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Algebra 2 Curriculum Guide |
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Objectives |
Core Curr. |
Instructional |
Assessment |
Resources |
GEPA |
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The student will be able to:
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Algebra 2: An Integrated Approach, Larson, Kanold, Stiff/Heath Pub. | ||||
| · Use the real number line to graph and order real numbers, and use the properties of real numbers. |
4.6
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Sec. 1.1: "Real Numbers and Number Operations", pp. 2-8; Warm-Up Ex. p. T2; Com. about Alg. p. 5; Guided Practice, p. 6; Extra Examples, p. T4 | Teacher Observation; Check Understanding, p. T5; Mid-Chapter Self-Test, p. 30; Chapter Review pp. 57-60; Chapter Test p. 61; Teacher-made Test |
Transparency 1 |
M. I |
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· Evaluate algebraic expressions, and use them as models of real-life situations. |
4.3 |
Sec. 1.2: "Algebraic Expressions and Models", pp. 9-14; Warm-Up Ex. p. T9; Com. About Alg. p. 11; Guided Practice, p. 12; Extra Examples, p. T10 |
Check Understanding, p. T11 |
Transparencies 2, 3 |
M. V |
| · Solve linear equations, and use them to answer questions about real-life situations. |
4.3 |
Sec. 1.3: "Solving Linear Equations", pp. 18-23; Warm-Up Ex. p. T18; Com. about Alg., p. 20; Guided Practice, p. 21; Extra Examples, p. T20 |
Check Understanding, p. T20 |
Extra Practice 1.3 | M. V |
| · Use problem-solving strategies to solve real-life problems. | 4.3 | Sec 1.4: "Problem-Solving Strategies", pp. 24-29; Warm-Up Ex. p. T24; Com. about Alg., p. 26; Math Journal Act. p. T28; Guided Practice, p. 27; Extra Examples, pp. T25-26 | Check Understanding, p. T26 |
Transparency 4 |
M. V |
| · Solve a literal equation for a specific variable, and evaluate it for specified values of the other variables. | 4.13 | Sec. 1.5: "Literal Equations and Formulas", pp. 31-36; Warm-Up Ex. p. T31; Com. about Alg., p. 33; Guided Practice, p. 34; Extra Ex. pp. T32-33 | Check Understanding, p. T33 |
Extra Practice 1.5 |
M. V |
| · Solve simple and compound inequalities, and use them to solve real-life problems. |
4.3 |
Sec. 1.6: "Solving Linear Inequalities", pp. 37-43; Warm-Up Ex. p. T37; Com. about Alg., p. 40; Guided Practice, p. 41; Extra Examples, p. T39 |
Check Understanding, p. T40 |
Transparency 1 |
M. V |
| · Solve absolute value equations and inequalities, and use them in real-life settings. |
4.3
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Sec. 1.7: "Solving Absolute Value Equations and Inequalities", pp. 44-49; Warm-Up Ex. p. T44; Com. about Alg., p. 46; Guided Practice, p. 47; Extra Examples, pp. T45-46 |
Check Understanding, p. T46 |
Transparency 1 |
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| · Organize data by using tables and graphs. | 4.12 | Sec. 1.8: "Exploring Data: Tables and Graphs", pp. 50-55; Warm-Up Ex. p. T50; Com. about Alg. p. 52; Guided Practice, p. 53; Extra Examples, pp. T51-52 | Check Understanding, p. T52 |
Transparencies 5, 6; Extra Practice 1.8; Color Transp. 6, 7, 8; Tech. Hbk. p. 4 |
M. IV |
| · Sketch a graph using a table of values, and identify equations whose graphs are horizontal or vertical lines. | 4.13 | Sec. 2.1: "The Graph of an Equation", pp. 64-69; Warm-Up Ex. p. T64; Com. about Alg. p. 66; Guided Practice, p. 67; Extra Examples, p. T66 | Teacher Observation; Check Understanding, p. T66; Mid-Chapter Self-Test, p. 93; Chapter Review pp. 115-118; Chapter Test p. 119; Teacher-made Test; Cross-Curr: Geography, p. 66; History, p. 69 # 47, 48 |
Transparencies 7, 8, 9
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M. V |
| · Find the slope of a line, identify parallel and perpendicular lines from their slopes, and interpret slope as a rate of change. | 4.13 | Sec. 2.2: "Slope and Rate of Change", pp. 70-76; Warm-Up Ex. p. T70; Com. about Alg., p. 73; Guided Practice, p. 74; Extra Examples, pp. T72-73 | Check Understanding, p. T73 | Transparencies 7, 8, 9; Extra Practice 2.2; Color Transp. 11; Technology hbk. p. 6; Graph Paper | M. V |
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· Use intercepts to sketch a quick graph of a line, and use the slope-intercept form of a line to sketch a quick graph. |
4.13 | Sec. 2.3: "Quick Graphs of Linear Equations", pp. 78-83; Warm-Up Ex. p. T78; Com. about Alg. p. 80; Guided Practice, p. 81; Extra Examples, pp. T79-80 | Check Understanding, p. T80 |
Transparencies 2, 3, 7, 8, 9; Extra Practice 2.3 |
M. V |
| · Write equations of lines, and use them to solve real-life problems. |
4.3 |
Sec. 2.4: "Writing Equations of Lines", pp. 86-92; Warm-Up Ex. p. T86; Com. about Alg. p. 89; Guided Practice, p. 90; Extra Examples, pp. T87-88 | Check Understanding, p. T89 | Transparencies 7, 8, 9; Extra Practice 2.4, Color Transp. 11, 12; App. Hbk. p. 41 | M. V |
| · Graph a linear inequality in two variables, and use them to model real-life situations. |
4.3
