Extra Practice - Nova Scotia Department of Education.docx

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1、BLM 8.1Extra Practice8.1 Investigate and Describe PatternsBLM 9.1Extra Practice9.1 Solve Equations1. a) What equation is modelled?What do you need to add to or subtract from both sides of the balance to solve the equation?b) Find the solution.2. How many cubes must go into each box in order to make

2、the following scales balance?a)b) Each box must contain the same number of cubes.9.9.3. Solve. You can model, use systematic trials, or the covcr-up method.a)4z = 16z = _b)3q = 18q =.c)8 + x= 12X = _d)6 - y = 30y =.e)5n = 35n =f)29-? = 3m =g)3o + 7 = 2a =h)4b + 17 = 41b =Pick any equation from quest

3、ion 3. Draw a diagram to illustrate each solution.4. Solve each equation.a) t + 2。+ 9 = 12a =b) 8 + 2m + 2tn = 28in =a) Six times a number plus 9 gives 75. Write this as an equation.b) What is the number?5. Study the pattern of unit squares.a) Write an equation that relates the number of squares, n,

4、 to the perimeter, p.b) If the perimeter is 50, how many squares are in the figure?6. It cost Doug S75 to set up his business selling lobster pins. He charges $3 a pin.a) In his first week, Doug made a profit of $120. Determine the equation modelling his profit.(Hint: Profit = Income - Costs.)b) How

5、 many pins did Doug sell?c) Explain your strategy. How else might you have solved the problem?BLM 9.：Extra PracticeGraph Linear Equations1. The cost of aa) Describeb) Use thea sandwichc) Use the toppings.Number of ToppingsCost ($)14.0024.7535.5046.25gourmet sandwich is shown, the relation using word

6、s.tabic to construct a graph that relates the cost of to the number of toppings.graph to find the cost of a sandwich with fiveDoes it make sense to join the points with a straight line? Why or why not?2. Refer to question 1.a) Write the equation that relates cost, (C), to number of toppings, ().b) C

7、heck your answer to question 1 part b) by substituting the values of n and C into your equation. Is the equation balanced for these values?3. Create a table of values fbr each linear relation. Use at least one negative value for x. Find at least three ordered pairs in each case. Then plot the ordere

8、d pairs and graph the line.c) y = -4xd) y = 9 -3xa) y = 5-x b) y = 2x +24. William is studying the growth of sun-flowers fbr his science project. His observations fbr one plant are given.a) Describe the relation using words.WeekHeight(cm)172325b) Use the table to construct a graph that relates the h

9、eight of the434sunflower to the number of weeks.543c) Use the graph to find the height of the plant fbr week 2.c) Does it make sense to join the points with a straight line? Why or why not?d) Approximately when did the plant reach a height of 30 cm?e) Predict when the plant will reach a height of 2

10、m. Describe any assumptions you must make.5. Refer to question 4.a) Write the equation that relates the height of the plant, (/:), to the number of days, (cl).b) Pick two ordered pairs from question 4 and verify that they satisfy this equation.Extra Practice田邪岫Analyse Graphs1. Sophie went rock climb

11、ing. The following tabic shows her height from the traifs starting point over time.Time, t (min)Height, h(m)Ordered Pair(5)00105201730304030503560427048802390101000a) Express each row as an ordered pair.b) Plot the points on a graph.c) Join the points using straight lines.d) Describe what Sophie may

12、 have been doing during each stage of her climb.2.State whether each table of values represents a linear or a non-linear relation.a) Complete the table so the result is a linear relation.X34567yb) Complete the table so the result is a non-linear relation.X123456y9The new squares added to each phase

13、arc shown in grey.a) Complete the table for phases 1 to 4.Phase, PNumber ofSquares, sOrderedPair (p, s)112334b) Continue the pattern to phase 5 and phase 6 in your table.Graph the relation. Describe the relation in words. Should you join the points? Explain why or why not.c) Is this a linear or a no

