Download NCP 505 507 508 Lesson

NCP 505, 507, & 508 Lessons/Notes CRS SKILL Numbers: Concepts & Properties NCP 505 NCP 507 NCP 508 Name_________________________________________ Period____________ LEVEL DESCRIPTION Level 1 – ALL students must attain NCP 401 Exhibit knowledge of elementary number mastery at this level 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 other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will attain NCP 508 Determine when an expression is mastery of the extension skill. undefined. NCP 604 Apply rules of exponents (rational exponents) VOCABULARY Rational Exponents, Exact Answer, Undefined REQUIRED SKILLS TO MASTER Square roots of perfect squares Cube roots Estimating square roots Dividing by zero Additional KHAN Skills Level 1 1. Write each number as a product of prime factors a. 51 b. 130 c. 315 2. Factor each monomial. To FACTOR a monomial, write the monomial as a product of prime numbers and variables with exponents of 1. a. 27x 2 b. 546x 3 y 5 c. 165x 4 y 7 z 1 3. Complete the table !x 1 2 3 4 5 6 7 8 9 10 11 12 2
!x 1 8 27 64 3
!x 125 366 124 565 997 100 250 360
0 0 0 Level 2 4. Simplify each radical expression a. 88 b. 693 5. Write the equivalent of each cube root expression in simplified form. a. 3 351 2 b. 3 176 c. 245 c. 3 3250 Nth Roots and Rational Exponents:
If n is any positive integer, then the principle nth root of a is defined as follows:
Rule
n
a = b means
n
ab = ( n a )( n b )
n
a
=
b
n
a
n
b
Example
5
− 32 = −2
b =a
n
n
an = a
if n is odd
n
an = a
if n is even
6. Simplify each radical expression a. 8x 7 y 3 d. 3 136x 7 y 3 3 (−2) 5 = −32
because
b. 98x 5 y 2 c. 242xy 8 e. 3 500x 2 y 9 f. 3 216x 5 y 10 Level 3 5. Find the length of the side (a) of each square for the area given. a. Area = 225 in2 Length of a side= b. Area = 169 yards2 Length of a side= 6. Find the length of the edge of each cube for the volume given. a. Volume = 8 cm3 Length of edge = b. Volume = 125 ft3 Length of edge = 7. Multiply each set of radical expressions writing your final answer in simplified radical form b. 14x 7 y 2 21x 3 y c. 3 20xy 4 3 50x 2 y d. 3 98x 2 y 5 3 84x 2 y a. 10x 3 y 15xy 4 8. Simplify each radical expression. Write your answer in simplified radical form 45x 2 y
420x 5 y 2
a b. 231x 3 y 5
20x 6 y 3
9. Multiply each radical expression. Write your answer in simplified radical form. a. 4q 2 r 5 9q 4 r 3 b. 7a 2 bc8 12b 5 10. Simplify each radical expression. Write your answer in simplified radical form. a. Level 4 5 14xyz 12xy 3 z10
2z 3 49x 3
b. 20a 2 b 4
6ab
25a 3b 5
Exact Answer 11. Solve each of the following equations using algebra. Provide the exact answer(s) (simplified radical) and a decimal rounded to the nearest hundredth if needed. Then graph the left side of the equation and the right side of the equation to verify the number of solutions (one solution or two solutions). a. x 2 − 10 = 5 6 7 b. 3x 2 − 7 = 4 c. x + 7 = 9 d. 3x − 7 = −4 12. Simplify each radical expression. a) 3 6 − 4 6 b) − 3 7 + 4 7 c) − 11 12 − 4 75 d) − 9 20 + 10 45 e) 14 2 +
f) 5 3 3 + 2 3 24 - 3 81 2
3
32
Level 5 Rational Exponents: Rule
Example
1
n
a =n a
m
n
a = n a m or equals
( a)
n
m
Rational Exponent 13. Write each expression using a rational expression. a) 5 x 3 = 8 b) 3 x 7 = c) 3 z 9 = d) 7 h 2 = 14. Write each expression using a rational expression. 3
1
a) x 3 = b) p 5 = 7
4
c) z 8 = d) p 9 = 15. Simplify each expression. Write your answer in simplest radical form. (
a) 4x 6 y10
)
1
2
(
b) 81m n
(
c) 300p 9 y 3
(
12
e) 27x y
9 )
1
2
1
5 3
)
8
(
1
5 2
d) 8x 6 y 10
(
8
)
1
3
) d) 432q p
1
15 3
)
Undefined 16. Find the value(s) that make each expression undefined then indicate the values it is defined for. 50
2x
a) b) X −5
4 − 2x
10 c) 3x d) 3x + 5