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Sec. 2.5: "Graphing Linear Inequalities in Two Variables", pp. 94-100; Warm-Up Ex. p. T94; Com. about Alg. p. 96; Guided Practice, p. 97; Extra Examples, pp. T95-96 | Check Understanding, p. T96 | Transparencies 7, 8, 10, 11; Extra Practice 2.5; Graph Paper | M. V |
| · Graph absolute value equations, and use them to answer questions about real-life situations. |
4.3
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Sec. 2.6: "Graphs of Absolute Value Equations", pp. 101-106; Warm-Up Ex. p. T101; Com. about Alg. p. 103; Guided Practice, p. 104; Extra Ex. p. T103 | Check Understanding, p. T104 | Transparencies 7, 8, 12; Extra Practice 2.6, Color Transp. 13; Technology Hbk. p. 9, 12; Graph Paper | |
| · Fit a line to a set of data, write an equation for the line, and identify whether a set of data shows positive or negative correlation, or no correlation. |
4.12
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Sec. 2.7: "Exploring Data: Fitting a Line to Data", pp. 107-113; Warm-Up Ex. p. T107; Com. about Alg. p. 110; Guided Practice, p. 111; Extra Ex. p. T108 | Check Understanding, p. T109 | Transparencies 5, 7, 8, 9; Extra Practice 2.7, Color Transp. 14, 15; Technology Hbk. p. 14; Graph Paper | M. IV |
| · Graph and solve a system of linear equations, and use it to answer questions about a real-life situation. |
4.3
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Sec. 3.1: "Solving Linear Systems by Graphing", pp. 122-127; Warm-Up Ex. p. T122; Com. about Alg. p. 124; Guided Practice, p. 125; Extra Examples, pp. T123-124 | Teacher Observation; Check Understanding, p. T124; Mid-Chapter Self-Test, p. 144; Chapter Review pp. 166-168; Chapter Test p. 169; Teacher-made Test; Cross- Curriculum: Business, p. 124 | Transparencies 2, 3, 8, 9; Extra Practice 3.1; Color Transp. 18, 19; Technology Hbk. p. 17; Graph Paper | M. V |
| · Use algebraic methods to solve a linear system, and use the system to answer questions about a real-life situation. |
4.3 |
Sec. 3.2: "Solving Linear Systems Algebraically", pp. 130-136; Warm-Up Ex. p. T130; Com. about Alg. p. 133; Guided Practice, p. 134; Extra Ex. p. T132 | Check Understanding, p. T132 | Transparencies 7, 8, 9; Extra Practice 3.2; Color Transp. 20, 21; Graph Paper | M. V |
| · Write and use linear systems to model real-life situations. |
4.3
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Sec. 3.3: "Problem Solving Using Linear Systems", pp. 138-143; Math Journal Ex. p. T138; Com. about Alg. p. 140; Guided Practice, p. 141; Extra Examples, pp. T139-140 | Check Understanding, p. T140 | Transparencies 4, 7, 8, 9; Extra Practice 3.3; Color Transparencies 21, 22 | M. V |
| · Graph a system of linear inequalities to find the solution to the system, and use a system to model a real-life situation. |
4.3
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Sec. 3.4: "Solving Systems of Linear Inequalities", pp. 145-150; Warm-Up Ex. p. T145; Com. about Alg. p. 147; Guided Practice, p. 148; Extra Ex. p. T146-147 |
Check Understanding, p. T147 | Transparencies 8, 10, 11; Extra Practice 3.4; Color Transp. 23, 24; Graph Paper | M. V |
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· Solve a linear programming problem, and use linear programming to answer questions about real-life situations. |
4.3 |
Sec. 3.5: "Exploring Data: Linear Programming", pp. 151-156; Warm-Up Ex. p. T151; Com. about Alg. p. 153; Guided Practice, p. 154; Extra Ex. p. T153 |
Check Understanding, p. T153
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Transparencies 8, 10, 11; Extra Practice 3.5; Color Transp. 25; Graph Paper | |
| · Solve a system of linear equations in three variables, and use a system to answer questions about real-life situations. |
4.3
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Sec. 3.6: "Solving Systems of Linear Equations in Three Variables", pp. 157-164; Warm-Up Ex. p. T157; Com. about Alg. p. 160; Guided Practice, p. 161; Extra Examples, p. T160 | Check Understanding, p. T160 |
Extra Practice 3.6
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| · Organize data into matrices and work with them, using addition, subtraction, and scalar multiplication, and use matrices in real-life settings. |
4.3
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Sec. 4.1: "Exploring Data: Matrix Operations", pp. 174-179; Warm-Up Ex. p. T174; Com. about Alg. p. 176; Guided Practice, p. 177; Extra Ex. pp. T175-176 | Teacher Observation; Check Understanding, p. T176; Mid-Chapter Self-Test, p. 203; Chapter Review pp. 223-236; Chapter Test p. 227; Teacher-made Test | Extra Practice 4.1 | M. IV |
| · Multiply two matrices, and use matrix multiplication to answer questions about real-life situations. |
4.3
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Sec. 4.2: "Matrix Multiplication", pp. 180-185; Warm-Up Ex. p. T180; Com. about Alg. p. 182; Guided Practice, p. 183; Extra Examples, p. T182 | Check Understanding, pp. T182-3 | Extra Practice 4.2 | |
| · Evaluate the determinant of a 2x2 or a 3x3 matrix, and use determinants to solve real-life problems. |
4.3 |
Sec. 4.3: "Determinants", pp. 187-193; Warm-Up Ex. p. T187; Com. about Alg. p. 190; Guided Practice, p. 191; Extra Examples, p. T189 | Check Understanding p. 190 |
