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1 1 Simplify. 1 You Try. 1) Simplify. AF Evaluate if, and. 2 You Try. 2) Evaluate if. 1.0 Page 1 of 19 (AUSD) 09/13/10

2 3 Simplify. 3 You Try. 3) Simplify. NS Simplify. 4 You Try. 4) Simplify. OR NS 1.2 Page 2 of 19 (AUSD) 09/13/10

3 5 is an example of which property? The Distributive Property. 5 You Try. 5A) is an example of which property of equality? 5B) is an example of which property of equality? Give a counterexample to the statement: If a number is an integer, then it is a whole number. is an integer, but it is not a whole number. 6 You Try. 6) Give a counterexample to the statement: The square of a number is greater than the number Write an equation that describes the following statement: 3 less than a number is 8. Less than indicates subtraction and any variable can represent the unknown number. Therefore, the answer is: 7 You Try. Write an expression that describes each of the following: 7A) Four subtracted from a number 7B) Seven times a number squared AF 1.1 Page 3 of 19 (AUSD) 09/13/10

4 8 Solve. 8 You Try. 8) Solve Solve. 9 You Try. 9) Solve. 4.0, 5.0 Page 4 of 19 (AUSD) 09/13/10

5 10 Solve and graph the solutions. 10 You Try. 10A) Solve and graph the solutions. 10B) Solve or and graph the solutions Solve. is less than 10 units from You Try. 11A) Solve. 11B) Solve and 0 and 3.0 Page 5 of 19 (AUSD) 09/13/10

6 12 Solve. 12 You Try. 12) Solve. OR 4.0 Page 6 of 19 (AUSD) 09/13/10

7 13 Find the domain and range for the set of ordered pairs. Then tell if the relation is a function. 13 You Try. 13) Find the domain and range for the given relation. Then tell if the relation is a function. Domain: Range: This is not a function because the x- coordinate is paired with two different y- coordinates Find the slope of the line through the points and. 14 You Try. 14) Find the slope of the line through the points and. Slope AF 3.3 Page 7 of 19 (AUSD) 09/13/10

8 15 Find the x- and y-intercepts of the line whose equation is. The x-intercept is the point where the line crosses the x-axis. All points on the x-axis have 0 for their y-coordinate. Therefore, 15 You Try. 15) Find the x- and y-intercepts of the line whose equation is. The x-intercept is. Similarly, The y-intercept is. 6.0 Page 8 of 19 (AUSD) 09/13/10

9 16 Graph. Graph means plot a point for all of the solutions. So find some solutions: 16 You Try. 16) Graph. One solution is substitute 0 for y, we ll get. Similarly, if we. And is a solution. If we continue to pick all numbers for x, the solutions form a line. Therefore, the graph is: , 7.0 Page 9 of 19 (AUSD) 09/13/10

10 17 Write an equation for a line that passes through the points and. where is the slope and is the y-coordinate of the y-intercept. 17 You Try. 17) Write an equation for a line that passes through the points and. Point-slope Method OR Therefore, the equation is. 7.0 Page 10 of 19 (AUSD) 09/13/10

11 18 Write the equation of the line passing through the point and parallel to the line. The line parallel to the line have the same slope, which is. will 18 You Try. 18) Write the equation of the line passing through the point and parallel to the line. OR The equation is What is the slope of a line perpendicular to? The slope of is. The slope of a line perpendicular to opposite reciprocal of. That is,. is the 19 You Try. 19) What is the slope of a line perpendicular to? 8.0 Page 11 of 19 (AUSD) 09/13/10

12 20 Solve the system: 20 You Try. 20) Solve the system: Using the Substitution Method, Solve the first equation for : Substitute for in the second equation: Substitute for in either equation: The solution is. 9.0 Page 12 of 19 (AUSD) 09/13/10

13 21 Solve the system: 21 You Try. 21) Solve the system: Make the y-terms be opposites by multiplying the first equation by 2 and the second equation by 3: By the Addition Property of Equality: Substitute for in either equation: The solution is. 9.0 Page 13 of 19 (AUSD) 09/13/10

14 22 Find the two numbers whose sum is 9 and difference is -5. Let and one of the numbers (the lesser one) the other (greater) one. 22 You Try. 22) Find the two numbers whose sum is 12 and difference is -4. Then: and. According to the second equation,. Substituting for in the first equation gives: Substituting for in the first equation gives: Therefore, the numbers are 2 and Page 14 of 19 (AUSD) 09/13/10

15 23 Solve the system by graphing: 23 You Try. 23) Solve the system by graphing: To graph, first graph. and solve the equation. All of the solutions will form the following line: The line should be dashed because we are graphing, not. The solutions to of and below the line (for example solution because ). are to the right is a Similarly, we graph. The solutions to the system are in the overlapping shaded region: 9.0 Page 15 of 19 (AUSD) 09/13/10

16 24 Two trains leave the same station at the same time, traveling in opposite directions. The first train travels at 80 mph and the second train travels at 90 mph. In how many hours will the trains be 425 miles apart? First, draw a diagram. 80 mph station 90 mph n 425 mi. 24 You Try. 24) An airplane flies from San Francisco to New York at a speed of 350 mph and takes x hours. The return flight is at a speed of 300 mph and takes y hours. The flight from New York to San Francisco takes 1 hour longer than the flight from San Francisco to New York. How long does each flight take? The distance the first train travels plus the distance the second train travels is equal to 425 miles. But distance is rate time. And the trains travel for the same amount of time. So: 80 mph x hrs mph x hrs. = 425 The trains will be 425 miles apart in 2½ hours End of Study Guide Page 16 of 19 (AUSD) 09/13/10

17 Answer Key Item Number Answer California Standard 1 52 AF NS NS 1.2 5A Inverse Property of Addition 1.0 5B Commutative Property of Addition Answers may vary. 0, 1, or any number between 0 and 1. AF 1.1 7A 5.0 7B 4.0, A B or Page 17 of 19 (AUSD) 09/13/10

18 AUSD High School Algebra I First Semester Study Guide A and B or D 17.0 R 14 AF x-intercept: y-intercept: , and 9.0 Page 18 of 19 (AUSD) 09/13/10

19 AUSD High School Algebra I First Semester Study Guide and and S.F. to NY: hours NY to S.F.: hours 15.0 Page 19 of 19 (AUSD) 09/13/10

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