Table of Contents
Introduction ................................................................................................... i–iv
What is Engaging Mathematics, Volume I: Algebra II? ......................................... iii
What is found in an Engaging Mathematics TEKS-based activity? .......................... iv
Attributes of functions and their inverses .................................................... 2–19
Attributes of Functions, Activity 1 2A(2)(A) ....................................................... 2
Attributes of Functions, Activity 2 2A(2)(A) ....................................................... 4
Graphing and Writing Inverse Functions, Activity 1 2A(2)(B) ............................... 6
Graphing and Writing Inverse Functions, Activity 2 2A(2)(B) ............................... 8
Graphing and Writing Inverse Functions, Activity 3 2A(2)(B) .............................. 10
Describing a Function and Its Inverse, Activity 1 2A(2)(C) ................................ 14
Describing a Function and Its Inverse, Activity 2 2A(2)(C) ................................. 16
Composition of Functions 2A(2)(D) ................................................................. 18
Systems of Equations and Inequalities ....................................................... 20–47
Formulating Systems of Three Linear Equations, Activity 1 2A(3)(A), 2A(3)(B) ...... 20
Formulating Systems of Three Linear Equations, Activity 2 2A(3)(A), 2A(3)(B) ...... 22
Solving Systems of Three Linear Equations, Activity 1 2A(3)(B) .......................... 24
Solving Systems of Three Linear Equations, Activity 2 2A(3)(B) .......................... 26
Solving Systems of Linear and Quadratic Equations, Activity 1 2A(3)(C) ............... 28
Solving Systems of Linear and Quadratic Equations, Activity 2 2A(3)(C) ............... 30
Solving Systems of Linear and Quadratic Equations, Activity 3 2A(3)(C) ............... 32
Reasonableness of Solutions to Systems of Linear and Quadratic
Equations 2A(3)(D) ..................................................................................... 36
Formulating Systems of Linear Inequalities 2A(3)(E) ......................................... 38
Solving Systems of Linear Inequalities, Activity 1 2A(3)(F) ................................. 42
Solving Systems of Linear Inequalities, Activity 2 2A(3)(F) ................................. 44
Solutions to Systems of Linear Inequalities 2A(3)(G) ......................................... 46
Quadratic and square root functions, equations, and inequalities .............. 48–81
Writing Quadratic Functions 2A(4)(A) .............................................................. 48
Writing the Equation of a Parabola, Activity 1 2A(4)(B) ...................................... 50
Writing the Equation of a Parabola, Activity 2 2A(4)(B) ...................................... 52
Graphing Square Root Functions, Activity 1 2A(4)(C) ........................................ 54
Graphing Square Root Functions, Activity 2 2A(4)(C) ........................................ 56
Graphing Square Root Functions, Activity 3 2A(4)(C) ........................................ 58
Transforming Quadratic Functions to Vertex Form 2A(4)(D) ............................... 62
Writing Quadratic and Square Root Equations from a Table 2A(4)(E) ................... 64
Solving Quadratic Equations, Activity 1 2A(4)(F) ............................................... 66
Solving Quadratic Equations, Activity 2 2A(4)(F) ............................................... 68
Solving Quadratic Equations, Activity 3 2A(4)(F) ............................................... 70
Solving Square Root Equations 2A(4)(F) .......................................................... 72
Identifying Extraneous Solutions to Square Root Equations 2A(4)(G) ................... 76
Solving Quadratic Inequalities, Activity 1 2A(4)(H) ............................................ 78
Solving Quadratic Inequalities, Activity 2 2A(4)(H) ............................................ 80
Exponential and logarithmic functions and equations ................................ 82–99
Graphing Exponential and Logarithmic Functions, Activity 1 2A(5)(A) .................. 82
Graphing Exponential and Logarithmic Functions, Activity 2 2A(5)(A) .................. 86
Formulating Exponential and Logarithmic Equations 2A(5)(B) ............................. 88
Rewriting Exponential and Logarithmic Equations 2A(5)(C) ................................ 90
Solving Exponential and Logarithmic Equations, Activity 1 2A(5)(D) .................... 94
Solving Exponential and Logarithmic Equations, Activity 2 2A(5)(D) .................... 96
Reasonableness of Solutions to Logarithmic Equations 2A(5)(E) .......................... 98