Transparencies 2, 3 |
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| · Find and use the inverse of a 2x2 matrix, and use inverse matrices in real-life settings. |
4.3 |
Sec. 4.4: "Identity and Inverse Matrices", pp. 196-202; Warm-Up Ex. p. T196; Com. about Alg. p. 199; Guided Practice, p. 200; Extra Ex. pp. T198-199 | Check Understanding, p. T199 |
Extra Practice 4.4 |
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| · Solve systems of linear equations using inverse matrices, and use such systems to solve real-life problems. |
4.3 |
Sec. 4.5: "Solving Systems Using Inverse Matrices", pp. 204-209; Warm-Up Ex. p. T204; Com. about Alg. p. 206; Guided Practice, p. 207; Extra Ex. pp. T205-206 | Check Understanding, p. T206 |
Extra Practice 4.5 |
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| · Use an augmented matrix to solve a system of linear equations, and use such a system to solve real-life problems. |
4.3
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Sec. 4.6: "Solving Systems Using Augmented Matrices", pp. 210-215; Warm-Up Ex. p. T210; Com. about Alg. p. 212; Math Journal Act. p. T212; Guided Practice, p. 213; Extra Examples, p. T211 | Check Understanding, p. T212 |
Extra Practice 4.6
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| · Use Cramer’s Rule to solve a system of linear equations, and use such system to solve real-life problems. |
4.3 |
Sec. 4.7: "Solving Systems Using Cramer’s Rule", pp. 216-221; Warm-Up Ex. p. T216; Com. about Alg. p. 218; Guided Practice, p. 219; Extra Ex. p. T218 | Check Understanding, p. T218 |
Extra Practice 4.7 |
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| · Solve a quadratic equation by finding square roots, and use such equations as models of real-life situations. |
4.3
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Sec. 5.1: "Solving Quadratic Equations by Finding Square Roots", pp. 230-235; Warm-Up Ex. p. T230; Com. about Alg. p. 232; Guided Practice, p. 233; Extra Examples, p. T232 | Teacher Observation; Check Understanding, p. T232; Mid-Chapter Self-Test, p. 251; Chapter Review pp. 278-290; Chapter Test p. 281; Teacher-made Test; Cross- Curriculum: Physics, p. 231 |
Extra Practice 5.1
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| · Graph a quadratic equation, and use such a graph in a real-life setting. |
4.3
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Sec. 5.2: "Parabolas: Graphs of Quadratic Equations", pp. 236-241; Warm-Up Ex. p. T236; Com. about Alg. p. 238; Guided Practice, p. 239; Extra Examples, p. T238 | Check Understanding, p. T238 | Transparencies 2, 3, 7, 8, 13; Extra Practice 5.2; Color Transparencies 32, 33; Technology Hbk. p. 25, 28 | |
| · Solve a quadratic equation by completing the square, and use this method to solve real-life problems. |
4.3 |
Sec. 5.3: "Completing the Square", pp. 245-250; Warm-Up Ex. p. T245; Com. about Alg. p. 247; Guided Practice, p. 248; Extra Ex. pp. T246-7 | Check Understanding, p. T247 |
Transparencies 7, 8, 13 |
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| · Use the quadratic formula to solve quadratic equations, and use quadratic models in real-life settings. |
4.3
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Sec. 5.4: "The Quadratic Formula", pp. 252-257; Warm-Up Ex. p. T252; Com. about Alg. p. 254; Guided Practice, p. 255; Extra Examples, p. T253 |
Check Understanding, p. T254
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Transparencies 7, 8, 13; Extra Practice 5.4; Color Transp. 33, 34; App. Hbk. pp. 46-48; Tech. Hbk. p. 33 | |
| · Identify, add, subtract, and multiply imaginary and complex numbers, and plot complex number in the complex plane. | 4.13 | Sec. 5.5: "Complex Numbers", pp. 258-264; Warm-Up Ex. p. T258; Com. about Alg. p. 261; Guided Practice, p. 262; Extra Examples, p. T260 | Check Understanding, p. T261 | Transparencies 7, 8; Extra Practice 5.5; Color Transp. 34, 35; App. Hbk. pp. 26-28 | |
| · Solve any quadratic equation (even ones that have complex number solutions), and use complex numbers and programmable calculators to solve real-life problems. |
4.3
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Sec. 5.6: "Solving Any Quadratic Equation", pp. 264-270; Warm-Up Ex. p. T265; Com. about Alg. p. 267; Guided Practice, p. 268; Extra Ex. p. T266 | Check Understanding, p. T266 |
Extra Practice 5.6
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| · Sketch the graph of a quadratic inequality, and use quadratic inequalities in real-life modeling. |
4.3 |
Sec. 5.7: "Graphs of Quadratic Inequalities", pp. 271-276; Warm-Up Ex. p. T271; Com. about Alg. p. 273; Guided Practice, p. 274; Extra Ex. pp. T272-273 | Check Understanding, p. T273 |
Transparencies 7, 8, 13; |
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| · Identify a relation and a function, and identify real-life relations that are functions. |
4.3
