Exponents Unit Assessment Review

Transcription

1 Name: Class: Date: ID: A Exponents Unit Assessment Review Multiple Choice Identify the choice that best completes the statement or answers the question. Simplify the expression.. 7x 8 6x 3 a. 42 x 5 b. 42x 5 c. 42x d. 3x a b. 3 2 c. 3 9 d a. 8 b. 9 6 c. 9 6 d Ê 7 ˆ a. 000 b c d Ê ( ) 5 ˆ ( 2) 3 a b. 64 c d Evaluate 9x 2 y 2 for x = 3 and y = 2. a. 324 b c. 9( 6) 0 d Which number is NOT written in scientific notation? a b c d Which number is written in scientific notation? a b c d

2 Name: ID: A Write the number in scientific notation. 9. 8,670,000,000 a b c d Which list shows the numbers in order from least to greatest? a , , c , , b , , d , , Simplify the expression. Write the answer using scientific notation.. Ê ˆ Ê ˆ a b c d Complete the equation, by supplying the missing exponent = 3 2 a. 8 b. 3 c. 8 d. 4 Find the common ratio of the sequence , 82, 4, 20.5,... a. 82 b. 2 c. 2 d. 82 Match the table with the function that models the data. 4. x y a. y = x 4 b. y = 4x c. y = 4 x 2

3 Name: ID: A Match the function rule with the graph of the function. 5. y = 0 4 x a. c. b. d. 3

4 Name: ID: A 6. y = 2 4x a. c. b. d. Short Answer 7. Order ,.2 0 7, , and 435 from least to greatest. 8. Write 32x 5 y 5 with only one exponent. Use parentheses. 9. Solve the equation. Show your work. 6 3 = 4 x 20. Find the next three terms of the sequence. Then write a rule for the sequence. 648, 26, 72, 24 4

5 Name: ID: A 2. A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 35 3 x models the number of bacteria after x hours. a. Graph the function. b. Use the graph to estimate when there will be about 550 bacteria in the culture. Essay 22. Write the answer in scientific notation. A virus has a volume of approximately cubic centimeters. Calculate the estimated volume of viruses. Show your work. 23. Simplify. Show your work. (3m n 4 ) 2 (2m 3 n 5 ) Write a rule and find the given term in the geometric sequence described below. Show your work. What is the eighth term when the first term is -4 and the common ratio is 2? Other 25. Explain why (2g) 4 is not in simplest form. 26. Explain how to write 8a 9 as an expression with only one exponent. 6 25a 27. What happens to the terms of a sequence if the common ratio is? Explain your answer. 28. Determine whether the following statement is always, sometimes, or never true. Explain your answer. If a > b, then a b > b a. 5

6 Exponents Unit Assessment Review Answer Section MULTIPLE CHOICE. ANS: A PTS: DIF: L2 REF: 8-3 Mulitplication Properties of Exponents OBJ: 8-3. Multiplying Powers NAT: ADP I..5 ADP J.. STA: NJ 4..2 B.4 TOP: 8- Example 2 KEY: exponential expression simplifying an exponential expression multiplying powers with the same base 2. ANS: D PTS: DIF: L2 REF: 8-5 Division Properties of Exponents OBJ: 8-5. Dividing Powers With the Same Base NAT: ADP I..5 ADP I.2.2 ADP J.. STA: NJ 4..2 B.4 TOP: 8-5 Example KEY: dividing powers with the same base exponential expression 3. ANS: A PTS: DIF: L2 REF: 8-5 Division Properties of Exponents OBJ: 8-5. Dividing Powers With the Same Base NAT: ADP I..5 ADP I.2.2 ADP J.. STA: NJ 4..2 B.4 TOP: 8-5 Example KEY: dividing powers with the same base exponential expression 4. ANS: A PTS: DIF: L2 REF: 8-5 Division Properties of Exponents OBJ: Raising a Quotient to a Power NAT: ADP I..5 ADP I.2.2 ADP J.. STA: NJ 4..2 B.4 TOP: 8-5 Example 3 KEY: raising a quotient to a power exponential expression 5. ANS: B PTS: DIF: L3 REF: 8-5 Division Properties of Exponents OBJ: Raising a Quotient to a Power NAT: ADP I..5 ADP I.2.2 ADP J.. STA: NJ 4..2 B.4 TOP: 8-5 Example 4 KEY: raising a quotient to a power exponential expression simplifying an exponential expression 6. ANS: B PTS: DIF: L2 REF: 8- Zero and Negative Exponents OBJ: 8-.2 Evaluating Exponential Expressions NAT: ADP J.. ADP J..6 STA: NJ 4..2 B.2 NJ 4..2 B.4 NJ C.e NJ C.a TOP: 8- Example 3 KEY: negative exponent simplifying an exponential expression evaluating exponential expression 7. ANS: D PTS: DIF: L2 REF: 8-2 Scientific Notation OBJ: 8-2. Writing Numbers in Scientific and Standard Notations NAT: NAEP 2005 Nd NAEP 2005 Nf ADP I..5 ADP I.2.2 STA: NJ 4..2 B.2 TOP: 8-2 Example KEY: scientific notation 8. ANS: A PTS: DIF: L2 REF: 8-2 Scientific Notation OBJ: 8-2. Writing Numbers in Scientific and Standard Notations NAT: NAEP 2005 Nd NAEP 2005 Nf ADP I..5 ADP I.2.2 STA: NJ 4..2 B.2 TOP: 8-2 Example KEY: scientific notation

