zMath 160  - Unit 1: Factors, Exponents, and Order of Operations; Prime Numbers and Prime Factorization

Factors and Powers


1)

Evaluate: 82


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2)

Evaluate: 43


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3)

Evaluate: 25


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4)

Which number is a squared number, 36 or 35? Explain why.


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5)

Which number is a cubed number, 28 or 27? Explain why.


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6)

Evaluate. 25 + 24 ÷ (10 – 2)


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7)

Evaluate: 43 – 20 + 49


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8)

Evaluate: 12 ÷ 3 + 2 × 9


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9)

Evaluate:  48 – 25


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10)

Evaluate: (7 – 3)2 × 5


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Prime and Composite Numbers


11)

Explain why 11 is a prime number.


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12)

Explain why 12 is a composite number.


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13)

What is the next prime number after 19?


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Prime Factorization


14)

Find the prime factorization of 24.


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15)

Find the prime factorization of 27.


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16)

3 × 2 × 5 × 5 is the prime factorization for what number?


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Review


17)

You have 60 meters of fencing and want to enclose an area for a garden; however, you want to set up the fence so that the largest possible area is enclosed within the fence. The shape may be a rectangle or a square. What is the length and width of the shape that will given the maximum area? (Hint: On paper, experiment by drawing rectangles and/or squares that have sides with lengths that total a perimeter of 60 meters. Then, calculate the area. Find the one that gives the largest area.)


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18)

Continue this pattern for three more places: 2, 5, 8, 11, ____, ____, ____


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19)

Roberta was adding these three numbers: 27 + 7 + 13. She decided to add (27 + 7) first, and then add on 13. Robert suggested that she add the 7 + 13 first since it totaled 20, then add on the 27 to get 47. What property of addition is Robert using to make the problem a little bit easier?


20)

Subtract “33 thousand 528” from “54 thousand 7”.


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21) What is the value of the digit that is underlined in this number? 

64,398

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22)

Find the sum of the first six odd numbers.


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23)

Find the sum of the first ten odd numbers


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24)

Print out and complete the chart below. Follow the pattern for “Odd Numbers Added” up through the first ten odd numbers. Look for a pattern in the sums. Write a rule to describe the pattern that you discover. Test your rule by using it to find the sum of the first 20 odd numbers. What is the rule? What is the sum of the first 20 odd numbers?

Printable Chart

 


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25)

Evaluate:


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