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Sec. 6.1: "Relations and Functions", pp. 284-290; Warm-Up Ex. p. T284; Com. about Alg. p. 287; Guided Practice, p. 288; Extra Examples, p. T286 | Teacher Observation; Check Understanding, p. T287; Mid-Chapter Self-Test, p. 305; Chapter Review pp. 334-338; Chapter Test p. 339; Teacher-made Test |
Transparencies 7,8
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M. III |
| · Perform operations with functions, and use function operations in real-life situations. |
4.3 |
Sec. 6.2: "Function Operations", pp. 291-296; Warm-Up Ex. p. T291; Com. about Alg. p. 293; Guided Practice, p. 294; Extra Ex. pp. T292-293 | Check Understanding, p. T293 | Extra Practice 6.2; Color Transparency 37; Technology Hbk. p. 35 | |
| · Identify inverse relations and inverse functions, verify that two functions are inverses of each other, and use inverse functions in real-life situations. |
4.3 |
Sec. 6.3: "Inverse Functions", pp. 298-304; Warm-Up Ex. p. T298; Com. about Alg. p. 301; Guided Practice, p. 302; Extra Examples, p. T300 | Check Understanding, p. T301 | Transparencies 7, 8, 9, 13; Extra Practice 6.3; Applications Hbk. p. 54; Graph Paper | |
| · Use special functions, such as compound functions and step functions, and use these functions in real-life situations. |
4.3
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Sec. 6.4: "Special Functions", pp. 306-311; Warm-Up Ex. p. T306; Com. about Alg. p. 308; Guided Practice, p. 309; Extra Examples, p. T308 | Check Understanding, p. T309 | Transparencies 2, 3, 7, 8, 12, 13; Extra Practice 6.4; Color Transp. 37; Graph Paper | |
| · Use translations and reflections to sketch the graph of a function, and use transformations of graphs of functions in real-life settings. |
4.3
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Sec. 6.5: "Transformations of Graphs of Functions", pp. 314-320; Warm-Up Ex. p. T314; Com. about Alg. p. 317; Guided Practice, p. 318; Extra Ex. p. T317 | Check Understanding, p. T317 | Transparencies 7, 8, 12, 13; Extra Practice 6.5; Technology Hbk. p. 37; Graph Paper | |
| · Identify and classify recursive functions, and use these functions as real-life models. |
4.3 |
Sec. 6.6: "Recursive Functions and Finite Differences", pp. 321-326; Warm-Up Ex. p. T321; Com. about Alg. p. 323; Guided Practice, p. 324; Extra Examples, p. T322 | Check Understanding, p. T323 |
Extra Practice 6.6
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| · Find the mean, median, mode, and quartiles of a set of numbers, and use measures of central tendency in real-life situations. | 4.12 | Sec. 6.7: "Exploring Data: Measures of Central Tendency", pp. 327-332; Warm-Up Ex. p. T327; Com. about Alg. p. 329; Guided Practice, p. 330; Extra Examples, p. T329 |
Check Understanding, p. T329
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Transparencies 1, 5; Extra Practice 6.7; Color Transp. 38, 39; Tech. Hbk. p. 40; Sci. Calculator; Graph Paper | M.IV |
| · Use properties of exponents to evaluate and simplify exponential expressions, and use powers as models in real-life problems. |
4.3
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Sec. 7.1: "Properties of Exponents", pp. 346-351; Warm-Up Ex. p. T346; Com. about Alg. p. 348; Guided Practice, p. 349; Extra Examples, p. T348 | Teacher Observation; Check Understanding, p. T348; Mid-Chapter Self-Test, p. 367; Chapter Review pp. 391-394; Chapter Test p. 395; Teacher-made Test; Cross- Curriculum: Astronomy, p. 350 # 50-53 | Transparencies 7, 8; Extra Practice 7.1; Applications Hbk. p.4 | M. I |
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· Use the compound interest formula and the exponential growth and decay formulas, and solve real-life problems modeled by exponential growth formulas. |
4.3 |
Sec. 7.2: "Exploring Data: Compound Interest and Exponential Growth", pp. 352-358; Warm-Up Ex. p. T352; Com. about Alg. p. 355; Guided Practice, p. 356; Extra Examples, p. T354 |
Check Understanding, p. T354
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Transparencies 5, 7, 8, 14, 15; Extra Practice 7.2; Color Transparency 41; Technology Hbk. p. 42, 45 | |
| · Evaluate nth roots of real numbers using radical notation and rational exponent notation, and use nth roots to solve real-life problems. |
4.3 |
Sec. 7.3: "nth Roots and Rational Exponents", pp. 360-366; Warm-Up Ex. p. T360; Com. about Alg. p. 363; Guided Practice, p. 364; Extra Ex. p. T362 |
Check Understanding, p. T362
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Extra Practice 7.3
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| · Use Properties of roots to evaluate and simplify expressions containing radicals and rational exponents, and use these properties to solve real-life problems. |
4.3 |
Sec. 7.4: "Properties of Roots of Real Numbers", pp. 368-373; Warm-Up Ex. p. T368; Com. about Alg. p. 370; Guided Pract. p. 371; Extra Ex. pp. T369-370 |
Check Understanding, p. T370 |
Extra Practice 7.4; Color Transparencies 41, 42; Applications Hbk. p. 56; Scientific Calculator
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| · Solve equations that have radicals and rational exponents, and use such equations to solve real-life problems. |
4.3 |
