. Determine if a dosage is reasonable or unreasonable. Convert among metric units. Solve word problems involving metric units of capacity and mass. SE/TE: , 493,

21 A Correlation of 2016 Topic M8.4: Metric and U.S. Customary Conversion Use unit fractions to convert from metric units to U.S. customary units. Use unit fractions to convert from U.S. customary units to metric units. Use unit fractions to convert the units used in rates. Solve word problems involving unit conversions. Topic M8.5: Surface Area Find the surface area of a prism or cylinder. Find the surface area of a pyramid or cone. Find the surface area of a sphere. Find the surface area of composite figures. Solve word problems involving surface area. Topic M8.6: Volume Find the volume of a prism or cylinder. Find the volume of a pyramid or cone. Find the volume of a sphere. Find the volume of composite figures. Solve word problems involving volume. Topic M8.7: Working With Surface Area and Volume Find the missing dimension of a figure given its surface area or volume. Find the surface area of a figure given its volume. Find the volume of a figure given its surface area. Solve word problems involving surface area or volume. SE/TE: 491, , 494 SE/TE: 491, , 494, 495 SE/TE:

22 A Correlation of 2016 Module M9. Interpreting Categorical and Quantitative Data Topic M9.1: Types of Data Understand the difference between quantitative and qualitative variables. Understand the difference between statistics and parameters. Understand the difference between discrete and continuous values. SE/TE: , , , Understand the difference between sample and population. Determine if a sample is representative of a population. Topic M9.2: Tables and Pictographs Interpret information from a table. Interpret information from a pictograph. Topic M9.3: Circle Graphs and Scatterplots Interpret circle graphs. Construct circle graphs. Interpret scatterplots. Construct scatterplots. Topic M9.4: Bar Graphs and Line Graphs Interpret bar graphs. Construct bar graphs. Interpret line graphs. Construct line graphs. Translate between pictographs, circle graphs, bar graphs, and line graphs. Module M10. Statistical Measures Topic M10.1: Mean and Weighted Mean Understand the difference between mean and weighted mean. Find the mean. Find the weighted mean. Find the missing data value of a list of numbers given the mean. Solve word problems involving mean and weighted mean. SE/TE: , 649, , 656, , SE/TE: 649, 653, 656 SE/TE: 648, SE/TE: , 664, 666,

23 A Correlation of 2016 Topic M10.2: Median and Mode Understand the difference between mean, median, and mode. Find the median. Find the mode. Solve word problems involving median and mode. Module M11. Probabilistic Reasoning Topic M11.1: Introduction to Probability Understand the differences between outcomes, sample spaces, and events. Use a tree diagram to count outcomes. Use Venn diagrams to count outcomes. Find theoretical probabilities. Topic M11.2: Empirical Probability Understand the difference between theoretical probability and empirical probability. Find empirical probabilities. Find the complement of the probability of an event. Calculate odds. Topic M11.3: Probability of Independent Events and Dependent Events Understand the difference between independent events and dependent events. Find probabilities of independent events. Find probabilities of dependent events. Topic M11.4: Probability of Mutually Exclusive Events and Overlapping Events Understand the difference between mutually exclusive events and overlapping events. Find probabilities of mutually exclusive events. Find probabilities of overlapping events. SE/TE: 657, , 663, 664, SE/TE: , 539, 541, , 577, , , , 604, 612 SE/TE: , , , , SE/TE: 593 (#8, 10), 604 (#34), SE/TE: , , 608, 610, 611,

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