14、n-linear relation? Explain.d) Will there ever be a phase that has 45 squares? Explain why or why not.Extra PracticeExplore and Analyse RatesRemember to include proper units in all rates and unit rates.Hours1. Olivia earns SlO.5O/h working as a lifeguard. How much will she earn ina) a 3-h shift?b) a

15、15-h work week?2. Find the unit rate in each situation.a) Alex rode his bicycle 40 km in 2 h.b) Erika earned S262.50 in 35 h.c) Zach was charged $36 fbr a 4-h ski rental.3. Ing is shopping fbr olives. Her favourite brand is available in two sizes: a 350-g jar fbr $2.99 and a 500-g tub fbr $3.99.a) E

16、stimate which is the better buy.Explain your choice.b) Calculate which is the better buy.4. A plane is cruising at a steady speed of 600 km/h.a) How far will the plane travel in 5 h?b) How long will it take the plane to travel 4800 km?5. Sandy runs a home repair sen ice. She charges an hourly rate b

17、ased on how long the job takes.How much docs Sandy charge fbr a:a) 2-hourjob?b) 6-hourjob?c) 10-hourjob?6. Refer to question 5. Sandy changes her rates so that she still charges $15/h fbr jobs less than 4 hours and $35/h fbr jobs 4 hours or more.a) Draw a graph to represent this relation.b) Compare

18、this to the previous graph. In what ways are the graphs: similar? different?c) How will Sandys customers react to the new rates? Explain your answer.Chapter 9 Extra Practice Answer KeyGet Ready1. A(2, 1),B (-2, 3), C (-1,-3), D (4, 2), E (0, 1)2. R3. a) 9 b) 18 c) 42 d) 75Answers may vary.4. No. Exp

19、lanations may vary. If you use an odd number of tiles, there will always be one tile without an opposite partner, so you cannot make the model equal zero.5. a)x= 12b)y = 8c)z= 11 d) k = 7 e)/? = 6 f)/= 216. a) $90 b) 19 people. Explanations may vary.9.1 Solve Equations1. a) /? + 3 = 7 b) subtract 3

20、c) /? = 42. a) 8 cubes b) 3 cubes3. a) z = 4 b) q = 6 c) j = 4 d) y = -24 e) w = 7 f) m = 26 g)。= -3 h) b = 64. Diagrams may vary.5. a) = 1 b) m = 56. a) 6 + 9 = 75 b) 117. a) P = 2 + 2 b) 24 squares8. a) 3p - 75 = 120 b) 65 pins c) Answers may vary.9.2 Graph Linear Equations1. a) A sandwich with on

21、e topping costs $4. Each additional topping costs $0.75.b) Sandwich Costc) $7 d) No. Toppings are not a continuous quantity so the points should not be joined.2. a) C = 3.25 +0.75n b) yes3. Points may vary, a) (2, 3), (0, 5), (-2, 7)b) (2, 6), (0,4), (-2, 2)c) (2, 8), (0, 0), (-2, 8) a) y = 5 - xb)y

22、 = 2x + 2Ac) y = -4x d) y = 9 - 3xD叩endant Variable4. a) The sunflower started at 7 cm and grew 9 cm each week,b)Sunflower Growthc) 16 cm d) Yes. Growth is a continuous quantity so the points can be joined.e) Between week 3 and 4. f) After about 23 weeks. Assume the sunflower continues to grow at th

23、e same rate.5. a)力=7 + 9d b) Answers may vary.1. a) Describe the pattern of the letters D, H, L, P,. How would you identify the next letter?b) Determine the next two letters.2. a) A circular pool has a circum如ence of 18.3 m. Estimate the diameter of the pool to the nearest metre. Explain your reason

24、ing.b) Another pool has a diameter of 18.3 m. Estimate the circumference.3. Describe how you can find the value of the next term in each pattern. Then find the values of the next two terms.a) 9,18,27,36,.b)Term Number1234Value of term12963c)Term Number1234Value of term71428564. Refcr to question 3,

25、part a).a) Write an algebraic expression fbr the value of a term. Use n fbr the term number.b) Suppose the numbers in the sequence represent the cost of 1, 2, 3,4, . movie tickets.9.3 Analyse Graphsa) (0, 0),( 10, 5), (20, 17), (30,30), (40, 30), (50, 35), (60, 42), (70,48), (80,23), (90, 10),(100,