Sec. 7.5: "Solving Radical Equations", pp. 374-380; Warm-Up Ex. p. T374; Com. about Alg. p. 377; Guided Practice, p. 378; Extra Examples, p. T376 |
Check Understanding, p. T377 | Transparencies 7, 8; Extra Practice 7.5; Color Transp. 42; Technology Hbk. p. 48 | |
| · Graph square root and cube root functions, and use such functions to solve real-life problems. |
4.3 |
Sec. 7.6: "Graphing Square Root and Cube Root Functions", pp. 381-387; Warm-Up Ex. p. T381; Com. about Alg. p. 383; Guided Practice, p. 384; Extra Examples, pp. T382-383 | Check Understanding, p. T383 |
Transp. 2, 3, 7, 8, 13, 16 |
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· Graph exponential functions, evaluate exponential expressions, and use such functions as models for real-life situations. |
4.3 |
Sec. 8.1: "Exponential Functions", pp. 398-404; Warm-Up Ex. p. T398; Com. about Alg. p. 401; Guided Practice, p. 402; Extra Ex. pp. T400-401 | Teacher Observation; Check Understanding, p. T401; Mid-Chapter Self-Test, p. 419; Chapter Review pp. 449-452; Chapter Test p. 453; Teacher-made Test | Transparencies 7, 8, 14, 15; Extra Practice 8.1; Color Transp. 44; Graph Paper; Scientific Calculator | |
| · Evaluate logarithmic expressions, graph logarithmic functions, and use logarithms in real-life situations. |
4.3 |
Sec. 8.2: "Logarithmic Functions", pp. 405-411; Warm-Up Ex. p. T405; Com. about Alg. p. 408; Guided Practice, p. 409; Extra Examples, p. T407 |
Check Understanding, p. T408 | Transparencies 8, 17, 18; Extra Practice 8.2; App. Hbk. p. 21; Graph Paper; Sci. Cal. | |
| · Use properties of logarithms, and use logarithms to solve real-life problems. |
4.3
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Sec. 8.3: "Properties of Logarithms", pp. 413-418; Warm-Up Ex. p. T413; Com. about Alg. p. 415; Guided Practice, p. 416; Extra Ex. pp. T414-415 | Check Understanding, p. T415 |
Extra Practice 8.3
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| · Use the number e as the base of an exponential function, as well as in real-life problems. |
4.3
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Sec. 8.4: "The Natural Base e", pp. 420-425; Warm-Up Ex. p. T420; Com. about Alg. p. 422; Guided Practice p. 423; Extra Examples, p. T422 | Check Understanding, p. T422 | Transparencies 7, 8, 19; Extra Practice 8.4; App. Hbk. p. 21; Graph Paper; Sci. Cal. | |
| · Evaluate natural logarithmic expressions, graph natural logarithmic functions, and use such functions as real-life models. |
4.3 |
Sec. 8.5: "Natural Logarithms", pp. 426-431; Warm-Up Ex. p. T426; Com. about Alg. p. 428; Guided Practice, p. 429; Extra Ex. pp. T427-428 | Check Understanding, p. T428 | Transparencies 2, 3, 7, 8, 19; Extra Practice 8.5; Color Transp. 44; Tech. Hbk. p. 50; Graph Paper; Sci. Calc. | |
| · Solve exponential and logarithmic equations, and use such equations to answer questions about real-life. |
4.3
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ec. 8.6: "Solving Exponential and Logarithmic Equations", pp. 434-440; Warm-Up Ex. p. T434; Com. about Alg. p. 437; Guided Practice, p. 438; Extra Examples, pp. T436-437 | Check Understanding, p. T437 | Extra Practice 8.6; Color Transp. 45; App. Hbk. p. 21; Tech. Hbk. p. 52: Sci. Calc. | |
| · Graph a logistics growth function, and use such functions to answer questions about real-life situations. |
4.3
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Sec. 8.7: "Exploring Data: Logistics Growth Functions", pp. 441-446; Warm-Up Ex. p. T441; Com. about Alg. p. 443; Guided Pract. p. 444; Extra Ex. p. T442 | Check Understanding, p. T443 | Transparencies 7, 8; Extra Practice 8.7; Color Transp. 45; Graph Paper; Sci. Calc. | |
| · Add, subtract, and multiply polynomials, and use polynomial operations to solve real-life problems. |
4.3
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Sec. 9.1: "Operations with Polynomials", pp. 456-462; Warm-Up Ex. p. T456; Com. about Alg. p. 459; Guided Practice, p. 460; Extra Ex. p. T458 | Teacher Observation; Check Understanding, p. T459; Mid-Chapter Self-Test, p. 487; Chapter Review pp. 509-512; Chapter Test p. 513; Teacher-made Test | Transparency 22; Extra Practice 9.1; Color Transparency 47 | |
| · Sketch the graph of a polynomial function, and use such functions as models of real-life situations. |
4.3
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Sec. 9.2: "Graphs of Polynomial Functions", pp. 463-469; Warm-Up Ex. p. T463; Com. about Alg. p. 466; Guided Practice, p. 467; Extra Ex. p. T465 | Check Understanding, p. T466 | Transparencies 2, 3, 7, 8, 20; Extra Practice 9.2; Color Transp. 48; Tech. Hbk. p. 54; Graph Paper; Graphing Cal. | |
| · Factor polynomial expressions and equations, and use factoring to solve real-life problems. |
4.3 |
Sec. 9.3: "Factoring Polynomials and Solving Polynomial Equations", pp. 473-479; Warm-Up Ex. p. T473; Com. about Alg. p. 476; Guided Practice, p. 477; Extra Examples, p. T475 | Check Understanding, p. T476 |
Extra Practice 9.3 |
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| · Divide polynomials using long division and synthetic division, relate the quotient to the Remainder Theorem and the Factor Theorem, and use polynomial division in real-life problems. |
