4-A5: Mid-Chapter 4 Review

Transcription

1 -A: Mid-Chapter Review Alg H Write the equations for the horizontal and vertical lines that pass through the given point.. (, 0) Horiz. Vert.. (0, 8) Horiz. Vert. Use the slope formula to find the slope of the line that passes through the two points. ) (9,, 7) (, 7. 6) (,, 6) (, 6. ( (,, ), ). ) (,, 0) (,. 6) (,, ) (,. Graph the following equations. 8. y = x + 9. y = x Sketch the line with the given slope through the given point. 0. (0, ), m = = m,(, ). Write each equation in slope-intercept form and graph.. x + y =. y x + = 0 Find the x and y-intercepts of the line. Write your answers as coordinate points and label them with the name of the intercept.. x + y = 0. y = 8x 6. x y 9 7. What is the slope of a line that contains the point (, -) and has the same x-intercept as x + y = 8? Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve. 8. If y = when x =, find y when x =. 9. If y = 8 when x = 6, find y when x = If y = when x =, find y when x =. Find the s l o p e and y - i n t e r c e p t of the lines.. x + y =. y = 7. y 7x = For 7 write a linear equation in Slope Intercept Form.. Passes through the point (, ) with a slope of.. ), ( and ) 7, ( points. Passes through the 6. Passes through the points ( 7, ) and (, ). 7. Passes through the points (, 6) and (, 8 ).

2 Find the value of x so the line that passes through the pair of points and has the given slope: 8. (, 9 ) and ( x, ), m = 9. The cab fare varies directly with the number of miles driven, as shown in the table. Miles Driven Cab Fare $. $.0 $.7 $.00 $6. Write and graph an equation that relates the cab fare, y, to the miles driven, x. 0. The monthly telephone bill consists of $ service charge plus $.0 per call. Write an equation in slope-intercept form for the total monthly bill if x represents the number of calls made in a month. Then graph the equation. If your bill last month was $0.0 use your equation to find the number of calls you made. Don't forget that A also includes: Page, # 6.

3 T- Rev A Review for Trimester Benchmark Exam Alg H Do in your spiral and show all support work!. = x. Evaluate the expression 7x + x when. Is x = 6 a solution of the equation x = x + 7? Simplify the expressions:. (x ) (x + x). (x 8) (x 7). 0 x Solve the equations: 6. x 7( x) = 6 7. x = 7 x 8. x + = (x + ) 9. (6 c) = c c 0. y (y + 9) = 9y (9 y). (a 8) + 7 = (a + ) a - 9. Solve the equation for b: ab + 7b = a.. Solve the equation for a: ab + 7b = a.. Find the slope and y-intercept of the line x 7y =.. Find the slope of the line containing the points, ) 8) and (, ). 6. Sketch the graph and label the intercepts of the equation x y = Make a table of values for y = x. Use the values 6,, 0,, 6, 9 for x. 8. Write the equation of the line passing through the points (, 7) and (7, 7). 9. What is the slope of the line from your equation in problem #8? 0. In 99 a company had 6 employees. By 998 the company had grown to 08 employees. Find the average rate of change and label your answer with units.. Write in slope-intercept form and sketch the line. x y =.. Write in slope-intercept form the equation of the line that passes through (,,( and (0, )..( (-, and ),, ). Write in slope-intercept form the equation of the line that passes through. Write the equation y = 6 x + in standard form with integer coefficients.. Write in point-slope form the equation of the line that passes through the point (, ( 9 with a slope of. 6. Identify the hypothesis and conclusion of the statement, then rewrite the statement in ifthen form. A quadrilateral with equal sides is a rhombus.

