Download Unit 11 NCP 505 507 508 worksheet

NCP 505, 507, 508 Worksheet CRS SKILL Numbers: Concepts & Properties NCP 505 NCP 507 NCP 508 Name_________________________________________________ Period____________ LEVEL Level 1 – ALL students must attain mastery at this level DESCRIPTION NCP 401 Exhibit knowledge of elementary number concepts Level 2 – MOST students will NCP 505 Work with squares and square roots attain mastery of the focus skill in isolation . NCP 507 Work with cubes and cube roots Level 3 – SOME students will attain mastery of focus skill with NCP 508 Determine when an expression is undefined. other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will NCP 604 Apply rules of exponents (rational attain mastery of the extension exponents) skill. Level 1 1. Write each number as a product of prime factors a. 38 b. 150 c. 110 2. Factor each monomial. To FACTOR a monomial, write the monomial as a product of prime numbers and variables with exponents of 1. a. !80x 3 c. !220x 3 y 2 d. !140xy 4 z 3 Level 2 3. Simplify each radical expression a. ! 90 b. ! 120 c. ! 98 4. Write the equivalent of each cube root expression in simplified form. a. !3 128 b. !3 120 c. !3 162 1 5. Simplify each radical expression a. ! 50x 4 b. ! 125x 3 y 6 d. 3 81x 3 y 6 e. 3 2000xy 7 !
!
Level 3 6. Find the length of the side (a) of each square for the area given. a. Area = 27 in2 Length of a side= b. Area = 625 yards2 Length of a side= 7. Find the length of the edge of each cube for the volume given. c. Volume = 342 cm3 Length of edge = c. 30x 8 y 9 !
f. 3 375x 4 y 12 !
d. Volume = 1000 ft3 Length of edge = 2 8. Multiply each set of radical expressions writing your final answer in simplified radical form a. 15x 3 y 5 ⋅ 10xy 4 !
b. 30x 3 y 6 z ⋅ 72xy 3z 5 !
c. 3 25x 3 y ⋅ 3 10x 5 y !
d. 3 8x 5 y 2z 4 ⋅ 3 20x 4 y 5 z 5 !
9. Simplify each radical expression. Write your answer in simplified radical form a
!
100x 3 y 8
5xy 3
32x 6 y 7 z 2
b. !
8xy 3z
10. Multiply each radical expression. Write your answer in simplified radical form. a. !2r 3t 4 30r 3t 7 c. 7x 2 y 5 18x 4 y ⋅8x 3 y 20x 5 y 3 !
b. 6p2 98p7v 6 !
d. 5x 3 y 8 10x 5 y 6 ⋅4x 5 y 15x 4 y 8 !
3 11. Simplify each radical expression. Write your answer in simplified radical form. a. 6x 5 y 8 20x 4 y 3z 6
3 8
2 3 2
! 4x z 15x y z
5
b. 5mn
!
60m2n10
3m5n6
Level 4 12. Solve each of the following equations. Provide the exact answer(s) (simplified radical) and a decimal rounded to the nearest hundredth. x2
− 3 = 1 a.
4
b. x 2 − 10 = −9 4 x − 2 = 1 c.
d. 2 x − 17 = −9 2. Simplify each radical expression. a) 9 5 − 7 5 b) − 7 3 + 8 3 c) 5 27 − 2 20 d) 7 50 + 4 98 e) 12 3 +
f) 2 3 2 + 2 3 16 - 3 54 1
3
48
5 Level 5 13. Simplify each expression. Write your answer in simplest radical form. (
4
a. 25x y
!
(
7
1
8 2
)
c. 108k w
!
(
1
9 2
) )
(
b. 121m p
!
(
3 6
) 1
5 2
)
d. 60c d w
!
f. 81a11r 7 3 !
1
e. 125z 12q9 3 !
1
3 8 2
(
)
1
14. Find the value(s) that make each expression undefined then report the values that make it defined. 12.5
5x
a) b) X +3
12 + 3x
c) 5x d) −
2x + 10 Review 15. Ken baked, frosted, and decorated a cake for the last Math Club meeting. The Math Club will pay Ken $5.00 for preparing a cake and will also pay him the cost of the cake mix at $1.73, the frosting mix at $2.67, and the sales tax of 5% on these 2 items (Note San Francisco has sales tax on all end-­‐
user sales). What is the total amount the Math Club will pay Ken? 6 16. To park a car at a short-­‐term parking lot costs $1.75 for the 1st hour or any part thereof, $1.50 for the 2nd hour or any part thereof, and $0.75 for each additional hour or any part thereof after the 2nd hour. Your ticket shows that you parked your car in this lot from 10:47 a. m. to 4:35 p.m. on the same day. What is the cost of parking your car, according to this ticket? (Note: Prices include all applicable sales tax.) 17. On September 1, a dress was priced at $90. On October 1, the price was reduced by 20%. On November 1, the price was further reduced by 25% of the October 1 price and marked FINAL. a. What was the FINAL price for the dress? b. What percent of the original price is this? c. What is the discount off of the original price? 18. A bus company always keeps 3 tires in stock for every bus it owns, plus an additional 30 tires in stock for emergencies. According to this policy, the bus company needs to have a total of 120 tires in stock. How many buses does the company own? 19. Vehicle A averages 17 miles per gallon of gasoline, and Vehicle B average 45 miles per gallon of gasoline. At these rates, how many more gallons of gasoline does Vehicle A need than Vehicle B to make a 1,530 mile trip? 20. Issa bought 2 cases of 12-­‐ounces cans of soda. Each case contained 24 cans. Issa could have bought the same amount of soda by buying how many 16-­‐ounce bottles of soda? 7