· Web view“Donkey Kong” is an arcade game that costs $1.50 to play. Once a player is eliminated, the play must insert another $.50 within 10 seconds to continue at the same

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Math 9Focused Problem Solving

Name: ____________________

GRASP

Give – Required – Analysis – Solution - Paraphrase

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Strand: Numbers1. If x=2 and y =3, then 2x4y3 – 9x3y0 is equal to

A. 864B. 792C. 621D. 424

2. If (n 3 ) 4 = 4096, then n equals _____________ (n6)(n2)

3. If (x 5 ) = 1, then x equals ________________ (x3)(x1)

4. If (y 3 ) 4 =6 25, then y equals _____________ (y6)(y2)

5. If (a 10 ) 10 = 10, then a equals _____________ (a50)(a49)

6. (-2)5 x (-2)2 can be simplified in exponential form as:A. (4)10

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B. (4)7

C. (-2)7

D. (-2)10

7. If x=5.0 x 10-23 and p=2.0x10-56 , then x÷p isA. 2.5 x 1079

B. 2.5 x 1033

C. 2.5 x 10-33

D. 2.5 x 10-79

8. (-3) 6 (-3) 2 simplified in exponential form as: (-3)10 (-3)1

A. (3) 8 (-3)11

B. -27C. (-3)-3

D. 91

9. If y=-8.4 x 105 and z=4.0 x 103, the product of x and y is:A. 2.1 x 108

B. -2.1 x 108

C. 2.1 x 1015

D. -2.1 x 1015

10. (-23)2 expressed in standard form is:A. -64B. 64C. 32D. -32

11. Super Student was given the following expression: 2 x2+3 x2whenx=2. Super student solved the question in the following way:

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Step 1: Substitute variable 2(2)2+3(2)2

Step 2: Multiply. 2x2=4 and 3x2=6 so the expression becomes 42+62

Step 3: Solve exponents 42=16 and 62=36 16+36Step 4: Add. 16+36=52

At Which Step did Super Student make an error?A. Step 1B. Step 2C. Step 3D. Step 4

12. Super Student was given the following expression: 2 y2when y=10 Which of the following calculator keystroke sequences is the one Super Student used to simplify the expression completely.A. 10 ^ 2 + 2B. 10 + 2 * 2C. 2 * 10 ^2D. 10 ^ 2 *2

13. Super Student was given the following expression: (2 x2+3 x2 )÷2 x when x=2. Super student solved the question in the following way:

Step 1: Substitute variables (2(2)2 + 3(2)2) ÷ 2(2)Step 2: Solve exponents and multiply. 22=4 4x2=8; 22+=4 4x3=12; therefore: (8+12)÷4Step 3: Divide. 12÷4=3 therefore: 8+3Step 4: Add. 8+3=11

At which step did Super Student make a mistake?

A. Step 1B. Step 2C. Step 3D. Step 4

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14. Which of the following expressions would equal 7 when x=2A. x2+x4-(20+9)B. (x3)(x2)-(x)(x2)C. x3+x4-(10+2)D. x3+x4-(20+9)

15. Which of the following expressions would equal (-25) when n=5A. n−2

B. (n2)C. −(n¿¿2)¿D. −(n¿¿−2)¿

16. Which of the following expressions would equal 18 when y=2

A. –y3

B. y-3

C. -(y)-3

D. y8

17. Which of the following expressions would equal 0.125 when n=5A. n 5 n5n3

B. −n3

C. n 8 n5

D. –(n-3)

18. Which of the following expressions would equal 10 when n=(-5)

A.n2

n1

B. (2) n10

n9

C. 2n

D. n10

n8

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19. (-m)-2 expressed as a positive exponent would be:A. (m)-2

B. 1m−2

C.1m2

D. m2

20. (−n−4) expressed in standard form when n =2 would be:A. 8

B.116

C.−116

D. 8

21. – (n−3) expressed in standard form when n=3 would be:A. -27B. 27

C.−127

D.127

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Strand: Patterns and Relations1. Suzie was answering the following algebra equation:

6x + 14 = 3x – 10

Identify the step in which she made her error.