26、0)b) , c)Time (min)c) Answers may vary.1. a) Linear. The difference between consecutive y-values is constant, b) Non-linear. The difference between consecutive y-values is not constant.2. Answers may vary.3. a) Phase 1: 1 square; (1, 1). Phase 2: 3 squares; (2, 3). Phase 3: 6 squares; (3, 6). Phase

27、4: 10 squares; (4, 10). b) Phase 5: 15 squares; (5, 15). Phase 6: 21 squares; (6, 21).c) The number of squares increases by one more each phase. Should not join the points because each phase is a discrete value.d) Non-lincar. The graph is curved, e) Yes. Phase 9 has 45 squares.9.4 Explore and Analys

28、e Rates1. a) $31.50 b) $157.502. a) 20 knVh b) $7.50/h c) $9/ha) Estimates may vary, b) The 500-g tub is a better buy. The 500-g tub costs about $0.80 per 100 g and the 350-gjar costs about $0.86 per 100 g.3. a) 3000 km b) 8 h4. a) $30 b)$150 c) $4005. a)New Hourly Repair RatesNew Hourly Repair Rate

29、sb) Answers may vary. Similar: Both graphs have a $15 rate, and have more than one rate. Different: In the second graph, there is only one rate fbr 4 hours and over.c) Explanations may vary. Customers with jobs 4 h to almost 7 h long will pay more so they will not like the change. Customers with job

30、s 7 h or more will pay less (so they will like the change. Customers with jobs under 4 h will see no change.Reviewa) x = 4 b) y = 5 c) b = -6 d) q = 12 e) ? = 2 f) = -41. a) Alicia: 10 km/h, Rani, 9 km/hAlicia: 2 h, Rani: 2 h 13.3 min. Assume they both run at a constant rate and do not stop to rest.

31、2. Points may vary, a) (2,-2), (0, -6), (-2,-10) b) (2, -2), (0, 4), (-2, 10)a) Points may vary. 0 games: $3; (0, 3). 1 game: $5.50; (1, 5.50). 2 games: $8; (2, 8).3 games: $10.50; (3, 10.50).b) The graph starts at S3 and increase by $2.50 for every game.Gamesb) $28 d)C = 3 + 2.5ga) 14 games c) 12 g

32、ames. Each game costs $2.50, so if Owen saves $5 fbr lunch, he8yersojn Limiied、a s lassrqom use by the一一 a) y = 2x - 6 b) y = -3x + 4Dependant VariableCopyright r 2007 This page may be irproducan play 2 fewer games.X12345y27121722b) Answers may vary.6. The 5-kg bag. The 5-kg bag costs $1.15/kg and t

33、he 2-kg bag costs about $ 1.23/kg.7. a) 6 min; interpolation b) about 24 minPractice TestLB2. D3. A4. C5. a) x = 4 b) n = 2 c) p = 5 d) J = 16 e) = -2 f) y = -36. a) about 55 000 km b) about S13 000 c) about 140 000 kmc) For part c). The graph does not show the cars odometer reading for $0 value.7.

34、a)P = 6n- 40 b) $50, $200 c) 7 jugs d) 27 jugsFind the cost of the tickets when n = 3.5, 6.5, -4, and 12. Which numbers make sense and why?4. a) Determine the number of shelves and posts in each diagram of the following pattern. Complete the table.Number of Posts234Number ofShelves4b) Detennine the

35、number of shelves when there are 5 posts 6 postsWrite an algebraic expression to model the pattern, using the variable s to represent the number of shelves and the variable p to represent the number of posts.c) Determine the number of shelves when there arc 20 posts.BLM 8.2Extra PracticeChapter 8.2

36、Describe Relationships with Algebraic Equations1. For each statement, indicate whether it can be represented by an algebraic expression or equation. Explain your choice. Then, write an algebraic expression or equation for each statement. Choose your own variables and indicate what they represent.a)

