Exam 2 Review. 2. What the difference is between an equation and an expression?

Transcription

1 Exam 2 Review Chapter 1 Section1 Do You Know: 1. What does it mean to solve an equation? 2. What the difference is between an equation and an expression? 3. How to tell if an equation is linear? 4. How can you check your solution to an equation? 5. How do you check your solution to a word problem? 1. Solve the equation: 2. Solve the equation: 3. Solve for c 4. A new game show requires a playing field with a perimeter of 54 yard and length 3 yards less than twice the width. What are the dimensions of the field? 5. A two-women rowing team can row 1,200 meters with the current in a river in the same amount of time it takes them to row 1,000 meters against that same current. In each case, their average rowing speed without the effect of the current is 3 meters per second. Find the speed of the current. Chapter 1, Section 2 Do You Know: 1. What the difference is between solving linear equations and linear inequalities? 2. What is the Union? 3. What is the intersection? 1. Write in inequality notation: 2. Write in interval notation: 3. Write in interval notation: 4. Write in inequality notation

2 5. Write in inequality and interval notation Solve and graph. 7. Solve and graph. 8. Solve and graph. 9. Graph the indicated set and write as a single interval if possible. 10. Graph the indicated set and write as a single interval if possible. 11. Solve and graph. 12. For what real number(s) x does each expression represent a real number? Chapter 1, Section 3 1. What the definition of absolute value is? 2. How to use absolute values to solve radical inequalities? 1. Write without absolute value signs. 2. Solve the equation. 3. Solve the inequality. Write solutions to inequalities using both inequality and interval notation. 4. Solve the inequality. Write solutions to inequalities using both inequality and interval notation. 5. Solve the inequality. Write solutions to inequalities using both inequality and interval notation. 6. Solve the inequality. Write solutions to inequalities using both inequality and interval notation.

3 Chapter 1, Section 4 1. What the standard form is for a complex number? 2. Do negative numbers have square roots? Explain. 3. Is it possible to square an imaginary number and get a real number? Explain. 4. What is the conjugate of a complex number? 5. How do we use conjugates? 6. Which statement is false, and which is true? Justify your response. (A) Every real number is a complex number. (B) Every complex number is a real number. 7. Is it possible to add a real number and an imaginary number? If so, what kind of number is the result? 1. For each number find the (A) real part, (B) imaginary part, and (C) conjugate. (d) 2. For the following, perform the indicated operation and write your answer in standard form. (d) 3. For the following, evaluate and express results in standard form.

4 (d) 4. Solve for x and y. 5. Solve for z and write your answer in standard form. Chapter 1, Section 5 1. How can you tell when an equation is quadratic? That is, what is standard form for a quadratic equation? 2. What do a, b, and c in the quadratic formula stand for? 3. How to explain the zero product property? 4. How to explain the square root property? 5. What is the Quadratic Formula? 6. How to explain the process of completing the square? That is, what are the steps to completing the square? 7. What does the discriminate tell us about a quadratic equation? Practice Problems (Remember with these problems you CAN have complex numbers as a solution): 1. Solve by factoring. 2. Solve by using the square root property. 3. Use the discriminate to determine the number of real roots of each equation, then solve using the quadratic formula. 4. Solve by completing the square. 5. Solve by completing the square. 6. Solve the following by any method.

5 Chapter 1, Section 6 1. What is meant by the term extraneous solution? 2. When is it necessary to check for extraneous solutions? 3. How can squaring both sides help in solving absolute value equations? 4. How can you recognize when an equation is of quadratic type? 1. Solve the following equations (Remember you CAN have answers which are complex numbers). (d) (e) (f) (g) 2. A hard court version of the game broomball becomes popular on college campuses because it enables people to hit each other with a stick. The court is rectangle with diagonal 40 feet and area 800 square feet. Find the dimensions to one decimal place. (Hint: Use the Pythagorean Theorem) Chapter 2, Section 1 1. How to explain how to graph an equation of two variables using point-by-point plotting. 2. How to tell if a graph is symmetric about the y-axis, x-axis, and/or origin?