a) 6x-3x + 14 = -10b) 3x = -10 + 14c) 3x = 4d) X = 4/3

2. Chris was answering the following algebra equation:

3(x+4)-(x-2)=14+12

Identify the step in which he made his error.

a) 3x+4-x-2=26b) 2x+2=26c) 2x=24d) X=12

3. Kelly was answering the following algebra equation:

x + (x-1) = 122 4Identify the step in which she made her error.

a) (4)x + 4(x-1) = 12 2 4b) 4x + (4x-4) = 12

2 4c) 2x + 1x – 1 = 12

3x – 1 = 12d) 3x = 13

X = 13/3

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4. Sam was solving the following math equation:

5y – 14 + 8 = 2y -8 - 6y

Identify the step he made his error:

a) 5y – 6 = -4y – 8b) 5y = -4y -2c) 1y = -2d) Y = -2

5. It costs $195 to rent a car for a week from a car rental company. After 100km, there is an additional charge of $.25/km. Which of the following equations defines the cost, c, of renting a car if x is the number of km’s over 100 km.

a) c = 195 + 100(.25x)

b) c= 195 + .25(x-100)

c) c= 195 + .25 – 100

d) c= 195 +.25x

6. “Donkey Kong” is an arcade game that costs $1.50 to play. Once a player is eliminated, the play must insert another $.50 within 10 seconds to continue at the same level. If c is the number of times a player chooses to continue, then which of the following equations can be used to determine, T, the total cost of playing the game?

a) T= 1.5 + .5cb) T = 1.5c + .5c) T = 1.5 - .5cd) T = 1.5(.5c)

7. A monthly mobile phone bill is calculated by adding $.10/minute onto a base charge of $15/month. If C represents the total bill and x represents each minute, which formula could you use to determine your monthly mobile phone bill?

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a) c = .10 + 10xb) c= 10x + .10xc) c = .10x + 10d) c = x + .1(10)

8. Recently an airplane called the Enviroplane established a world record for altitude for a solar powered aircraft. Temperatures at a higher altitudes tend to be lower. There is about a 1 C decrease in the temperature for every 1 000 m increase in altitude.

If it is 35 C at sea level when the plane takes off, which equation can be used to estimate the air temperature as the plane gains altitude. (let T be the temperature and a be the altitude)

a) T = 35 + 1000ab) T = 35 + a/1000c) T = 35 – a/1000d) T = 35 – 1/1000a

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9. Which of the following number lines represents the solution to the inequality

4x – 12 > 8x + 4 when x is a rational number?

10. Which of the following number lines represents the solution to the inequality

6x - 4 ≤ 12 + 8 when x is a rational number?

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11. . Which of the following number lines represents the solution to the inequality

x-4 ≥ 2x – 8 when X is a rational number. 2 5

12. Simplify (2 x−3 )2

A. 4 x2+9 B. 4 x2−9 C. 2 x2−12+9 D. 4 x2−12 x+9

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Use the following algebra tile legend to answer all algebra tile questions

13. Which of the following diagrams represent the products of( x+3 ) ( x−4 ) ?

A. B. C. D.

14. Find the area of the following rectangle:

(3 x−3 )

A. 4 x+7 B. 3 x2+x−12 C. 4 x+1 D. 3 x2−x−12

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( x+4 )

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15. Simplify (5 x−2 ) (−x−4 )

A. −5 x2−18 x+8 B. 5 x2+18 x+8 C. −5 x2−22 x+8 D. 5 x2−18 x+8

16. Solve for x; 2 x−4=8

A. x=5 B. x=2 C. x=20 D. x=8

17. What is the value of x in the equation6(2 x−3 )=30 ?

A. −5B. 1C. 4D. 24

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Numerical Response

18. What is the value of x after simplifying?

x4+3=1

3

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19. In a toolbox, a construction worker has twice as many screwdrivers as wrenches, and has 5 fewer hammers than wrenches. If he has 19 tools in his tool box, then the number of wrenches in his toolbox is

