Pre-Calculus

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Directions: Solve the problems below...

Directions: Solve the problems below. Make sure to show your work when applicable.

1. Simplify the expression.

+ (32 – 42)

2. Simplify the expression.

√625

3. Evaluate the expression for a = –1 and b = 5.

5a – 7

4. Evaluate the expression for a = –1 and b = 5.

(ab)2

5. Simplify the expression.

9xy2 – 11xy2

6. Simplify the expression.

-3(b – 7)

7. Solve the equation. Check your answer.

m/20 = 5/4

8. Solve the equation. Check your answer.

4y + 5 = – 31

9. Solve the equation. Check your answer.

3x – 7 = 5x + 19

10. A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s average speed in miles per hour?

11. Write a compound inequality that the graph could represent.

12. Find the solutions of the inequality.

b – 3 > –1

13. Find the solutions of the inequality.

| x - 5 | ≥ 3

14. A taco stand sells tacos for $3.25 each. The stand’s expenses for the day are $210. Write an inequality to represent the amount of tacos they need to sell per day to make a profit, and then solve the inequality.

15. Represent the above relationship between the number of triangles and the perimeter of the figures they form by filling in the table below.

Number of Triangles Perimeter

1

2

3

16. Write the equation that represents the relationship between n the number of triangles and p the perimeter of the figures formed.

17. Model the function rule y = -2x - 3 with a table of values.

18. For the function rule y = -2x - 3, provide the x-y coordinates of the y-intercept and the x-intercept.

19. Identify the domain and range of the relation.

{(-9, 2), (-4, 2), (3, 2), (9, 2)}

20. The function g(t) = 2t represents the number of guitar lessons, g(t), you can complete in t months. How many guitar lessons can you complete in 7 months?

21. The scatter plot below shows the height of a tree over time. What is the approximate height of the tree after 10 years?

22. Write an equation of a line whose graph is parallel to the graph of y = 3x – 10.

23. Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Find the number of months after which they will have the same number of CDs.

24. Determine the solution of the system.

y = x + 6

y = 2x

25. A farmer plans to create a rectangular garden that he will enclose with chicken wire. The garden can be no more than 30 ft wide. The farmer would like to use at most 180 ft. of chicken wire. Write a system of linear inequalities that models this situation.

1. Simplify the expression.

+ (32 – 42)

2. Simplify the expression.

√625

3. Evaluate the expression for a = –1 and b = 5.

5a – 7

4. Evaluate the expression for a = –1 and b = 5.

(ab)2

5. Simplify the expression.

9xy2 – 11xy2

6. Simplify the expression.

-3(b – 7)

7. Solve the equation. Check your answer.

m/20 = 5/4

8. Solve the equation. Check your answer.

4y + 5 = – 31

9. Solve the equation. Check your answer.

3x – 7 = 5x + 19

10. A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s average speed in miles per hour?

11. Write a compound inequality that the graph could represent.

12. Find the solutions of the inequality.

b – 3 > –1

13. Find the solutions of the inequality.

| x - 5 | ≥ 3

14. A taco stand sells tacos for $3.25 each. The stand’s expenses for the day are $210. Write an inequality to represent the amount of tacos they need to sell per day to make a profit, and then solve the inequality.

15. Represent the above relationship between the number of triangles and the perimeter of the figures they form by filling in the table below.

Number of Triangles Perimeter

1

2

3

16. Write the equation that represents the relationship between n the number of triangles and p the perimeter of the figures formed.

17. Model the function rule y = -2x - 3 with a table of values.

18. For the function rule y = -2x - 3, provide the x-y coordinates of the y-intercept and the x-intercept.

19. Identify the domain and range of the relation.

{(-9, 2), (-4, 2), (3, 2), (9, 2)}

20. The function g(t) = 2t represents the number of guitar lessons, g(t), you can complete in t months. How many guitar lessons can you complete in 7 months?

21. The scatter plot below shows the height of a tree over time. What is the approximate height of the tree after 10 years?

22. Write an equation of a line whose graph is parallel to the graph of y = 3x – 10.

23. Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Find the number of months after which they will have the same number of CDs.

24. Determine the solution of the system.

y = x + 6

y = 2x

25. A farmer plans to create a rectangular garden that he will enclose with chicken wire. The garden can be no more than 30 ft wide. The farmer would like to use at most 180 ft. of chicken wire. Write a system of linear inequalities that models this situation.

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