7 9. ANS: C PTS: DIF: L2 REF: 8-2 Scientific Notation OBJ: 8-2. Writing Numbers in Scientific and Standard Notations NAT: NAEP 2005 Nd NAEP 2005 Nf ADP I..5 ADP I.2.2 STA: NJ 4..2 B.2 TOP: 8-2 Example 2 KEY: scientific notation 0. ANS: B PTS: DIF: L2 REF: 8-2 Scientific Notation OBJ: Using Scientific Notation NAT: NAEP 2005 Nd NAEP 2005 Nf ADP I..5 ADP I.2.2 STA: NJ 4..2 B.2 TOP: 8-2 Example 5 KEY: standard notation scientific notation ordering. ANS: A PTS: DIF: L3 REF: 8-3 Mulitplication Properties of Exponents OBJ: Working With Scientific Notation NAT: ADP I..5 ADP J.. STA: NJ 4..2 B.4 TOP: 8-3 Example 3 KEY: multiply a number using scientific notation scientific notation multiplying powers with the same base exponential expression 2. ANS: C PTS: DIF: L3 REF: 8-3 Mulitplication Properties of Exponents OBJ: 8-3. Multiplying Powers NAT: ADP I..5 ADP J.. STA: NJ 4..2 B.4 KEY: multiplying powers with the same base simplifying an exponential expression exponential expression 3. ANS: C PTS: DIF: L2 REF: 8-6 Geometric Sequences OBJ: 8-6. Geometric Sequences NAT: NAEP 2005 Aa NAEP 2005 Ai ADP I..2 STA: NJ A.a TOP: 8-6 Example KEY: geometric sequence common ratio 4. ANS: C PTS: DIF: L2 REF: 8-7 Exponential Functions OBJ: Graphing Exponential Functions NAT: NAEP 2005 Ae ADP J.2.3 ADP J.4.7 ADP J.5.4 STA: NJ 4..2 B.4 NJ B. TOP: 8-7 Example 3 KEY: exponential function graphing 5. ANS: B PTS: DIF: L2 REF: 8-7 Exponential Functions OBJ: Graphing Exponential Functions NAT: NAEP 2005 Ae ADP J.2.3 ADP J.4.7 ADP J.5.4 STA: NJ 4..2 B.4 NJ B. TOP: 8-7 Example 3 KEY: exponential function graphing arithmetic sequence 6. ANS: D PTS: DIF: L3 REF: 8-7 Exponential Functions OBJ: Graphing Exponential Functions NAT: NAEP 2005 Ae ADP J.2.3 ADP J.4.7 ADP J.5.4 STA: NJ 4..2 B.4 NJ B. TOP: 8-7 Example 3 KEY: graphing exponential function SHORT ANSWER 7. ANS: , , , PTS: DIF: L2 REF: 8-2 Scientific Notation OBJ: Using Scientific Notation NAT: NAEP 2005 Nd NAEP 2005 Nf ADP I..5 ADP I.2.2 STA: NJ 4..2 B.2 TOP: 8-2 Example 4 KEY: ordering scientific notation standard notation 2

8 8. ANS: (2xy) 5 PTS: DIF: L3 REF: 8-4 More Multiplication Properties of Exponents OBJ: Raising a Product to a Power NAT: ADP I..5 ADP J.. STA: NJ 4..2 B.4 KEY: raising a product to a power multiplying powers with the same base raising a power to a power 9. ANS: 6 3 = 4 x (4 2 ) 3 = 4 x 4 6 = 4 x 6 = x PTS: DIF: L4 REF: 8-4 More Multiplication Properties of Exponents OBJ: 8-4. Raising a Power to a Power NAT: ADP I..5 ADP J.. STA: NJ 4..2 B.4 KEY: raising a power to a power exponential expression simplifying an exponential expression 20. ANS: 8, 8 3, 8 n 9 ; A(n) = 648 Ê ˆ 3 PTS: DIF: L3 REF: 8-6 Geometric Sequences OBJ: Using a Formula NAT: NAEP 2005 Aa NAEP 2005 Ai ADP I..2 STA: NJ A.a TOP: 8-6 Example 5 KEY: formula geometric sequence terms 3

