Name ______Date ______Period ______
· Please keep this in the homework section of your binder.
What to expect….
Thursday: In assigned groups complete the “Day 1” review problems. These problems put sections 5.2 and 5.3 together and review section 5.4. As you complete these problems, answers to select problems will be placed on the board so you can check for correctness and appropriate work. Anything not complete by the end of the period is homework and due Friday. This assignment will be counted as a homework grade.
Friday: In assigned groups complete the “Day 2” word problems. These problems apply concepts learned in 5.2 – 5.4 to real-world scenarios. As you complete these problems, answers to select problems will be placed on the board so you can check for correctness and appropriate work. Anything not complete by the end of the period is homework and due Monday. It is essential that you show ALL work and explain your answers. This assignment will be counted as a homework grade.
Wednesday: 35 point quiz on problems similar to this review.
Day 1: REVIEW PROBLEMS (Putting 5.2 & 5.3 together!)
1. Solve the following equation in two ways: First by factoring (as learned in section 5.2) and then by using square roots (as learned in section 5.3.)
X2 = 121
a. Factoring:
b. Square Roots:
2. Solve: 3x2 = 108
a. Factoring:
b. Square Roots:
3. Solve: 7-10u2 = -3993
a. Factoring:
b. Square Roots:
4. Sometimes problems are best solved using factoring and sometimes they are best solved using square roots.
a. Which method would be best to solve: –x2 – 12 = -87? Why? Solve using the method you chose.
b. Which method would be best to solve: x2 + 13x + 40? Why? Solve using the method you chose.
c. Which method would be best to solve: 12v2 – 25v – 7? Why? Solve using the method you chose.
5. By solving for x we are finding the places the graph would cross the x-axis. Solve the following and give the coordinates where the graph would cross the x-axis.
x2 + 3x – 18 = 0
6. What does i equal? ______
7. What does i2 equal? ______
8. Solve or simplify the following: (5.4 Review)
a. x2 = -9
b. 2x2 + 9 = -41
c. (6 + 2i) + (5 – i)
d. –i + (8 – 2i) – (5 – 9i)
e. 4i(3 – i)
f. -7+6i9-4i
g. 6-i23+i3
Day 2: WORD PROBLEMS
1. You have just planted a rectangular flowerbed of red roses in a park near your home. The length of the flowerbed is 12 feet and the width is 8 feet. You want to plant a border of yellow roses around the flowerbed. Since you bought the same number of red and yellow roses, the areas of the border and inner flowerbed will be equal. What should the width (thickness), x, of the border be? (Hint: Think of the border like a frame around a picture.)
a. Draw and label a diagram.
b. What are you trying to find?
c. Set up an equation.
d. Solve the equation.
e. Answer the questions by writing a sentence.
2. Many birds drop shellfish onto rocks to break the shell and get to the food inside. Crows along the west coast of Canada use this technique to eat whelks (a type of small sea snail.) Suppose a crow drops a whelk from a height of 20 feet. The equation, h = -16t2 + 20, can be used to determine the height of a whelk at a given time.
a. Use the equation to find the height of the whelk after:
i. 0 seconds
ii. 0.5 seconds
iii. 1 second
b. Use the equation to determine the time the whelk is:
i. 5 feet high
ii. 2.34 feet high
iii. 0.2 feet high
3. Use the falling object equation: h = -16t2 + s, where t is measured in seconds and h is measured in feet to find the time required for an object to reach the ground from a height of s = 100 feet and s = 200 feet. Does an object that is dropped from twice as high take twice as long to reach the ground?
4. The path of a large stone fired from a catapult can be modeled by y = -0.00545x2 + 1.145x, where x is the distance the stone traveled (in yards) and y is the height of the stone (in yards.) Find the distance the stone has traveled when it is 2 yards high.