ALGEBRA 1 FINAL EXAM JUNE 2004 YOU MAY WRITE ON THIS TEST

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1 ALGEBRA 1 FINAL EXAM JUNE 00 YOU MAY WRITE ON THIS TEST

2 1. Simplify: 8x x( x 5) ( x + x) A. 3x + 11x B. x x C. x 37x 5x 33x 5x 37x. Solve: 3 x = 8 5x 7 A. 17 B. 3 C Solve: = x x 6 x A. 6 B. 3 C Solve for y in terms of x: y+ = x + A. 1 y= x B y= x C y= x y= x y= x+ 1

3 5. Solve: 5 x 1 = x 6 A. 0 B. 1 6 C Solve: ( x) x= 3.5 A. 13 B. 11 C Three times the largest of four consecutive odd integers is three less than four times the smallest of the four consecutive odd integers. What is the smallest of the four consecutive odd integers? A. 15 B. 17 C The regular price of a refrigerator is $1100. It is going to be discounted by 0%. What is the discounted (sale) price? A. $0 B. $880 C. $900 $910 $990

4 9. Which of the following properties is illustrated by the equation: = ? ( ) A. Reflexive Property of Equality B. Commutative Property of Subtraction C. Associative Property of Subtraction Distributive Property of Multiplication over Subtraction Substitution Property of Equality 10. Which of the following properties is illustrated by the equation: a+ b= a + b? A. Reflexive Property of Equality B. Transitive Property of Equality C. Associative Property of Addition Distributive Property of Multiplication over Addition Commutative Property of Addition 11. Expand: ( 3x y) A. 9x 16y B. 9x + 16y C. 3x + 16y 9x xy+ 16y 9x 1xy 16y 1. Expand: ( 3x 11) ( x+ 5) A. 1x 55 B. 1x + 55 C. 1x 9x 55 1x 59x 55 1x + 39x+ 55 3

5 13. Expand: ( x 1) 3 A. 3 8x 1 B. 3 8x x 1 C. 3 8x + 1x x 1 3 8x x + x 1 3 8x 1x + 6x 1 1. Solve: 15 x = 33 A. ±.5 B..5,1 C..5, , 1 7.5,1 15. Solve: 1 x < 1 A. 11 x < and < x < 13 x > B. 13 x < or < x < 13 x > C. 11 x < or 13 x >

6 16. Graph the solution set of the following inequality: x + > 10 A. B. C Phil T. Rich put together a large bowl full of many pieces of candy. Phil knew that the bowl contained 00 pieces of red candy. After the candies were thoroughly stirred and mixed, he randomly withdrew 0 pieces of candy, of which 5 were red. Approximately how many pieces of candy were in the bowl before Phil drew out any pieces? A. 1,60 B.,80 C. 3,00 16,00 3,000 5

7 18. Will Power is comparing costs to join a gym. Will finds that Silver s Gym cost $100 to join and $15 per month. He also found out that Abs of Steel Gym cost $150 to join and $1 per month. Will can only sign up for complete months (no part of a month). What is the minimum number of months needed before Abs of Steel is cheaper than Silver s. A. 1 B. 15 C Solve for x in terms of a and b. ax+ 15b= 9 ab A. 8x 1ab B. 9 ab 15b C. 15b ab a + 9 a b( 15 + a) a 9 a 15b 9b a 0. Which of the following is a factor of: 6x 3x A. ( 3x ) B. ( 3x + ) C. ( x + 1) ( 6x + 1) ( 6x 1) 1. Factor completely: x y xy x A. ( x y) ( 3x 5) B. ( x y) ( 3x 5) C. ( x+ y) ( 6x 5) ( x y) ( 6x 5) ( x y) ( 3x+ 5) 6

8 . If Jerry was factoring a factor? 0x 9x 33 completely, which of the following would be A. ( x 3) B. ( 5x 3) C. ( 5x + 3) ( x + 11) ( 5x 11) 3. Find the following quotient by performing the long division: 3 18x + 7x x 0 x + 3 A. 9x + x 1 + x + 3 9x 1+ x + 3 B. 9x x+ 1 + x + 3 9x 1+ x + 3 C. 9x x 1+ x + 3. Bea Kurr is hired by the local chemical plant to create mixtures for use in various labs at the chemical plant. On Bea s first day on the job she finds 0 liters of 1% boric acid and only 3 liters of 0% boric acid. Bea s new boss wants exactly 30 liters of an 18% solution. How many liters of the 1% solution should she use to get exactly 30 liters of 18% solution? A. 5.5 liters B. 7.5 liters C. 10 liters 15 liters.5 liters 7