9 2. ANS: about 2.5 hours PTS: DIF: L4 REF: 8-7 Exponential Functions OBJ: Graphing Exponential Functions NAT: NAEP 2005 Ae ADP J.2.3 ADP J.4.7 ADP J.5.4 STA: NJ 4..2 B.4 NJ B. TOP: 8-7 Example 4 KEY: exponential function graphing multi-part question word problem problem solving ESSAY 22. ANS: [4] Ê ˆ Ê ˆ = (4.7 4.) Ê ˆ = (9.27) Ê 4+ 6ˆ 0 = = [3] final answer correct but not written in scientific notation [2] one computational error [] two or more computational errors PTS: DIF: L4 REF: 8-3 Mulitplication Properties of Exponents OBJ: Working With Scientific Notation NAT: ADP I..5 ADP J.. STA: NJ 4..2 B.4 TOP: 8-3 Example 4 KEY: word problem problem solving rubric-based question extended response exponential expression scientific notation multiplying powers with the same base 4

10 23. ANS: [4] (3m n 4 ) 2 (2m 3 n 5 ) 4 = 3 2 m 2 n m 2 n 20 = (3 2 )(2 4 )m 2 m 2 n 8 n 20 = (3 2 )(2 4 )m 4 n 28 Ê ˆ = 9 (6)m4 n 28 = 6m4 9n 28 [3] one computational error [2] incorrect application of a law of exponents OR two computational errors [] more than two computational errors PTS: DIF: L3 REF: 8-4 More Multiplication Properties of Exponents OBJ: Raising a Product to a Power NAT: ADP I..5 ADP J.. STA: NJ 4..2 B.4 KEY: raising a product to a power exponents multiplying powers with the same base extended response rubric-based question 5

11 24. ANS: Ê [4] A rule for the sequence is A(n) = 4 ˆ 2 A(n) = 4 n Ê ˆ 2 A(8) = 4 8 Ê ˆ 2 = 4 7 Ê ˆ 2 Ê = 4 ˆ 28 = 4 28 n. = 32 [3] one computational error [2] incorrect rule [] more than one error PTS: DIF: L3 REF: 8-6 Geometric Sequences OBJ: Using a Formula NAT: NAEP 2005 Aa NAEP 2005 Ai ADP I..2 STA: NJ A.a KEY: geometric sequence formula extended response rubric-based question OTHER 25. ANS: Each term should be raised to the fourth power and simplified. PTS: DIF: L3 REF: 8-4 More Multiplication Properties of Exponents OBJ: Raising a Product to a Power NAT: ADP I..5 ADP J.. STA: NJ 4..2 B.4 KEY: raising a product to a power simplifying an exponential expression exponential expression writing in math reasoning 6

12 26. ANS: First, simplify a 9 since the powers have the same base. 6 a 8a 9 = 8a 9 6 = 8a 3 25a Then write 8 and 25 as numbers raised to the third power. 8a 3 25 = (2)3 a Since all of the bases are raised to the third power, write them as a single base. (2) 3 a 3 3 Ê 2a ˆ = PTS: DIF: L3 REF: 8-5 Division Properties of Exponents OBJ: Raising a Quotient to a Power NAT: ADP I..5 ADP I.2.2 ADP J.. STA: NJ 4..2 B.4 KEY: raising a quotient to a power exponential expression reasoning writing in math 27. ANS: All of the terms will equal the first term. For A(n) = 5 () n, () n will always equal so A(n) will equal 5 for any value of n. PTS: DIF: L3 REF: 8-6 Geometric Sequences OBJ: 8-6. Geometric Sequences NAT: NAEP 2005 Aa NAEP 2005 Ai ADP I..2 STA: NJ A.a KEY: geometric sequence formula writing in math reasoning 28. ANS: Sometimes. If a = 3 and b = 2, then 3 2 = 9 and 2 3 = 8 and a b > b a. But if a = 4 and b = 3, then 4 3 = 64 and 3 4 = 8 so a b < b a. PTS: DIF: L3 REF: 8- Zero and Negative Exponents OBJ: 8-.2 Evaluating Exponential Expressions NAT: ADP J.. ADP J..6 STA: NJ 4..2 B.2 NJ 4..2 B.4 NJ C.e NJ C.a KEY: exponential function evaluating exponential expression writing in math 7