( _ ~+-')(X+2.) ) _ (.Y.. + "~.Ct( M - )(-~ o + ~ - 0+ (-',2.) 17G 4-~ -.;t [-~/-4) U (-2,00)

Transcription

1 Algebra \I Pre AP Review Worksheet 11.1, 11.3, 11.6 Name ~+~ _ Use a sign chart to solve each inequality. Verify using a calculator. X2 +x-12 ~ 0 {-~ -'IJ 3 x+6 l <0 3. ;:::0 x-i U(I13J x-2 X2 +6x )(- 2- (~.&.#)()C+z.) L. (1C+q)(X-3) ~ )< t{ -l.. 'x-i - 0 -" -I 'Z.. x..... ".....; t 3 X+l )(+ Cf ~ + + of X'f-4 D )(+l. - - t.a--.l ++ + ~-z ~ t -.\'-?> ~4- ~ ~ - )( -, -~ o + ~ - 0+ (-',2.) [-~/-4) U (-2,00) State the restrictions for each equation 2 x d.t.j=-x,4( 4. --=-+1 (' x-12 (.-3J~J and solve. ~(x-/) (-x"-, ).:(: +f) (2.('1(-/)) 4.: 1C2--~ -4-2.)(-2. o ::. ~ Z--Io- ~ - G. o = (X-4-~)(X'-2.) 5. x + 3 = 2 _ x + 1 x+2 x+? ()(+2.) -( 1c+-3 ) ::: x l +-~.: ~)C +- 4f ~: 1c4-2. f ~I ~:f ( _ ~+-')(X+2.).::l )( (1(-1-1 ) 3 ~ '3 17G 4-~ -.;t 6. _2_+~=L ~: ~=I()J'X~-5/~.lf+_6_=~ x+5 4-x x [-2.,0 I J x-3 x-3 - ()(_q) I 'Ie ()(-'I) c. X +-S'") (~ _~);: (..L\ ~()(-4) (\(.{..~-J \X+S"" )<-4 X) ~ $L()(-Ll) -:J. ~(~+-s-)=' (X-LfJ (~+S) -<~l..._ey: - J~'-I()Y:': -)C lor J{ - ~6 1C 2-_ ~ X +- ~::: ;t '\.?c2.._ SJ( +- G:. =- a 1C z, -I- I 't ~ -:"(0 :: 0 ( )( +-2.0) (x -, ) : 0 x+3 x +I x = x -6x-16 X2 +6x+8 X2-4x-32 ()(-i) ()C+2-.) (x+-co(r +-l) ClC-~) ~+4) 3x 2x = = x-4 x-3 x -7x+12 ( )C -3) (x -2.) ::. 0 C1t-4)(\(-!)(3~ ) _ (.Y.. + "~.Ct( M - )(-~.3"()c-~) ~ ~~()(-,,) +(;, ( )(+ 3) (x +4) -= (\( +-,) ( )( -i) - C)( - f 4) ()(+z:) x'l--+-7~+-i2...:; )(1.._7)< - ~ - Xl.+I2.X + z.~ 1C X - 8 z: 0 /2La: ~.t -t/ I ~ -:f - 2- ()( + 4) ()(- 2.) :. 0 [ J. 3 3>cl--'t)C = 2,..)Cl.-R'lC +-(p )(1-_ X - ~ = 0 (~-3)()c+-2..)~ C;I

2 Direct, Inverse and Joint Variation and Additional Applications 10. Find x when y = 1000, if y varies directly as x and y = 50 when x = 200. x~ ' If P varies inversely as the square root of q, and p = 12 when q = 36, find p when q = 16. '/J =/g 12. If s varies directly as r and inversely as t, and s = 10 when r = 5 and t = 3, for what value of twill s = 3 when r = 4? t = If z is inversely proportional to rand z = 32 when r = 1.5, find r when z = If w is inversely proportional to the square of v, and w = 3 when v = 6, find w when v = 3. co s: 12, 15. Suppose that z varies jointly as u and v and inversely as w, and that z = 0.8 when u = 8, v = 6 and w = 5. Find z when u = 3, v = 10 and w = 5. i!: ::. () S- 16. The volume V of a gas varies inversely as the pressure P on it. If the volume is 240 em" under pressure of 30 kg/ern", what pressure has to be applied to have a volume of 160 ern"? 45~/~1-17. The heat loss through a glass window varies jointly as the area ofthe window and the difference between the inside and outside temperatures. If the loss through a window with area 3 m 2 is 720 BTUwhen the temperature difference is 15 (, what is the heat loss through a window with area 4.5 m 2 when the temperature difference is 12 C? 18. The cost per person to rent a chartered bus varies inversely to the number of people who ride the bus. If 40 people pay $9.50 each to ride the chartered bus, what is the cost per person if only 25 people go? 19. When air is pumped into an automobile tire, the pressure required varies inversely as the volume. If the pressure is 80 pounds when the volume is 140 cubic inches, find the pressure when the volume is 100 in 3. I /cj.. ~ 20. A sprocket gear 8 in. in diameter is connected to a gear 3 in. in diameter. a. How fast does the smaller gear rotate when the larger one rotates at 216 r/min (revolutions per minute)? b. If the smaller gear is attached to the 28-inch-diameter rear wheel of a bicycle, how fast does the wheel rotate? (Hint: r/rnin * circumference of gear = k) a.) b) ~, r. 7 I 'f rplvl a.) J. /, 'Err = ~ r..3'i7" == 17 a. fj 11'

