Math 65A Elementary Algebra A Exam II STUDY GUIDE and REVIEW Chapter 2, Sections 3 5, and Chapter 3, Sections 1-3

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1 Exam II STUDY GUIDE and REVIEW Chapter 2, Sections 5, and Chapter, Sections 1 - Exam II will be given on Thursday, April 10. You will have the entire class time for the exam. It will cover Chapter 2, Sections 5, and Chapter, Sections 1. Cell phones must be off during the exam. Use of a simple or scientific calculator is allowed for this exam (no graphing calculators or calculator apps). When you have finished taking the exam, you may leave. STUDY GUIDE and REVIEW EXERCISES Wherever feasible, show ALL steps of your work/thinking. You may use a simple or scientific calculator to perform computations. When sketching graphs, your sketch must include appropriately labeled axes and scale to receive credit. CHAPTER 2, SECTIONS 5 Here is a summary of the core concepts and skills you should know from Chapter 2, Sections - 5. The numbers in parentheses indicate the section number where the item is discussed. Work the exercises and check your answers with the answer key. Get help with problems you don t understand. Applications of Linear Equations (2., 2.4) Use Lab No. 4 to review for this topic and work the problems below. You must know the following formulas: Area of a rectangle Area of a square Area of a triangle Area of a circle Circumference of a circle Volume of a box You should be able to figure out the perimeter of a rectangle, square or triangle. 1. For each word problem below: Choose a letter to represent one of the unknowns in the problem. Then, if necessary, represent any other unknowns with expressions that use the same letter. Identify what quantity the letter represents. Write an equation that can be used to solve the problem. Solve the equation and answer any questions asked in the problem. NO CREDIT for solutions that do not include these steps. You may use a calculator to assist you with calculations, but you must show all steps of your work to receive credit. a. Find two consecutive integers such that when the smaller is added to twice the larger, the result is 2 more than the larger integer. b. Two angles are supplementary if the sum of their measures is 180. Find the measures of two supplementary angles if one of them is 5 degrees larger than the other.

2 Page 2 of 6 c. A triangular garden plot is to be enclosed by 0 feet of edging. Two sides of the bed are the same length. The third side is feet longer than the other two sides. Find the lengths of the sides of the garden plot. d. Two search-and-rescue teams leave a base at the same time looking for a lost boy. The first team, on foot, heads north at 2 mph and the other, on horseback, south at 4 mph. How long will it take them to search a combined distance of 21 miles between them? e. A solution contains 15% acid. How much water should be added to 50 milliliters of this solution to dilute it to a 2% solution? 2. Find the perimeter and area of: a. A rectangle with length 11 m and width.5 m. b. A triangle with height 4 cm and base 6 cm and two sides of 5 cm.. Find the area and circumference of a circle if the diameter is 12 ft. Write your answers in exact form (in terms of ), and then approximate your answers to the nearest tenth of a foot. Solve an equation for a specified variable. (2.4) 4. Solve each formula for the specified variable. a. I Prt, for t b. A P Prt, for t c. y mx b, for m d. A h B b, for b Solve linear inequalities and graph their solution sets on the number line. Solve applied problems by writing and solving a linear inequality. (2.5) 5. Solve each linear inequality. Graph the solution set on the number line. a. 2x 7 9 b. 4 7x 5x 40 c. 5 7x x 25 d. x 4 2 x 8 6. Write and solve a linear inequality to solve the following problem: A student scores 87 and 78 on two different 100-point tests. If the maximum score on the next test is also 100 points, what score does the student need to maintain an average of at least 85?

3 Page of 6 CHAPTER, SECTIONS 1 - Here is a summary of the core concepts and skills you should know from Chapter, Sections 1. The numbers in parentheses indicate the section number where the item is discussed. Work the exercises and check your answers with the answer key. Get help with problems you don t understand. Given data in a table form, make a scatter plot or line graph of the data. Answer questions about the data based on the table or graph. (.1) 7. The table shown below contains real data about federal income tax receipts I (in billions of dollars) during year t. t I a. Make a line graph of the data. Be sure to label the axes and indicate scale. Use broken axes if appropriate. b. Comment on any trends in the data. Does it appear that income tax receipts grew more during some decades than others? c. From the graph, estimate the federal income tax receipts received in d. Calculate the percent change in federal income tax receipts from 1990 to Determine whether or not an ordered pair xy, is a solution of a linear equation in two variables by substituting the values into the equation and simplifying. (.2) 8. Which of the following ordered pairs is a solution to the equation: x 2y 6. Show all work. a. 2,4 b. 1 11, 2 4 c. 6, 6 Make a table of solutions for a linear equation in two variables and use the table to sketch the graph of the linear equation. Your table should contain at least three solutions. (.2) 9. Make a table of solutions for the equation and then use the table to graph the equation. Include at least three solutions in your table. 1 a. 2x y 12 b. y x 4 c. y x When making a table of solutions for a linear equation, it is best to avoid fraction solutions. Why?