4 7. Find a counterexample for the statement: If a and b are real numbers, (a + b) = a + b. 8. Identify each as rational or irrational numbers: Solve the proportion:. x x 0. Does the pair of ratios form a proportion?. 9, 6. Find the final price of the item. Printer $.00 discount 0% tax.%. Is the relation a function? (-, ), (, -), (7, 6), (9, 6), (, ). If f(x) = x +, find f(n).. Identify the domain and range of the function. (, ), (, -), (, -6), (-6, ), (-, -6).. Find the value of r so that the line through (8, r) and (, ) has a slope of Find the value of r in (, r), (r, ) so that the slope of the line containing them is. 7. Find the slope-intercept form of an equation for the line that passes through (-, ) and is parallel to the equation y = x. 8. Find the slope-intercept form of an equation of the line perpendicular to the line x y = and passing through the point (0, 6). 9. The table of ordered pairs shows the coordinates of two points on the graph of a function. What is the equation that describes the function? x y Write the equations of the horizontal and vertical lines that pass through the point (-, -7).

5 T- Rev B Multiple Choice Review for T- Benchmark Exam Algebra H Do in spiral and show all support work! ) Which is an example of the Distributive Property? A) ( ) + = (- + ) + B) ( ) = C) ( ) + = + (- + ) D) ( ) = 0 ) Which equation is equal to y = + (8 ) A) y = 6 B) y = C) y = D) y = 8 ) What is the solution of (x ) (x ) = A) B) C) ) Which set of numbers is closed under the operation of division? A) integers B) rational numbers, except division by 0 C) irrational numbers D) none of the above D) ) Which property makes it easier to evaluate the expression (87 ) mentally? A) Commutative Property B) Associative Property C) Distributive Property D) Multiplicative Inverse 6) For which set of numbers is the inequality x x true? A) real numbers B) rational numbers C) integers D) all of the above 7) Which is a counterexample for the conjecture, the difference between two negative integers is always positive? A) -7 = -9 B) 7 = C) - (-) = - D) - (-7) = 8) What is the domain of the function given by 0,,,,, 6 7,,?, 6, 7,,, 6 A) 0,, 7 B),,, 7 C), D) 9) What is the opposite of the reciprocal of? A) B) C) D) 0) What is the solution for the equation (y + ) (y ) = A) B) C) D) ) Adult tickets for the school concert cost $ and student tickets cost $.0. The school sold $6.0 worth of tickets. If 0 more students than adults attended the concert, how many students attended the concert? A) 0 B) C) D) 7 ) What is the solution for the equation? x x 0 6 A) B) C) D) 0 ) A movie discount pass, which has an annual fee of $0, allows a moviegoer to pay $6 per movie. If a movie ticket normally costs $8.0, how many movie tickets must a moviegoer buy to make the discount pass a bargain? A) at least B) more than 0 C) 0 or fewer D) more than 9

6 ) What is the solution for the equation?.96 = 0.08(x ) A). B) C) D) 87 ) The Morena family drove to Yosemite National Park in hours. On the way home, they averaged miles per hour less and the trip took hours. How far from Yosemite National Park do they live? A) 60 miles B) 80 miles C) miles D) 0 miles 6) What is the value of m to the nearest tenth when 0.m 0.7m = 0. A) -0. B) -. C).0 D) -0. 7) It would take each member of the -member dance committee hours to inflate all the balloons alone. How long would it take them to inflate the balloons together? A) hours B) hours C) hours D) hours n n n 7 8) What is the solution for the equation? A) B) C) D) ) Your brother starts out 0 minutes before you on a bike path and rides at a rate of 9 miles per hour. If you ride at a rate of miles per hour, how long will it take you to catch up to him? A) hour B) hour C) hour D) hour 0) Which relation is a function? 0, 0,,,,,,,,,, 6,, 6 A), B) C),,,,,,, D),,,,,,, ) In the equation t = 000p, where tons are a function of pounds, what does t represent? A) the dependent variable B) the independent variable C) the intercept D) the slope ) What is the y-intercept for the equation? 6x y = - A) - B) C) D) ) Which statement is true about the relationship between the domain (D) and the range (R) of a function? A) For every element in D, there is only one corresponding element in R. B) For every element in R, there is only one corresponding element in D. C) There must be the same number of elements in D and R. D) The elements of D are the dependent variables. ) Which equation represents the line that passes through the point (-, ) with a slope of? A) x y = 7 B) x + y = C) x + y = D) x y = -8 ) Which situation is most likely represented by the graph? A) amount of tip money earned by a waiter every night B) price of a stock on the stock market C) wages paid to an hourly employee at a factory D) daily commissions earned by a real estate agent 6) What is the x-intercept for the equation?x y = 0 A) B) - C) - D) Money Time 7) What is the slope of the line? x + y = 6 A) B) C) D) -