37、one-third of Dexter earningsb) the area of a rectangle is length times widthc) five more years than Miriams ageLouis is nine years older than Erika.a) Write an equation that relates Louis age to Erikas age.b) Find Louis, age when Erika is 3.c) How old is Erika when Louis is 26?2. A taxi charges $6 p

38、lus $2.75 fbr every kilometre driven.a) Create a table of values fbr the cost of trips of between 1 km and 5 km.b) Graph the relationship.c) Use the graph to find the cost of a 10-km trip.d) Write an equation that relates cost and trip distance.e) Use the equation to find the cost of a 10-km trip. D

39、o your answers to parts c) and c) agree? Explain.ComerTrim3. Kim is making a tile border along a wall. She always starts with a comer pattern and makes the rest of theborder with the trim pattern.a) Create a table of values to shows the number of grey tiles are required fbr: 1 pattern piece (1 comer

40、)? 2 pattern pieces (1 corner, 1 trim)? 3 pattern pieces (1 corner, 2 trim)?b) Extend the pattern to find the number of grey tiles required fbr 4 and 5 pattern pieces.c) Describe how you can find the number of grey tiles required if you know the number of pattern pieces.d) Write an equation to relat

41、e the number of grey tiles, r, and the number of pattern pieces, p.e) Use the equation to find the number of grey tiles in a boarder of 25 pattern pieces.f) A border requires 55 grey tiles. How many pattern pieces arc there?Extra PracticeChapter 8.3 Collect Like Terms1. Classify each pair of terms a

42、s like or unlike. Explain your choice.a) 2x and 2y b) 4x and 3c) -3 and 6d) 2n and -6nSimplify each expression, if possible. If it is not possible, explain why.a) 3x + 4x b) 2x + 5y c) 4,r + 1d) 7 + 3Model each expression using algebra tiles. Draw the models.a) 5x + 3x b) 4y + yc) 6p + 2p d) 5m + 2n

43、t + 4?2. Write three different expressions that can be simplified to 6y - 2.3. Simplify each expression. Give a realistic situation that each expression could represent, a) 7y - 2yb) 5x + (-X)c) 5z-4zSimplify by collecting like terms.a) 8.r + 4x + 6y- 2y b) 3x - 5x + 4 - 13c) 5y +2 - 7y + 8d) 5x + 6

44、)，一 1 + x + (-9y) + 2Liam and Tilda both tutor Grade 8 students in mathematics. Liam charges $8.00 per house visit plus an hourly rate of $10.00. Tilda charges $12 per house visit plus an hourly rate of $7.00.a) Use algebra tiles to model the total cost of a tutoring session with each person.b) Writ

45、e expressions to model the cost of a tutoring session by each person.c) Write a simplified expression that describes the total fbr both tutoring sessions.d) Find the combined total earnings fbr both tutors fbr 1 h and fbr 3 h.Chapter 8 Extra Practice Answer KeyGet Ready1. a) -8 b) -2 c) -8 d) 7 e) 1

46、 0 4 g)-15 h)-4 i) -5 j) -6a) -6 b) 15 c) 1 d)213 perimeter: 26 m; area: 32 m24. Natalie has $30 in her savings account and she adds $5 at the end of each week, a) For table, w is week and s is savings in dollars.w12345s3540455055b) Graph s nould show the points (1, 35), (2,40), (3,45), (4, 50), (5,

47、 55). c) $70 d) 12 weeks5 a) = b)尹 c)尹 d)=5. Answers fbr e) to h) may vary, a) 2 b) 8 c) 6 d) 5 e) 4, 3 f) 24, 5 g) 3, 5 h) -18, 38.1 Investigate and Describe Patterns1. a) Write every 4th consecutive letter in the alphabet. Find the 4th letter after P. b) T, Xa) 6 m. Explanations may vary, b) 54.9

48、m2. Descriptions may vary, a) Start with 9 and then add 9 to each term following. 45, 54.b) Start with 12 and then subtract 3 from each term following. 0, -3. c) Start with 7 and then multiply each term following by 2. 112, 224.3. a) 9n b) $31.50, $58.50, $36.00, $108.00. Only 12 tickets makes sense