Introduction ................................................................................................... i–iv
What is Engaging Mathematics, Volume I: Algebra II? ......................................... iii
What is found in an Engaging Mathematics TEKS-based activity? .......................... iv
Attributes of functions and their inverses .................................................... 2–19
Attributes of Functions, Activity 1 2A(2)(A) ....................................................... 2
Attributes of Functions, Activity 2 2A(2)(A) ....................................................... 4
Graphing and Writing Inverse Functions, Activity 1 2A(2)(B) ............................... 6
Graphing and Writing Inverse Functions, Activity 2 2A(2)(B) ............................... 8
Graphing and Writing Inverse Functions, Activity 3 2A(2)(B) .............................. 10
Describing a Function and Its Inverse, Activity 1 2A(2)(C) ................................ 14
Describing a Function and Its Inverse, Activity 2 2A(2)(C) ................................. 16
Composition of Functions 2A(2)(D) ................................................................. 18
Systems of Equations and Inequalities ....................................................... 20–47
Formulating Systems of Three Linear Equations, Activity 1 2A(3)(A), 2A(3)(B) ...... 20
Formulating Systems of Three Linear Equations, Activity 2 2A(3)(A), 2A(3)(B) ...... 22
Solving Systems of Three Linear Equations, Activity 1 2A(3)(B) .......................... 24
Solving Systems of Three Linear Equations, Activity 2 2A(3)(B) .......................... 26
Solving Systems of Linear and Quadratic Equations, Activity 1 2A(3)(C) ............... 28
Solving Systems of Linear and Quadratic Equations, Activity 2 2A(3)(C) ............... 30
Solving Systems of Linear and Quadratic Equations, Activity 3 2A(3)(C) ............... 32
Reasonableness of Solutions to Systems of Linear and Quadratic
Equations 2A(3)(D) ..................................................................................... 36
Formulating Systems of Linear Inequalities 2A(3)(E) ......................................... 38
Solving Systems of Linear Inequalities, Activity 1 2A(3)(F) ................................. 42
Solving Systems of Linear Inequalities, Activity 2 2A(3)(F) ................................. 44
Solutions to Systems of Linear Inequalities 2A(3)(G) ......................................... 46
Quadratic and square root functions, equations, and inequalities .............. 48–81
Writing Quadratic Functions 2A(4)(A) .............................................................. 48
Writing the Equation of a Parabola, Activity 1 2A(4)(B) ...................................... 50
Writing the Equation of a Parabola, Activity 2 2A(4)(B) ...................................... 52
Graphing Square Root Functions, Activity 1 2A(4)(C) ........................................ 54
Graphing Square Root Functions, Activity 2 2A(4)(C) ........................................ 56
Graphing Square Root Functions, Activity 3 2A(4)(C) ........................................ 58
Transforming Quadratic Functions to Vertex Form 2A(4)(D) ............................... 62
Writing Quadratic and Square Root Equations from a Table 2A(4)(E) ................... 64
Solving Quadratic Equations, Activity 1 2A(4)(F) ............................................... 66
Solving Quadratic Equations, Activity 2 2A(4)(F) ............................................... 68
Solving Quadratic Equations, Activity 3 2A(4)(F) ............................................... 70
Solving Square Root Equations 2A(4)(F) .......................................................... 72
Identifying Extraneous Solutions to Square Root Equations 2A(4)(G) ................... 76
Solving Quadratic Inequalities, Activity 1 2A(4)(H) ............................................ 78
Solving Quadratic Inequalities, Activity 2 2A(4)(H) ............................................ 80
Exponential and logarithmic functions and equations ................................ 82–99
Graphing Exponential and Logarithmic Functions, Activity 1 2A(5)(A) .................. 82
Graphing Exponential and Logarithmic Functions, Activity 2 2A(5)(A) .................. 86
Formulating Exponential and Logarithmic Equations 2A(5)(B) ............................. 88
Rewriting Exponential and Logarithmic Equations 2A(5)(C) ................................ 90
Solving Exponential and Logarithmic Equations, Activity 1 2A(5)(D) .................... 94
Solving Exponential and Logarithmic Equations, Activity 2 2A(5)(D) .................... 96
Reasonableness of Solutions to Logarithmic Equations 2A(5)(E) .......................... 98