9 5. Which of the following is a point on the line which passes through ( 3, 17) and ( 1, 7) A. ( 75,33 ) B. ( 75,35 ) C. ( 75,37 ) ( 75,39 ) ( 75,1 )? 6. Which of the following equations is in point-slope form and hence would be most easily graphed by using the given point and the slope? A. y = B. 3 y 7 = + 5 ( x ) C. x+ y= 1 1 y= x 7 x y + = 3 7. What is the solution set for the equation A. { } 7x = x? 0 B. { 3 3 C. } { 0,3 3 } { 7 } { 0, 7 } 8. Solve for x : x = x+ 5 A. 5, 1 B.,5 C.,0 5, 5 5,1 8

10 9. What is the solution set of the equation 6 x = x? A. { 3} B. { 3,} C. {} {6} {0, 6} 30. Simplify: A. 10 B..1 C Simplify: 1 1 A. 7 B. 1 C What is the y-intercept of the line passing through ( 8, 1) with a slope of A. 6 B. C. 8 3? 9

11 33. What is the y-coordinate of the point of intersection of the graphs of: x+ y = 6 and x+ y=? A. 18 B. 15 C Which of the following is the equation of the line passing through ( 9,1) and ( 1, )? A. 1 B y= x 6 y= x+ y= x 6 y= x+ 33 C. 1 y= x If f ( x) = 3x 10 then which of the following is equivalent to ( ) f a? A. a 0 B. 3a 10 C. 3x 10 6x 0 6a Factor 6x 13x 6 +? A. ( 3x ) B. ( x+ 3) ( 3x ) C. ( 3x ) ( x 3) ( 3x+ ) ( x+ 3) ( 6x 1)( x 6) 10

12 37. x 5kx + 5 is the square of binomial. What is a possible value of k? A. 10 B. 5 C Solve: x x 1= 0 A. 0,1 B. ± 1 C. 1 ± 3 1± 5 1± Solve: x x= 1 A. 0, 1 B., 1 C. ± 37 ± 3 5 ± 37 x 0. Which of the following expressions is equivalent to? x A. - B. 1 x 3 x C. x 11

13 1. Simplify: 6xy 7 ( x 5xy) A. 6 7x y B x y C x y 11xy x y 30xy 8 7 1x y 30xy. Simplify: 5x 10x 3 5x 9 3 A. 3 3x B. 6 3x C. 6 5x 9 5x 6 3 5x 11x 3. Simplify: x 1x x A. 5 x 7 + x x 5 x 7 B. x 5 x + 7 1x C. x + 5 x 7 x 7. Simplify: x x 1 A. x 3 B. 0 C. 1 x 7 x x 7 x +3 1

14 x= 3 5. Which of the following shows the graph of the system of equations: y + 6 = 3( x 1)? A. B. C. 13

15 6. Simplify: + ( x+ 3 ) ( x+ ) ( x+ )( x+ 5 ) A. ( x+ 3) ( x+ )( x+ 5) B. ( x+ 3) ( x+ ) ( x+ 5) C. ( x+ 3) ( x+ ) ( x+ ) ( x+ 5) ( x+ 3) ( x+ 5) 7. Simplify: x x x x x x x A. 1 B. 1 C. x + x x x Ky Yack takes 50 minutes to paddle 500 meters upstream. Ky takes only 1.5 minutes to return 500 meters downstream. Assuming that Ky always paddles at a constant speed, how long will it take him to paddle 565 meters across a lake where there is no current? A minutes B. 5 minutes C minutes 50 minutes 6.5 minutes 1

16 9. If 3x+ y= 7andx 3y= 67 then which of the following is the value of xy? A. 187 B. 33 C Which of the following is an equation of a line passing through ( 6, 3) and perpendicular to the graph of x+ 5y= 8? A. 5 y 3= 6 5 y+ 3= x 6 ( x ) ( ) B. 5 y 3= ( x+ 6) y+ 3= x 6 5 ( ) C. y 3= ( x ) 51. What is the simplified form of the reciprocal of 8? A B. 1 C. 15