3 21. Members of a high school band are going to play in a college bowl game. The trip will cost $750 per band member plus a $10000 deposit for the band's travel. Write an equation that models this situation. a. If there were 40 band members, what would the trip cost per member? b. What if the administration said that at least 5 chaperones must go on the trip and the cost of their trip would be funded by the members of the band attending the event. What would be the cost per member? a) a'.d K= #~ ha. (..c..,j h) r: S-~ 22. t..m:i/lvtt.._hav -= /0000 -I- '7$7))( C = S{J(X+ 5"') ~ ~.r ~o h<-t--- 6-,44.I ~ ~ ~ 1':' ta...t'-j IOd 0 as: A-t- $' Slc.IiZL ~ The Johnson family is preparing to vacation at a famous amusement park. The park offers a family ticket discount package for $120 for an unlimited number of rides and will charge an entry fee of $7.50 for each person in the family. If the Johnson family takes their four cousins, it would reduce the cost per person by $5. How many people are in the Johnson family (excluding cousins)? ~d ~= -II. ~ ~c-r.f..-'--' ~ ~. :~ X= -/2. b"t.. '8 23.?~~~ A pharmacist wishes to make 1.8 L of a 10% solution of boric acid by mixing 7.5% and 12% solutions. How 1 much of each type of solution should be used? ''K= ~ 'I ~. z..;... I.f,... 'lc ;:: 6A-t 1l.,"ll ~..y.;", "g~~ 7.s-7. ~ I c: "0 /,;z.% ~ 24. How much pure antifreeze must be added to 12 L of a 40% solution of antifreeze to obtain a 60% solution? ~::: ~ if ~ Ti" c 4(t.J 1t -I- I~ (. t./o) = 6 (1{ + IJ..) -t: -+ 'I.~= ~ IC ;L. 25. How much water must be evaporated from a 300 L tank of a 2% salt solution to obtain a 5% solution? ctj!r(300-x) 26. IKo t- 00 II:J,Q ~ ~~ Suppose you have 100 ml of a solution that is 30% acid and 70% water. How many ml of acid do you need to add so that your new mixture is 60% acid?, 3 ((00) + 1C =., (~-+ 1(0)

4 27. A landscaper can prepare and seed a new lawn in 6 h. His assistant can prepare and seed the same size lawn in 7 h. How long will it take them together ~=~1t:.:-~~ 3~ ~~ to prepare and seed three of the same size lawns? :-- -I- ;: = 3 JI>-~ d ~ Wu.- ~ 9.~9t1.. ~ 28. A boat, which moves at 36 mi/h in still water, travels 28 mi downstream in the same amount of time that it takes to travel 20 mi upstream. Find the speed of the current. '~-=~Z' ~ ;l 3, +-)( 3,-K T 2.8 3c.+)t" 2.0 3(. -IC 29. A small jet has an airspeed (the rate in stili air) of 300 mi/h. During one day's flights, the pilot noted that the plane could fly 85 mi with a tailwind the rate of the wind? in the same time it took to fly 65 mi against that same wind. What was 30. T '8~ l~.e..u-:...j 30ot- X 30of-Jc -I-c..-e~ 300-)( ~ "5 306-)( I George takes 15 hours to do a job that his father can do in 6 hours. If George works for 4 }i hours before his father joins him, how long will it take the two of them working together to finish the job? I ~ = ~ ~ ~ "-"J ~ ~~ X+L ~ 2._+ --r-=i ~ ~.' 3-L-.. ~ +r=:: Is- L-~' ~ Howard and Josh work together at Starbucks and can make a pumpkin spice la~tes. It takes Josh 5 minutes to make the latte by himself. How long does it take Howard to make the latte alone? x!:,~ ~~~ * ~Q... ~~ 5K (3 3) 5" + T = I 5K d-..v~ ~ 7i~~~ ~~ On a round trip of 540 miles in each direction, the average rate of travel going was30 mph more than the rate returning. Find the rate for each direction if the entire trip took 15 hours. ~= ~ '1 ~ 1';;:":,, L',., ~ 1C+3Q 5Vo ~X X+-30 6'10 k ~ w--v Cjo A.. tl~4.' "~ ~4 C ~4'" ~~~O~L $l/o + 5 O =/~ )(-1-30 r SZ/o J( + S- ())( -I- 1~2-()6== /J"K '-Iso ~ /]{=--18 ~O I

5 33. Dylan can row 30 km downstream in the same amount of time he can row 18 km upstream. The rate of the current is 2 km/h. Find Dylan's rate. ~: --',u ~~tj~ /L..,.. 1) (<6 =- )( ~+~ ~ X- 2. J2- If )(-2- Jason and Hillary are asked to repaint the mascot on the gym wall. If Jason worked alone, it would take him 5 h to repaint it. Working alone, Hillary could do the job in 6 h. They begin painting at 11 am. After a while, Hilary takes a break while Jason continues to paint. How long of a break can Hillary take If they must have the job finished by 2:30 pm? What time would they have finished if Jason took a half hour for lunch and Hillary took 45 minutes for lunch with no other breaks? 1C 1C 7" +-;;=1 1{= ~~ 't: ~ -L-t"t-4 ~3, '3 ~ J - /,3,~ S-lj s: I S "!:J -:. /, 7 "--,, v ~~~~ ~~ 6)