4.3
|
Sec. 9.4: "Polynomial Division, Factors, and Remainders", pp. 480-486; Warm-Up Ex. p. T480; Com. about Alg. p. 483; Guided Pract. p. 484; Extra Ex. p. T482 | Check Understanding, p. T483 | Extra Practice 9.4; Color Transparencies 49-51; Technology Hbk. p. 59 | |
| · Find the rational zeros of a polynomial function, and use such zeros to solve real-life problems. |
4.3
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Sec. 9.5: "Finding Rational Zeros", pp. 488-493; Warm-Up Ex. p. T488; Com. about Alg. p. 490; Guided Practice, p. 491; Extra Examples, p. T489 | Check Understanding, p. T490 | Transparency 8; Extra Practice 9.5; Color Transp. 51, 52; Tech. Hbk. p. 61 | |
| · Look at zeros of polynomial functions, factors of polynomials, and solutions of polynomial equations to see their connections, and use polynomials to solve real-life problems. |
4.3
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Sec. 9.6: "Connections: Zeros, Factors, and Solutions", pp. 494-500; Warm-Up Ex. p. T494; Com. about Alg. p. 497; Guided Practice, p. 498; Extra Examples, p. T496 | Check Understanding, p. T496 |
Extra Practice 9.6
|
|
| · Find the range and standard deviation of a collection of numbers. | 4.12 | Sec. 9.7: "Exploring Data: Measures of Dispersion", pp. 501-507; Warm-Up Ex. p. T501; Com. about Alg. p. 503; Guided Practice, p. 504; Extra Ex. p. T502 | Check Understanding, p. T502 | Transparency 5; Extra Practice 9.7; Color Transp. 52, 53; Applications Hbk. p. 11; Technology Hbk. p. 68; Scientific Calculator | |
| · Graph a rational function using asymptotes, and use such functions as real-life models. |
4.3
|
Sec. 10.1: "Graphs of Rational Functions", pp. 518-523; Warm-Up Ex. p. T518; Com. about Alg. p. 520; Guided Practice, p. 521; Extra Ex. p. T519 | Teacher Observation; Check Understanding, p. T520; Mid-Chapter Self-Test, p. 540; Chapter Review pp. 562-566; Chapter Test p. 567; Teacher-made Test; Cross-Curriculum: Business, p. 520 | Transparencies 2, 3, 7, 8, 21; Extra Practice 10.1; Color Transparency 54; Graph Paper | |
| · Create and use real-life models using inverse variation and joint variation. |
4.3 |
Sec. 10.2: "Inverse and Joint Variation", pp. 526-531; Warm-Up Ex. p. T526; Com. about Alg. p. 528; Guided Practice, p. 529; Extra Ex. pp. T527-8 |
Check Understanding, p. T528 |
Extra Practice 10.2 |
|
| · Multiply and divide rational expressions, writing the result in simplest form, and use such expressions as real-life models. |
4.3
|
Sec. 10.3: "Multiplying and Dividing Rational Expressions", pp. 533-539; Warm-Up Ex. p. T533; Com. about Alg. p. 536; Guided Practice, p. 537; Math Journal Act. p. T539; Extra Ex. pp. T534-535 |
Check Understanding, p. T536
|
Extra Practice 10.3 | |
| · Solve equations that contain rational expressions, and use such equations to solve real-life problems. |
4.3 |
Sec. 10.4: "Solving Rational Equations", pp. 541-547; Warm-Up Ex. p. T541; Com. about Alg. p. 544; Guided Practice, p. 545; Extra Examples, p. T543 |
Check Understanding, p. T544 |
Transparency 8; Extra Practice 10.4; Color Transparency 56; Technology Hbk. p. 71 | |
| · Add and subtract rational expressions, simplify complex fractions, and use rational expressions as models of real-life situations. |
4.3
|
Sec. 10.5: "Addition, Subtraction, and Complex Fractions", pp. 548-554; Warm-Up Ex. p. T548; Com. about Alg. p. 550; Guided Practice, p. 551; Extra Examples, p. T550 | Check Understanding, p. T550 | Extra Practice 10.5 | |
| · Construct an amortization table for a loan, and find the monthly payment for an installment loan. |
4.3 |
Sec. 10.6: "Exploring Data: The Algebra of Finance", pp. 555-560; Warm-Up Ex. p. T555; Com. about Alg. p. 557; Guided Practice, p. 558; Extra Ex. p. T556 |
Check Understanding, p. T557 |
Extra Practice 10.6 |
|
| · Write an equation of a parabola, sketch its graph, and use parabolas to solve real-life problems. |
4.3 |
Sec. 11.1: "Parabolas’, pp. 570-575; Warm-Up Ex. p. T570; Com. about Alg. p. 572; Guided Practice, p. 573; Extra Examples, pp. T571-572 | Teacher Observation; Check Understanding, p. T572; Mid-Chapter Review pp. 615-618; Chapter Test p. 619; Teacher-made Test |
Transparencies 7, 8, 13 |
|
| · Write an equation of a circle, sketch its graph, and use such equations and graphs in real-life problems. |
4.3
|
Sec. 11.2: "Circles and Points of Intersection", pp. 576-581; Warm-Up Ex. p. T576; Com. about Alg. p. 578; Guided Practice, p. 579; Extra Ex. pp. T577-578 | Check Understanding, p. T578 | Transparencies 7, 8: Extra Practice 11.2; Color Transp. 58, 59; Applications Hbk. p. 57; Technology Hbk. p. 77; Graph Paper | |
| · Write an equation of an ellipse, sketch its graph, and use ellipses to solve real-life problems. |
4.3
|
Sec. 11.3: "Ellipses", pp. 583-588; Warm-Up Ex. p. T583; Com. about Alg. p. 585; Guided Practice, p. 586; Extra Examples, pp. T584-585 |
Check Understanding, p. T585; |
Transparencies 7, 8; Extra Practice 11.3; Technology Hbk. p. 79; Graph Paper | |
| · Write the equation of a hyperbola and graph it, using asymptotes, and use hyperbolas to solve real-life problems. |