17 5. Simplify:.6 A B. 3 C What is the simplified form of 1? A. 1 B. 0 C During the filming of Master and Commander the film crew used a huge tank filled with enough water to float the HMS Surprise. The crew used two different pipes to fill the tank. If the second pipe was used alone then it would take 10 hours longer than if the first pipe alone was used. If the pipes are used together the job of filling the tank takes 1 hours. How long would the slower pipe take to fill the tank alone? A. 15 hours B. 0 hours C. 5 hours 30 hours 35 hours 16

18 55. Which of the following is the graph of y< x? x 3y< 6 A. B. C. 17

19 8 + =? Which of the following is the graph of y 5 ( x ) A. B. C. 18

20 57. What are all the intercepts of y x x = ? A. x-intercept 6; y-intercept 3 B. x-intercept 9; y-intercept 6 C. No x-intercepts; y-intercepts of 6 and 9 x-intercept 3; y-intercept 9 No x-intercept; y-intercept Alby Boch knows how to find the y-intercept using several different ways in equations like 3x 6y=. One of these methods works on x+ xy + 3y =? What is the y- intercept of the graph of x+ xy + 3y =? A. 3 B. C y = 59. Buford is attempting to solve the system: x. He decides that even x + y = 16 though he hasn t seen a system that looks like this one he thinks he can use substitution. When Buford solves this system, he obtains two values for y. What are those two values? A. 3, B. 3, 1 C., 6 6, 8 8, 1 19

21 60. Which of the following is the graph of: x+ 10y< 0? A. B. C. 0

61. Which of the following is a reason why f ( ) not a function? x as described by the following graph, is a relation but A. f (0) does not exist. B. Neither f (10) nor f (0) exists. f 1 = f 3. C.

22 61. Which of the following is a reason why f ( ) not a function? x as described by the following graph, is a relation but A. f (0) does not exist. B. Neither f (10) nor f (0) exists. f 1 = f 3. C. ( ) ( ) f ( 1) has different values. It is unknown what formula or equation to use for f(x). 6. Since a rational expression involves division, the denominator may not have a value of zero. Therefore any values of a variable, which results in a denominator of zero, must be excluded from the domain of that variable. These are called excluded values of the rational expression. What are the excluded value(s) of the variable for x x the expression? x x 0 A. 0 B. 10 C.,5,1 1, 1

23 63. What is the simplified form of ( ) ( )? A B C Cliff no fencing along here corral w fence A rectangular corral is built against a cliff in such a way that only 150 feet of fencing is needed for the three sides. The width, w, of the corral is as shown. Which of the following would be an expression for the area of the enclosed rectangle? A. w( 150 w) B. w( 150 w) C. w( 150w 1) w w 75w w w 150

24 65. With no air resistance, the time, t, it takes an object to fall h feet, can be determined by the h equation t =. What is the height when the time to reach the ground is 5 seconds? A. 6.5 ft. B. 10 ft. C. 1,000 ft. 6,50 ft. 10,000 ft. 66. When solving ax + bx+ c = 0for x, the following steps could be taken. 1) ax + bx+ c = 0 b c 0 ) x + x+ = (divide both sides of the equation by a) a a a b c 3) x + x = 0+ a a (add c a to both sides of the equation) Which of the following expressions needs to be added to both sides of the equation, in order to complete the square? A. b x a b a B. c x a b x C. b a 3

25 67. Solve for y in terms of x: 8y xy = x + 5 A. xy+ x+ 5 y = 8 xy + 5 y = 8x B. xy + 5 y = 8 x + 5 y = 8 x C. x + 5 y = 8x 68. What is the y- intercept of the graph of x 5y 100 =? A. 0 B. 5 C On Planet X, the height, in meters, of an object, t seconds after being launched from a device, 30 meters above the ground, is given by ht ( ) = 88t 11t At what time(s), in seconds, will the object be 16 meters above ground? A. 3, 10 B. 3, 9 C. 3, 8, 8, 6

26 70. Determine which of the following is the graph of: f ( x) ( x x ) ( x 3) intercepts. A. B. =, by checking x and y C. 5

My Math Plan Assessment #2 Study Guide

My Math Plan Assessment #2 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4 2. Use factoring to solve the quadratic equation. x 2 + 9x + 1 = 17. Multiply and simplify