20. Simplify (4 x−1 )+(2x+3 )−( x−2 )

A. 7 x−5 B. 7 x+5 C. 5 x−5 D. 5 x+5

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Use the following information to answer question #21

21. The simplified equation you would use to find the perimeter of the triangle is

A. 5 x−1 cmB. 6 x+1 cmC. 6 x

2+9 cmD. 6 x−1 cm

22. Simplify (4 x−1 )+(2x+3 )−( x−2 )

A. 7 x−5 B. 7 x+5 C. 5 x−5 D. 5 x+5

23. What is the perimeter of the figure expressed as an algebraic expression?

A. 4m2n4

B. 4m+n4

C. 4m+4n

D. 4m2+n4

GRASP


The sides of a particular triangle measure

(3 x−1 ) cm

( x+3 ) cm

(2 x−3 ) cm

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Numerical Response

24. What is the coefficient of the x term after simplifying? (17−4 x )+(−x+8 )+(3 x−5 )

GRASP


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Statistics and Probability

1. Wayne placed 8 pairs of shorts and 6 T-shirts in the dryer. Once dry, what is the probability that the first item pulled from the dryer will be a pair of shorts?

2. Sandy planted 10 Roma tomato seeds and 10 Beefsteak tomato seeds at the same depth in the soil and gave them identical heating, lighting, and moisture. Assuming that their germination characteristics are identical, what is the probability that a Roma tomato plant will emerge from the soil first?

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3. Mr. Ferguson organizes the school ski club. He has a list of 55 students who have paid to go skiing tonight. 25 of the students are in grade 9, 18 are in grade 8, and 12 are in grade 7. What is the probability that the first student on the bus to the ski hill will be in grade 8?

4. Mary is a local town's caterer. At the town's Volunteer Appreciation Dinner buffet, she put out 42 slices of apple pie and 36 slices of blueberry pie. Assuming that the pies are equally well-liked in the community, what is the probability that the first piece taken will be blueberry?

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Shape and Space

4.5 m

3.2 m

1. Above shows the floor plan to Betty’s bedroom.

How much would it cost to carpet Betty’s bedroom if the cost of the carpet is

$45.00/m2?

2. A new gym was constructed that was 20m by 30m. In one corner a locker room

needs to be constructed that is 5m by 10m.

a) What is the area on the gym not including the locker room?

b) If the plans are revised and the dimensions of the locker room are reduced by 20%,

what percent will the area of the locker room decrease from the original plans?

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3. Justin wants to build a flower bed for gardening club. If the flower bed has the greatest

possible area within a perimeter of 24m, and if the sides of the flower bed must be

whole numbers, what is the length of the longest side of his flower bed?

4. Mike wants to build a flower bed for gardening club. If the flower bed has the greatest

possible area within a perimeter of 36m, and if the sides of the flower bed must be

whole numbers, then what is the length of the longest side of his flower bed?

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5. The formula for the volume of a cylinder is V= πr2h. Where r is the radius and h is the height of the cylinder. If the height of the cylinder is 10 cm and the radius is 2cm, what happens to the volume of the cylinder if:

a) The radius is doubled?

b) The radius is tripled?

c) The radius is halved?

d) The radius is quartered?

6. The volume of a rectangular box is 288 cm3. Its dimensions are the following:

length = 2x cm width = 2x cm height = 8 cm.

a) Find the length and width of the rectangular box.

b) Inside the rectangular box is a cylinder with the same height and a diameter equal to the width of the box.

If the formula for the surface area of a cylinder is SA = 2π r2 + 2πrh, then find the surface area of the cylinder to the nearest square centimeter.

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7. What would be the area of a square having side length, a, from the diagram below?

8. If a dock is built across the river, what width of the dock be?

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9. From a point 100 meters from the base of a tower, the angle of elevation to its top is 38 degrees.

a) Find the height to the nearest tenth.

b) If a square flag was constructed that had the same side length as the height of the

tower, what would be the area of the flag?

GRASP


Documents

· Web view“Donkey Kong” is an arcade game that costs $1.50 to play. Once a player is eliminated, the play must insert another $.50 within 10 seconds to continue at the same