4 Page 4 of 6 Graph a linear equation in two variables by first solving for y and then making a table of solutions. Your table should contain at least three solutions. (.2) 11. Graph the linear equation by solving for y first, and then making a table of solutions. Include at least three solutions in your table. a. x y 6 b. x 4y 12 c. 2x 4y 0 Solve an applied problem by graphing an equation and interpreting or answering questions about the graph. (.2) 12. The United States spends more money than any developed nation on health care relative to its economy. The nation s 2001 health expenditures were $505 per person, up from $277 in 1990 and only $14 in For the years after 1980, the formula E 18.6 x 992 approximates per capita expenditures E for health care, in dollars, while x represents the number of years after a. In the table below, actual data collected from is given. Use the formula E 18.6 x 992 to complete the two blank columns on the right in the table below. Round your answers to the nearest whole dollar. (NOTE: x 0 corresponds to the year 1980) Year Per Capita Expenditure for Health Care in the U.S. Data Formula Health Expenditures per Person (in dollars) x (Years after 1980) E Health Expenditures per Person (in dollars) , , , , , ,05 b. Make a line graph of the data in the left-hand side of the table. 1 Source: U.S. Department of Health and Human Services

5 Page 5 of 6 c. According to the formula, how much did each American pay for health care in 2000? Does the formula underestimate or overestimate the actual amount shown in the table? By how much? d. According to the formula, how much did each American pay for health care in 1995? Does the formula underestimate or overestimate the actual amount shown in the table and bar graph? By how much? e. Assuming the trend shown in the data continues, use the formula to estimate how much each American should have expected to pay for health care in 2010? Find the x-intercept and the y-intercept for a linear equation. Use the intercepts, together with a third solution to the linear equation, to sketch the graph. (.) 1. Given a linear equation in two variables, how do you find the x-intercept? (Describe the steps you would take.) 14. Given a linear equation in two variables, how do you find the y-intercept? (Describe the steps you would take.) 15. Find the x-intercept and the y-intercept for each of the following linear equations. a. 2x y 8 b. 9x 7y 6 c. 5x 2y 9 d. x 4y The x-intercept and y-intercept of a linear equation can be useful in sketching in the graph, but not if they are fractions. Why are fraction intercepts not very useful? 17. For each of the following linear equations, find the x-intercept and the y-intercept, together with one or two additional solutions. Then sketch the graph of the linear equation. 1 a. 2x y 6 b. y x c. x 5y 5 d. 5x 2y 10 Interpret the x-intercept and the y-intercept of a linear equation in the context of an applied problem. (.) 18. Often the value of an item declines over time (this type of decline is called depreciation). The graph at the right shows the depreciation of a printing press over x years. a. What is the y-intercept for this graph? What does it mean in the context of the graph? (Be specific)

6 Page 6 of 6 b. What is the x-intercept for this graph? What does it mean in the context of the graph? (Be specific) Know the formulas for horizontal and vertical lines. Sketch the graphs of horizontal and vertical lines. Given a point on a horizontal or vertical line, write the equation of the line. (.) 19. State the formula for the graph of horizontal line that passes through the point 0,b. 20. State the formula for the graph of vertical line that passes through the point a, Sketch the graph of each line. a. x b. y 4 c. 2x 1 d. 1 2 y 22. In each part below, the coordinates of a point are given. Write the equation of the vertical line that passes through the point and write the equation of the horizontal line that passes through the point. 2,1 5,0 a. b. 0,4 c. 2. Graphing Summary: given a table of values or an equation, sketch the graph using the method of your choice. (.1-.) a. x 5y 15 b. 2 y x c. y x 4 d. t (seconds) d (feet) e. y 1