6 1. Plot the given points in a rectangular coordinate system. Now reflect the points Reflect the points Reflect the points over the y-axis. over the x-axis over the origin. 2. Test for symmetry with respect to the x-axis, y-axis, and the origin. (d) Chapter 2, Section 2 1. What is the Pythagorean Theorem? 2. How do can you calculate the distance between two points in the plane if you know their coordinates? 3. How can you calculate the midpoint of a line segment if you know the coordinates of the endpoints? 4. What is the standard form of a circle? 5. Can you explain how to find the standard form of the equation of the circle with center (1,5) and radius? 1. Find the distance and the midpoint of the line segment with end points 2. Find the indicated point when M is the midpoint and A and B are endpoints. 3. Find the center and radius of the circle. 4. Find the standard form of the equation of the circle knowing Center: (0,5), and point on circle: (2,-4). Chapter 2, Section 3 1. What is the standard form for a line?

7 2. How to explain how to find the x and y intercepts of a line if the equation is written in standard form? 3. What is slope-intercept form of a line? Why do you think it is called slope-intercept form? 4. What is point-slope form of a line? Why do you think it is called point slope form? 5. How do you know if two lines are parallel? How do you know if they are perpendicular? 6. What is the slope of the line? How do you find it? 7. What is the slope of a horizontal line? 8. What is the slope of a vertical line? 1. Graph the equation and indicate the slope, if it exists. 2. Find an equation for a line with slope= -3 and y intercept=7, write your answer in standard form. 3. Find an equation for a line which passes through the point (-5,4) and m=, write your final answer in slope-intercept form. 4. Given the x-intercept of -4 and y-intercept of -5, find an equation for the line and write your final answer in slope-intercept form. 5. Write an equation of the line that contains the point (-3,4) and is parallel to 6. Write an equation of the line that contains the point (-2,4) and is perpendicular to Chapter 3, Section 1 1. Is every correspondence between two sets a function? Why or why not? 2. What are the four different ways that we represented functions? 3. Can you explain what the domain and range of a function are? 4. What do the terms input and output refer to when working with functions? 5. How can we tell if an equation defines a function by looking at the graph of the equation? 1. Look in your book at page numbers Can you identify which ones are functions and which are not. Also, which are one-to-one? Why are they one-to-one? 2. Page 173 numbers

8 3. Page 173 numbers Page 174 numbers Chapter 3, Section 2 1. How to find the domain and range from a graph of a function? 2. What does it mean for a function to be increasing or decreasing or constant? 3. What does it mean for a function to be defined piecewise? 1. Page 184 number Page 185 number Page 185 number Page 185 number Page 186 number Chapter 3, Section 3 Should Know: 1. It would be important to know and understand the table on page 195 labeled Graph Transformation Summary. 2. It would be important to know the six elementary graphs found on page How to tell if a function is even or odd or neither. 1. Page Page 199 numbers Page 200 numbers Page 200 numbers Chapter 3, Section 4 Do you Know: 1. What is standard form for a quadratic function? 2. What is the vertex form of a quadratic function?

9 3. How to tell if a quadratic function is open up or open down? When does it have a max or min value? 4. Using transformations, explain why the vertex of is (h,k). 5. Explain how to find the maximum or minimum value of a quadratic function. 6. What information does the constant a provide about the graph of the function in the form? 1. Page 217 numbers Page 218 numbers Page 218 numbers Page 219 numbers Chapter 3, Section 5 1. Explain how to find the sum of two functions. 2. Explain how to find the product of two functions. 3. Is the domain of always the same as the intersection of the domains of and? Explain. 1. Page 232 numbers Page 232 numbers Chapter 3, Section 6 1. When a function is defined by ordered pairs, how can you tell if it is one-to-one? 2. When a function is defined by a graph, how can you tell if it is one-to-one? 3. What is the relationship between the graphs of two functions that are inverses? 1. Page 247 number Page 248 number Page 249 number