PLTL #1 Name ________________________

Introduction to Elementary Algebra

Practice Review

1. Write as a decimal. 2. Write 50% as a fraction.

3. Write as a percent. 4. Write 60% as a decimal

5. Write 0.32 as a fraction. 6. Write 0.07 as a percent.

Geometry

7. Find the missing portion of the circles below (The portions total 100%.)

8. Find the area of the following figures.

Balance in a Savings

9. Use the following data from a newly opened savings account.

Date	Deposit	Withdrawal	Interest Earned	Balance
June 1	$50.00			$50.00
June 15	$50.00
June 30			$0.37
July 15		$30.00
July 30			$0.58

a. What was the balance on June 15? b. What was the balance on June 30?

c. What was the balance on July 15? d. What was the balance on July 30? $70.95

10. Evaluate (17 ‑ 9) + 28. ´ 1.1 11. What is 10% of $245?

12. Write the sum as a fraction: and 3 13. Which is greater, ½ or 0.75?

14. What is the product of 9 and 4? 15. What is the difference of 13 and 5?

16. Evaluate 9 ¸ 13 + (11 ‑ 5)] 17. Evaluate [(7 × 3) –2] + (8 ¸ 4)

18. Evaluate 3x + 1 when x = 2. 19. Evaluate (x ‑ 7) when x = 11.

20. Write an expression for the perimeter of a square with sides of length x.

21. Find the perimeter of a rectangular field 103 feet long and 210 feet wide.

22. What is the average height: 72 in., 68 in., 60 in., 76 in., 64 in.?

23. What is the value of when a = 9 and b = 4?

Calculator Exercises

Use a calculator to evaluate the expressions. Round your result to two decimal places.

24. 1.6⁵ 25. 3.9³ 26. 6.9²

27. What value of x would make the expression x² + 1 equal to 10?

28. What value of x would make the expression x³ – 3 equal to 5?

29. Use the triangle provided to provide x =

30. Write an expression that is: the difference of x and 4 is equal to 18.

31. The sum of three times x and 12 is equal to 32.

32. The surface temperature, V (in degrees Celsius), of the planet Venus is 380 degrees more than the temperature at which water boils.

In Exercises 33‑34 write a verbal phrase or sentence to represent the expression or equation.

33. 5 ‑ 2x 34. 3y ‑ 4

34. This rhyme is one of the world's oldest mathematical riddles:

As I was going to St. Ives,

I met a man with seven wives.

Each wife had seven sacks.

Each sack had seven cats.

Each cat had seven kittens,

Kittens, cats, sacks, and wives,

How many were going to St. Ives?

The number of kittens, cats, sacks, and wives is 7⁴ + 7³ + 7² + 7¹ = 2800

But what is the answer to the riddle?

Teamwork

Volume The volume of a sphere of radius r is . To two decimal places, find the volume of the sphere when given the following radii.

a. 4 b. 2 c. 6

Geometry The area of a trapezoid with parallel bases of lengths b₁ and b₂, and height h is given by

A = . (The variable b₁, is read “b sub l,” and the variable b₂, is read "b sub 2.") Find the area of a trapezoid whose height is 2 meters and whose bases are 6 meters and 10 meters.

Pit‑Stop Problem The highest average lap speed attained on a closed circuit motorcycle race is 160.3 miles per hour. The driver of the cycle was Yvon du Hamel, at Daytona international Speedway, Florida, March 1973 (Source: Guinness Book Of World Records, 1991)

Suppose you enter a closed‑circuit motorcycle race. Your goal is to cross the finish line at 10:20 A.M. At 6:20 A.M., you resume racing after making an unexpected pit stop that is 640 miles from the finish line. Do you think you can reach your goal?

a. How much time do you need to reach your goal?

b. Write a verbal model that relates the travel time you have, the distance, and the rate at which you must travel.

c. Use the labels to translate your verbal model into an equation. 4x = 640

d. Use mental math to solve the equation. x = 160

e. Do you think you will meet your goal

Key to Introduction to Elementary Algebra

1.2
½
75%
0.60
8/25
7%
a. 25%; b. 23%
a. 36; b. 128
a. $100.00; b. $100.37; c. $70.37; d. $70.95
36
$24.50
11/3
.075
36
8
1
21
7
2
626
68 in
3
10.49
59.32
47.61
3
5
62
x – 4 = 18
3x + 12 = 32
V = 100 + 380
How many were going to St. Ives? Just I