4.3 |
Sec. 11.4: "Hyperbolas", pp. 590-596; Warm-Up Ex. p. T590; Com. about Alg. p. 593; Guided Practice, p. 594; Extra Examples, pp. T592-593 |
Check Understanding, p. T593 |
Transparencies 7, 8 |
|
| · Write an equation of a parabola with a vertex at (h, k) and an equation of a circle, an ellipse, or a hyperbola with its center at (h, k), and use translations to solve real-life problems. |
4.3 |
Sec. 11.5: "Translations of Conics", pp. 597-603; Warm-Up Ex. p. T597; Com. about Alg. p. 600; Guided Practice, p. 601; Writing Act. p. T601; Extra Examples p. T599 | Check Understanding, p. T600 |
Transparencies 2, 3, 7, 8 |
|
| · Classify a conic from its general equation, and use equations of conics to solve mathematical and real-life problems. |
4.3
|
Sec. 11.6: "Classifying Conics", pp. 606-613; Warm-Up Ex. p. T606; Com. about Alg. p. 609; Guided Pract. p. 610; Writing Act. p. T611; Extra Ex. p. T608 | Check Understanding, p. T609 | Transparencies 7, 8, 23; Extra Practice 11.6; Color Transp. 60, 61; Technology Hbk. pp. 34-35; Graph Paper | |
| · Write sequences and series, and use them as models of real-life situations. |
4.3
|
Sec. 12.1: "Sequences and Series", pp. 622-628; Warm-Up Ex. p. T622; Com. about Alg. p. 625; Guided Practice, p. 626; Extra Examples, p. T624 | Teacher Observation; Check Understanding, p. T625; Mid-Chapter Self-Test, p. 644; Chapter Review pp. 667-670; Chapter Test p. 671; Teacher-made Test |
Extra Practice 12.1
|
M. III |
| · Find the nth term and the sum of an arithmetic series, and use such a series in real-life problems. |
4.3
|
Sec. 12.2: "Arithmetic Sequences and Series", pp. 629-635; Warm-Up Ex. p. T629; Com. about Alg. p. 632; Guided Practice, p. 633; Extra Ex. p. T631 |
Check Understanding, p. T632
|
Extra Practice 12.2
|
M. III |
| · Find the nth term and the sum of a geometric series, and use such a series in real-life problems. |
4.3 |
Sec. 12.3: "Geometric Sequences and Series", pp. 637-643; Warm-Up Ex. p. T637; Com. about Alg. p. 640; Guided Practice, p. 641; Extra Ex. p. T639 |
Check Understanding, p. T640 |
Extra Practice 12.3 |
M. III |
|
· Find the sum of an infinite geometric series, and use such a series as a model of real-life problems. |
4.3 |
Sec. 12.4: "Infinite Geometric Series", pp. 645-650; Warm-Up Ex. p. T645; Com. about Alg. p. 647; Guided Practice, p. 648; Extra Examples, p. T647 |
Check Understanding, p. T647
|
Extra Practice 12.4 |
M. III |
| · Use the Binomial Theorem to expand a binomial that is raised to a power, and use the Binomial Theorem in real-life situations. |
4.3
|
Sec. 12.5: "The Binomial Theorem", pp. 651-657; Warm-Up Ex. p. T651; Com. about Alg. p. 654; Guided Practice, p. 655; Extra Examples, p. T653 | Check Understanding, p. T653 | Transparency 24; Extra Practice 12.5; Color Transp. 65; Technology Hbk. p. 87 | |
| · Find the balance of an increasing annuity, and find the monthly deposit to reach a specified balance in such an annuity. |
4.3
|
Sec. 12.6: "Exploring Data: The Algebra of Finance", pp. 658-663; Warm-Up Ex. p. T658; Com. about Alg. p. 660; Guided Practice, p. 661; Extra Ex. p. T659 |
Check Understanding, p. T660
|
Transparencies 2, 3; Extra Practice 12.6; Color Transp. 66; Technology Hbk. p. 89 | |
|
· Use trigonometric relationships to evaluate the trigonometric functions of acute angles, and use trigonometric ratios to solve real-life problems. |
4.3
|
Sec. 13.1: "Right Triangle Trigonometry", pp. 678-684; Warm-Up Ex. p. T678; Com. about Alg. p. 681; Guided Practice, p. 682; Extra Ex. pp. T680-681 | Teacher Observation; Check Understanding, p. T681; Mid-Chapter Self-Test, p. 702; Chapter Review pp. 723-726; Chapter Test p. 727; Teacher-made Test |
Extra Practice 13.1
|
|
| · Measure angles in standard position using degree measure and radian measure, and use radian measure in real-life problems. |
4.3
|
Sec. 13.2: "Angles of Rotation and Radian Measure", pp. 685-691; Warm-Up Ex. p. T685; Com. about Alg. p. 688; Guided Practice, p. 689; Extra Ex. p. T687 | Check Understanding, p. T688 |
Transparencies 6, 25
|
|
| · Evaluate trigonometric functions of any angle, and use such functions to solve real-life problems. |
4.3
|
Sec. 13.3: "Evaluating Trigonometric Functions", pp. 693-699; Warm-Up Ex. p. T693; Com. about Alg. p. 696; Guided Practice, p. 697; Extra Ex. p. T695
|
Check Understanding, p. T695
|
Transparencies 2, 3, 6, 25; Extra Practice 13.3; Color Transp. 67-69; App. Hbk. pp. 3, 46-48; Tech. Hbk. p. 93; Scientific Calculator | |
|
· Evaluate inverse trigonometric functions, and use such functions to solve real-life problems. |
4.3 |
Sec. 13.4: "Inverse Trigonometric Functions", pp. 703-708; Warm-Up Ex. p. T703; Com. about Alg. p. 705; Guided Practice, p. 706; Extra Ex. p. T705 |
Check Understanding, p. T705 |
Extra Practice 13.4; Color Transp. 70; App. Hbk. pp. 38-39; Sci. Calc. | |
| · Use the Law of Sines to find the sides and angles of any triangle, and solve real-life problems. |
4.3 |
Sec. 13.5: "The Law of Sines", pp. 709-715; Warm-Up Ex. p. T709; Com. about Alg. p. 711; Guided Practice, p. 712; Extra Ex. pp. T710-711 |