49、 because you cannot buy negative or fractional parts of a ticket.4. a)b) 16 shelves, 20 shelves c) s = 4p - 4 or s = 4( - 1) d) 80 shelvesNumber of Posts234Number of Shelves48128.2 Describe Relationships With Algebraic Equations1. a) expression; a ： 3, where e represents Dexters earnings.b) equation

50、; A = 1 x w, where A represents area, I represents length, and w represents width.c) expression; m + 5, where ni represents Miriams age.2. a) L = E + 9, where L represents Louis age, and E represents Erikas age.b) 12 years old c) 17 years old3 a) For table, d is distance in kilometres and c is cost

51、in dollars.d12345c8.7511.5014.2517.0019.75b) Graph shou d show the points (1, 8.75), (2, 11.5), (3, 14.25), (4, 17), (5, 19.75), c) $33.50c = 2.75 + 6 e) $33.50, yes4,a)b) 19 grey tiles; 23 grey tiles c) The number of grey tiles is 7 fbr the first pattern piece (the comer) plus 4 fbr every additiona

52、l pattern piece (trim), d) r = 7 + 4(/? 一 1) or，= 4p + 3Number of Pattern Pieces123Number of Grey Tiles71115d) 103 grey tiles f) 13 pattern piecesCollect Like Terms1. Explanations may vary, a), b) unlike terms c), d) like terms.2. a) lx b) unlike terms c) unlike terms, d) 10a) 5 x-tilcs and 3 x-tilc

53、s b) 4 y-tilcs and 2 y-tilcs c) Use x-tilcs to represent p. 6 x-tilcs and 1 x- tilc d) Use y-tilcs to represent m. 5 y-tilcs, 2 y-tilcs and 4 y-tilcs.3. Answers may vary.4. Situations may vary, a) 5y b) 4x c) ta) 12x + 4y b) 一2)，+ 10 c) x - 5y d) 6x - 3y + 15. a) Use an .r-tile to represent the numb

54、er of hours worked by each tutor. Liam: 10 x-tiles and 8 unit tiles. Tilda: 7 x-tiles and 12 unit tiles.b) Liam: 10/z + 8. Tilda: 7)+12 c) 17A + 20 d) $37; $71Review La)Review La)b) For tabic, s is the stage number and n is the number of white triangle in each stage.s12345i3579c) Graph should show t

55、he points (1, 1), (2, 3), (3, 5), (4, 7), (5, 9). Scatterplot. The stage number and triangles are whole numbers, d) 13First stage has a triangle made of 3 white triangles surrounding 1 black triangle. For each new stage, 1 black and 2 white triangles are added to the right side of the shape.e) = 2s

56、+ 1 h) 15 white triangles; yesa) 23.6 mm b) 30.8 cm2. a) 7 x-tilcs and 3 unit tiles b) 2 y-tiles and I x-tile c) 5 y-tilcs, 3 x-tilcs, and 4 unit tiles4 x-tiles, 1 y-tile, and 2 unit tiles3. a) Start with 3, and then add 4 to each term following. 19, 23, 27. b) Start with 9 and then add 10 to each t

57、erm following. 49, 59, 69. c) Start with 20 and then subtract 8 from each term following. -12, -20, -28.4. a) 1 Lv b) 6y c) 5x + 2y d) 5p e) -2a f) 7a - 5ba) 22 b) -6 c) 8 d) 5 e) -4 f) -36Practice Testl.C 2. A 3.B 4. B4. a) 51.5 cm b) 17.0 mma) i) 12x; 72 b) -2m; 8 c) lOy + 2; 2 d) 2k; 05. Explanat

58、ions may vary. 5 ma) White squares: start with 4 and multiply the number by 4 each day. Grey squares: use consecutive square numbers starting with 1. b) Day 4: a square of 16 grey squares with a row of 4 white squares on each side. Day 5: a square of 25 grey squares with a row of 5 white squares on each side, c) For able, d is day and b is the number of blocks after each day.d12345b512213245d) 了 + 4d e) 252 blocks f) 18 days