quiz for lessons 1 - 1 through 1 - 6
1 - 1 numbers and patterns
identify a possible pattern. use the pattern to write the next three numbers or figures.
1. 8, 15, 22, 29,...
2. 79, 66, 53, 40,...
3.
1 - 2 exponents
find each value.
4. 8^4
5. 7^3
6. 4^5
7. 6^2
8. the number of bacteria in a sample doubles every hour. how many bacteria cells will there be after 8 hours if there is one cell at the beginning? write your answer as a power.
1 - 3 metric measurements
convert each measure.
9. 17.3 kg to grams
10. 540 ml to liters
11. 0.46 cm to millimeters
12. cat ran in the 400 - meter dash and the 800 - meter run. hilo ran in the 2 - kilometer cross - country race. all together, who ran the farthest, cat or hilo?
1 - 4 applying exponents
multiply.
13. 456·10^5
14. 9.3·10^2
15. 0.36·10^8
write each number in scientific notation.
16. 8,400,000
17. 521,000,000
18. 29,000
19. in may 2005, the worlds population was over 6,446,000,000 and was increasing by 140 people each minute! write this population in scientific notation.
1 - 5 order of operations
simplify each expression.
20. 8 - 14÷(9 - 2)
21. 54 - 6·3 + 4^2
22. 4 - 24÷2^3
23. 4(3 + 2)^2 - 9
1 - 6 properties
simplify each expression. justify each step.
24. 29 + 50 + 21
25. 5·18·20
26. 34 + 62 + 36
27. 3·11·20
32 chapter 1 algebraic reasoning

