Winter Break Project
Name:______Date:______Per:______
Directions: You are to solve all of the following questions on a separate sheet of paper. Make sure to SHOW ALL WORK!!!!!!!!!!!!!
1. Solve for v in this equation:
2. Simplify each expression.
a.9x + 6 – 4x – 2x + 1 – 15
b.(6x2 – 2x + 5) + (2x2 – 7x – 11)
c7x2 – 5 – 2x – 3 + 5
3. Solve for x.
4. Write the equation represented below on your paper. Simplify as much as possible then solve for x. Be sure to record all your steps.
5. Explain the steps required to solve the equation shown on the equation mat at right. Solve the equation and be sure to show all of your steps.
6. Juan is buying soda for a class party. He can go to the vending machine and buys 12-oz cans for $0.60 each, to the corner store and get 20-oz bottles for $0.95, or to the grocery store and get 32-oz jugs for $1.55. Which is the best deal? Be sure to organize, label, and justify your work.
7. MacKensie solved the following equation showing all of her steps. Estefan, a member of her group, thinks that there is an error. Who is correct? Explain how you know. If Estefan is correct, then explain MacKensie’s mistake and make changes to solve the problem correctly.
2(y + 1) – 2 = 4 + 2y – y
2y + 2 – 2 = 4 + y
2y = 4 + y
2y – y = 4 + y – y
8. The graph of the equation is shown at right. Is the point (101, 294) on this line? How do you know? Justify your answer completely.
9. Each side of the figure is either horizontal or vertical. Calculate the area and the perimeter. Show any rectangles you see and use in your solution.
10. Simplify the expression comparison mats shown below to determine which is greater. Record each move and the simplified expression that remains after the move. Be sure to give an explanation for each move.
AB
Left expression / Right expression / Explanation11. A scale on a map of Bellingham, Washington is as follows: 1 centimeter on the map represents 5 kilometers in real life. This scale, which can also be written as 1cm:5km, is shown as a pattern in the table below.
a.Write an algebraic rule for kilometers using x and y.
b.State what x and y represent in your rule.
c.Use your rule to find out the real-life distance for 25 cm on the map.
d.135 km would be how many cm on the map? Show how to use your rule to find the answer.
12.12. Find the mistake in the solution below and explain how to correct it. Find the correct answer.
13. Consider the equation mat at right.
a.Write the equation algebraically.
b.Solve the equation for x. Show all your steps.
c.Check that your solution is correct. Be sure to show how you check your solution.
14. Solve each equation below.
a.b.c.d.
15. Complete the empty spaces in the Diamond problem at right. Show any work!
16. Josea has a tomato plant that comes back every summer, growing bigger and stronger than the year before. She has had the plant for five years, but it has only been during the last three years that she has kept track of the number of tomatoes she has picked off of her tomato plant that season. This information is recorded in the table below:
Number of years Josea has had the plant / 3 / 4 / 5Number of tomatoes she had picked that year / 38 / 50 / 62
a.Assuming the tomato plant continues to produce tomatoes at its current rate, write a rule for the number of tomatoes produced, using x and y.
b.In your rule, what real-world quantity does x stand for? What real-world quantity does y stand for?
c. How many tomatoes will Josea be picking after she has had the plant for 15 years?
d.Assuming Josea’s plant lives and continues at its present rate, will it ever produce 300 tomatoes in a summer? Explain how you know. Be clear and complete.
17.Burt’s teacher asked him to write the different representations for his tile pattern. All four are shown below.
Rule:
Figure Number / 0 / 1 / 2 / 3Number of Tiles / 2 / 4 / 8 / 12
How did Burt do? Are all his representations correct? If so, justify why they are correct. If not, what did he do incorrectly, and how can it be corrected? Be clear and complete.