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# Algebra- Practice Problems

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A. Solve using the five-step problem-solving process.
Familiarize, Translate, Carry Out, Check, State
Show all steps necessary to arrive at your solution.

1. A square support unit in a television is made with a side measuring 5 centimeters. A new model being designed for the upcoming year will have a larger square with a side measuring 5.3 centimeters. By how much will the area of the square be increased?
2. Round your answer to 2 decimal places when necessary.
The area of a circle is 35 square meters. What is its circumference? (Use &#1087; = 3.14. Hint: Area of Circle: A = &#1087;r2 and Circumference of Circle: C = 2&#1087;r)
3. Round your answer to 2 decimal places.
For a holiday party, Marcus is making a five-layer torte, which consists of five 9-inch diameter cake layers with a cream topping on each layer. He knows that one recipe of cream will cover 60 square inches of cake. How many batches of the topping must he make to complete his torte? (Use &#1087; = 3.14 as an approximate value)

B. Express the answer in scientific notation to two decimals places unless requested otherwise.

1. A computer can do one calculation in 1.4 × 10^-7 seconds. How long would it take the computer to do a trillion (10^12) calculations? (Round to one decimal place.)

C.
Simplify. Show all necessary steps.
(x^2yz^2/3x^-2y^2z^-1)^2

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#### Solution Preview

The solution file is attached.

1. A square support unit in a television is made with a side measuring 5 centimeters. A new model being designed for the upcoming year will have a larger square with a side measuring 5.3 centimeters. By how much will the area of the square be increased?
Familiarize Need to calculate the difference between the areas of two squares to find out how much is the increase in area
Translate Increase in area = Area of the new square - Area of the old square
= x2^2 - x1^2, where x2 and x1 are respectively the sides of the new square and the old square
Carry Out Increase in area = 5.3^2 - 5^2 = 3.09 cm^2
Check 5.3^2 = 28.09 and 5^2 = 25, and 28.09 - 25 = 3.09
State The area of the square will be increased by 3.09 ...

#### Solution Summary

Practice problems in algebra are determined. The decimal places which are necessary are determined. A Complete, Neat and Step-by-step Solution is provided in the attached file.

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