Question

Accepted Answer

1. **For the sequence 8, 15, 22, 29,...**:
   - **Explanation**:
     - **Step1: Identify the common - difference**
       The common difference $d$ between consecutive terms is found by subtracting consecutive terms. For example, $15 - 8=7$, $22 - 15 = 7$, $29 - 22=7$.
     - **Step2: Find the next three terms**
       The next term after 29 is $29 + 7=36$, the term after 36 is $36+7 = 43$, and the term after 43 is $43 + 7=50$.
   - **Answer**: 36, 43, 50
2. **For the sequence 79, 66, 53, 40,...**:
   - **Explanation**:
     - **Step1: Identify the common - difference**
       The common difference $d=66 - 79=- 13$, $53 - 66=-13$, $40 - 53=-13$.
     - **Step2: Find the next three terms**
       The next term after 40 is $40+( - 13)=27$, the term after 27 is $27+( - 13)=14$, and the term after 14 is $14+( - 13)=1$.
   - **Answer**: 27, 14, 1
3. **For $8^{4}$**:
   - **Explanation**:
     - **Step1: Expand the exponent**
       $8^{4}=8\times8\times8\times8$.
     - **Step2: Calculate the product**
       $8\times8 = 64$, $64\times8=512$, $512\times8 = 4096$.
   - **Answer**: 4096
4. **For $7^{3}$**:
   - **Explanation**:
     - **Step1: Expand the exponent**
       $7^{3}=7\times7\times7$.
     - **Step2: Calculate the product**
       $7\times7 = 49$, $49\times7=343$.
   - **Answer**: 343
5. **For $4^{5}$**:
   - **Explanation**:
     - **Step1: Expand the exponent**
       $4^{5}=4\times4\times4\times4\times4$.
     - **Step2: Calculate the product**
       $4\times4 = 16$, $16\times4 = 64$, $64\times4=256$, $256\times4 = 1024$.
   - **Answer**: 1024
6. **For $6^{2}$**:
   - **Explanation**:
     - **Step1: Expand the exponent**
       $6^{2}=6\times6$.
     - **Step2: Calculate the product**
       $6\times6 = 36$.
   - **Answer**: 36
7. **For the bacteria problem**:
   - **Explanation**:
     - **Step1: Identify the pattern**
       Since the number of bacteria doubles every hour, and we start with 1 cell, the number of bacteria after $n$ hours is $2^{n}$. Here $n = 8$.
     - **Step2: Calculate the result**
       The number of bacteria after 8 hours is $2^{8}$.
   - **Answer**: $2^{8}$
8. **Convert 17.3 kg to grams**:
   - **Explanation**:
     - **Step1: Use the conversion factor**
       We know that $1\ kg=1000\ g$.
     - **Step2: Multiply**
       $17.3\ kg\times1000 = 17300\ g$.
   - **Answer**: 17300 g
9. **Convert 540 mL to liters**:
   - **Explanation**:
     - **Step1: Use the conversion factor**
       We know that $1\ L = 1000\ mL$, so to convert mL to L, we divide by 1000.
     - **Step2: Calculate**
       $540\ mL\div1000=0.54\ L$.
   - **Answer**: 0.54 L
10. **Convert 0.46 cm to millimeters**:
   - **Explanation**:
     - **Step1: Use the conversion factor**
       We know that $1\ cm = 10\ mm$.
     - **Step2: Multiply**
       $0.46\ cm\times10 = 4.6\ mm$.
   - **Answer**: 4.6 mm
11. **For Cat and Hilo's running distance**:
   - **Explanation**:
     - **Step1: Convert all distances to the same unit**
       Cat ran $400 + 800=1200$ meters. Hilo ran $2$ kilometers. Since $1\ km = 1000$ meters, $2$ kilometers $=2\times1000 = 2000$ meters.
     - **Step2: Compare the distances**
       Since $2000>1200$, Hilo ran the farthest.
   - **Answer**: Hilo
12. **For $456\times10^{5}$**:
   - **Explanation**:
     - **Step1: Move the decimal point**
       $10^{5}$ means moving the decimal point 5 places to the right. For $456$, it becomes $45600000$.
   - **Answer**: 45600000
13. **For $9.3\times10^{2}$**:
   - **Explanation**:
     - **Step1: Move the decimal point**
       $10^{2}$ means moving the decimal point 2 places to the right. So $9.3\times10^{2}=930$.
   - **Answer**: 930
14. **For $0.36\times10^{8}$**:
   - **Explanation**:
     - **Step1: Move the decimal point**
       $10^{8}$ means moving the decimal point 8 places to the right. $0.36\times10^{8}=36000000$.
   - **Answer**: 36000000
15. **Write 8400000 in scientific notation**:
   - **Explanation**:
     - **Step1: Rewrite the number**
       $8400000 = 8.4\times1000000$.
     - **Step2: Express in scientific notation**
       Since $1000000 = 10^{6}$, the number in scientific notation is $8.4\times10^{6}$.
   - **Answer**: $8.4\times10^{6}$
16. **Write 521000000 in scientific notation**:
   - **Explanation**:
     - **Step1: Rewrite the number**
       $521000000=5.21\times100000000$.
     - **Step2: Express in scientific notation**
       Since $100000000 = 10^{8}$, the number in scientific notation is $5.21\times10^{8}$.
   - **Answer**: $5.21\times10^{8}$
17. **Write 29000 in scientific notation**:
   - **Explanation**:
     - **Step1: Rewrite the number**
       $29000 = 2.9\times10000$.
     - **Step2: Express in scientific notation**
       Since $10000 = 10^{4}$, the number in scientific notation is $2.9\times10^{4}$.
   - **Answer**: $2.9\times10^{4}$
18. **Write 6446000000 in scientific notation**:
   - **Explanation**:
     - **Step1: Rewrite the number**
       $6446000000=6.446\times1000000000$.
     - **Step2: Express in scientific notation**
       Since $1000000000 = 10^{9}$, the number in scientific notation is $6.446\times10^{9}$.
   - **Answer**: $6.446\times10^{9}$
19. **Simplify $8 - 14\div(9 - 2)$**:
   - **Explanation**:
     - **Step1: Solve the parentheses first**
       $9 - 2=7$.
     - **Step2: Do the division**
       $14\div7 = 2$.
     - **Step3: Do the subtraction**
       $8-2 = 6$.
   - **Answer**: 6
20. **Simplify $54-6\times3 + 4^{2}$**:
   - **Explanation**:
     - **Step1: Calculate the exponent**
       $4^{2}=16$.
     - **Step2: Do the multiplication**
       $6\times3 = 18$.
     - **Step3: Do the subtraction and addition from left - to - right**
       $54-18+16=36 + 16=52$.
   - **Answer**: 52
21. **Simplify $4-24\div2^{3}$**:
   - **Explanation**:
     - **Step1: Calculate the exponent**
       $2^{3}=8$.
     - **Step2: Do the division**
       $24\div8 = 3$.
     - **Step3: Do the subtraction**
       $4 - 3=1$.
   - **Answer**: 1
22. **Simplify $4(3 + 2)^{2}-9$**:
   - **Explanation**:
     - **Step1: Solve the parentheses**
       $3 + 2=5$.
     - **Step2: Calculate the exponent**
       $5^{2}=25$.
     - **Step3: Do the multiplication**
       $4\times25 = 100$.
     - **Step4: Do the subtraction**
       $100-9 = 91$.
   - **Answer**: 91
23. **Simplify $29 + 50+21$**:
   - **Explanation**:
     - **Step1: Use the commutative and associative properties of addition**
       $(29 + 21)+50$.
     - **Step2: Calculate**
       $29+21 = 50$, $50 + 50=100$.
   - **Answer**: 100
24. **Simplify $5\times18\times20$**:
   - **Explanation**:
     - **Step1: Use the commutative and associative properties of multiplication**
       $(5\times20)\times18$.
     - **Step2: Calculate**
       $5\times20 = 100$, $100\times18=1800$.
   - **Answer**: 1800
25. **Simplify $34 + 62+36$**:
   - **Explanation**:
     - **Step1: Use the commutative and associative properties of addition**
       $(34 + 36)+62$.
     - **Step2: Calculate**
       $34+36 = 70$, $70+62 = 132$.
   - **Answer**: 132
26. **Simplify $3\times11\times20$**:
   - **Explanation**:
     - **Step1: Use the commutative and associative properties of multiplication**
       $(3\times20)\times11$.
     - **Step2: Calculate**
       $3\times20 = 60$, $60\times11=660$.
   - **Answer**: 660

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