Check Understanding, p. T711 |
Extra Practice 13.5; Color Transparency 71 |
|
| · Use the Law of Cosines to find the sides and angles of any triangle, and solve real-life problems. |
4.3
|
Sec. 13.6: "The Law of Cosines", pp. 716-721; Warm-Up Ex. p. T716; Com. about Alg. p. 718; Guided Practice, p. 719; Extra Ex. pp. T717-718 |
Check Understanding, p. T718
|
Extra Practice 13.6; Color Transp. 71; App. Hbk. p. 38; Scientific Calculator | |
| · Sketch the graphs of the sine and cosine functions, and use these functions as models of real-life problems. |
4.3
|
Sec. 14.1: "Graphs of Sine and Cosine Functions", pp. 730-736; Warm-Up Ex. p. T730; Com. about Alg. p. 733; Guided Practice, p. 734; Extra Ex. p. T732 | Teacher Observation; Check Understanding, p. T733; Mid-Chapter Self-Test, p. 752; Chapter Review pp. 773-776; Chapter Test p. 777; Teacher-made Test; Cross-Curriculum; Music, p. 733 | Transparencies 26, 27, 28; Extra Practice 14.1; Color Transp. 73; App. Hbk. pp. 49-51, 56, 57; Tech. Hbk. p. 95; Graph Paper; Sci. Calc. | |
| · Graph vertical and horizontal shifts and reflections of the graphs of the sine and cosine functions, and use these functions to solve real-life problems. |
4.3
|
Sec. 14.2: "Translations and Reflections of Graphs", pp. 737-742; Warm-Up Ex. p. T737; Com. about Alg. p. 739; Math Journal Act. p. T740; Guided Practice, p. 740; Extra Examples, p. T739 |
Check Understanding, p. T739
|
Transparencies 26, 27, 28; Extra Practice 14.2; Color Transp. 74; App. Hbk. p. 3; Tech. Hbk. p. 97; Graph Paper, Scientific Calculator | |
| · Use trigonometric identities to simplify trigonometric expressions, verify trigonometric identities, and use such identities to solve real-life problems. |
4.3 |
Sec. 14.3: "Trigonometric Identities", pp. 744-749; Warm-Up Ex. p. T744; Com. about Alg. p. 746; Guided Practice, p. 747; Extra Examples, p. T746 | Check Understanding, p. T746 |
Transparencies 2,3 |
|
| · Solve trigonometric equations, including ones that model real-life problems. |
4.3 |
Sec. 14.4: "Solving Trigonometric Equations", pp. 753-759; Warm-Up Ex. p. T753; Com. about Alg. p. 756; Guided Practice, p. 757; Extra Ex. p. T755 |
Check Understanding, p. T755 |
Extra Practice 14.4 |
|
| · Use the sum and difference formulas to evaluate trigonometric functions of the sum and difference of two angles, and use these formulas to solve real-life problems. |
4.3
|
Sec. 14.5: "Sum and Difference Formulas", pp. 760-765; Warm-Up Ex. p. T760; Com. about Alg. p. 762; Guided Practice, p. 763; Extra Ex. pp. T761-762 |
Check Understanding, p. T762
|
Extra Practice 14.5
|
|
| · Use double-angle and half-angle formulas, and use trigonometry to solve real-life problems. |
4.3 |
Sec. 14.6: "Double and Half-Angle Formulas", pp. 766-771; Warm-Up Ex. p. T766; Com. about Alg. p. 768; Guided Practice, p. 769; Extra Ex. pp. T767-768 |
Check Understanding, p. T768 |
Extra Practice 14.6 |
|
| · Find the probability of an event, and use probability to answer questions about real-life. |
4.3
|
Sec. 15.1: "Introduction to Probability", pp. 782-87; Warm-Up Ex. p. T782; Group Act. pp. T782-; Com. about Alg. p. 784; Guided Practice, p. 785; Extra Examples, pp. T784-5 | Teacher Observation; Check Understanding, p. T785; Mid-Chapter Self-Test, p. 804; Chapter Review pp. 824-827; Chapter Test p. 828; Teacher-made Test; Cross-Curriculum: Genetics, p. 784; Health, p. 786-787 # 20, 22, 23 |
Extra Practice 15.1
|
M. IV |
| · Use the Fundamental Counting Principle and permutations to find probabilities. | 4.12 | Sec. 15.2: "Counting Methods: Permutations", pp. 788-794; Warm-Up Ex. p. T788; Group Act. pp. T790; Com. about Alg. p. 791; Guided Practice, p. 792; Extra Examples, pp. T790-791 | Check Understanding, p. T791 |
Extra Practice 15.2
|
|
| · Use combinations to count the number of ways an event can happen, and use them to find probabilities. | 4.12 | Sec. 15.3: "Counting Methods: Combinations", pp. 796-801; Warm-Up Ex. p. T796; Com. about Alg. p. 798; Guided Practice, p. 799; Extra Ex. p. T798 | Check Understanding, p. T798 | Transparencies 2, 3, 24; Extra Practice 15.3; Tech. Hbk. p. 101; Scientific Calc. | |
|
· Use unions, complements, and intersections to find probabilities. |
4.12 | Sec. 15.4: "Probability, Unions, and Intersections", pp. 805-810; Warm-Up Ex. p. T805; Com. about Alg. p. 807; Guided Practice, p. 808; Extra Ex. p. T807 |
Check Understanding, p. T808 |
Extra Practice 15.4 |
|
| · Find the probability of independent events, and use the complement of the event to find the probability of the event. | 4.12 | Sec. 15.5: "Independent Events", pp. 811-816; Warm-Up Ex. p. T811; Com. about Alg. p. 813; Guided Practice, p. 814; Extra Ex. pp. T812-813 | Check Understanding, p. T813 |
Extra Practice 15.5
|
|
| · Find the expected value of a sample space, and use it to answer questions about real-life situations. |
4.3
|
Sec. 15.6: "Expected Value", pp. 817-822; Warm-Up Ex. p. T817; Com. about Alg. p. 819; Guided Practice, p. 820; Extra Examples, p. T819 | Check Understanding, p. T819 | Extra Practice 15.6 | |
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