7 8) Which point is on the line? x y = - A) (, ) B), C) (, 7) D) all of the above 9) Which ordered pair represents the x-intercept of the line? x y = A) (0, ) B) (, 0) C) (0, -) D) (-, 0) 0) What is the equation of the line that passes through the point (, ) and has a slope of ) Which point is a solution to the inequality? x + y < 6 A) (, ) B) (-, ) C) (0, ) D) (-, )? x A) y x B) y x C) y x D) y ) What is the equation of the line that passes through the point (, ) and is parallel to the graph of x y = 9? A) x y = - B) x y = C) x + y = 6 D) x + y = 9 ) Which ordered pair represents where the graph of x y = 0 intersects the y-axis? A) (0, -) B) (-, 0) C) (0, ) D) (, 0) ) On a scatter plot, the x-axis represents the latitude from the equator to the North Pole and the y-axis represents the average temperature. Which type of correlation is represented? A) positive correlation B) negative correlation Temperature C) no correlation D) none of the above ) The graph of a linear function contains the following data points. What is the slope of the line? A) B) C) D) Latitude Number of cars Car wash $ 0 $0 $7 0 $00 $ 6) Which point is not on the line? 6x 8y = - A) (, ) B), C) (, ) D) (0., 0.6) 7) Which point is on the line? y x A) (, 7) B) (, -) C) (0, ) D) (-, 0) 8) What is the equation of the line that passes through the point (, -) and is perpendicular to the line x y = 8? A) x y = 7 B) x + y = C) x + y = D) x y =

8 T- Rev. C Review for Trimester Benchmark Exam For 9, define variables, write a verbal sentence, write an equation, and solve. Show all support work.. Kathy started a savings account with $0. After 7 months she had $60 in the account. When did she have exactly $800 in the account?. Erik has 6 more nickels than dimes in his wallet. If he has a total of $.0 in nickels and dimes, find the number of each type of coin.. The length of a rectangle is five less than twice its width. If the perimeter is 68 cm, find the dimensions of the rectangle.. The sum of four consecutive even integers is 0. Find the integers.. Tickets for a play cost $6 for adults and $ for students. A total of 07 tickets worth $07 were sold. How many adult tickets were sold? 6. A grocer has dried apples selling for $.0/lb. and dried bananas selling for $./lb. How many pounds of each did he use to make a mixture of 0 pounds that will sell for $.0/lb.? 7. A small city park has a rectangular-shaped lawn surrounded on all sides by a border of crushed gravel that is meters wide. The lawn is meters longer than it is wide. The area of the crushed gravel border is 6 m. Find the dimensions of the lawn. 8. Two trains left Chicago, one traveling east at 0 mph and the other traveling west at 0 mph. After how many hours were the two trains miles apart? 9. A car going 0 mph left Thousand Oaks, heading toward South Bend, Indiana. Three hours later a second car going 70 mph left, traveling on the same road. How many hours will it take for the second car to overtake the first car? Solve: 0. Y varies directly as x. If y = 7 when x =, find x when y = 0.. Charles s Law states that, at a constant pressure, volume of a gas V varies directly as its temperature, T. A volume of cubic feet of a certain gas has a temperature of 00. Find the volume of the same gas at 0. Solve:. x x x. x x 6. m 6 m 0 y y [(y + ) (y + )] = ( + y) 7. x x 6