Equations
1. Solve and Explain the Process for solving: 3x + 8 = 44
What is x= 12
3(12) +8 = 44
36 + 8 = 44
44 = 44
2. What does it mean to be less than of equal or greater than or equal to?
What is the value can be both equal to or less than or greater than the given value.
3. Name the part of the circle that is a line that goes all the way across the circle. It has a relationship with both the radius and the circumference.
What is Diameter
4. Find the Exact Circumference of a circle whose radius is 2. Explain the process.
What is 4PI
2x2= 4= Diameter
C= dPI
C= 4PI
5. How would you determine the area of a half-circle?
What is use the 1/2PIr^2 or 1/2PIrsquared (also acceptable use area formula and divide the answer by two).
6. Solve and Explain the process for solving: 1/4(2n + 6)= 4
What is n= 5
1/4[2(5)+6)=4
1/4 [ 10+16]=4
1/4[16]=4
16/4=4
4=4
7. How do you graph inequalities that are equal to a value?
What is with a closed circle on the graph and the shaded part going in the correct direction.
8. Name the part of the circle that is 1/2 of the Diameter.
What is Radius.
9. Find the Approximate Circumference of a circle whose diameter is 2.5in. Explain the process for solving.
Approximate Circumference 2.5 (3.14) = 7.85in
10. Members of a baseball team raised $967.50 to go to a tournament. They rented a bus for $450 and budgeted $28.75 per player for meals. How many players did they take if they spent all their money? You must explain how you solved.
Equation: 28.75x +450 = 967.50
x= 18
28.75 (18) + 450 = 967.50
517.5 + 450 = 967.50
967.50 = 967.50
11. Solve and Explain the process for solving: -3= 3n -2(n +3)
What is n= 3
-3 = 3(3) -2[(3) + 3]
-3= 9 -2[6]
-3= 9- 12
-3 = -3
12. Solve and explain the process for solving: -10.2 > 3/4n +(-4.5)
n < -7.6
-10.2 > 3/4(8) -4.5
-10.2 > 6 -4.5
-10.2 > 1.5 False
-10.2 > 3/4 (-8) -4.5
-10.2 > -6 -4.5
-10.2 > -10.5 True (Satifies the inequality)
13. Name the part of the circle that is related to the Diameter by PI.
What is Circumference.
14. Determine the circumference three different ways where r= 5
Estimate quickly with π = 3
Find an approximate answer using π = 3.14
Find the exact answer
Explain the process for each.
Estimate= 30 units (3 x d)
Exact= 30PI units (d x PI)
Approximate= 94.2 units (d x 3.14)
15. For each question on a test, Nathalie receives 5 points. She also answered the extra credit questions right for an additional 6 points. If she needs to get a minimum of an 81 to keep her “B” average, write an inequality that models the number of problems she needs to get right? Solve and explain the process for solving the inequality.
Inequality Expression: 5q + 6 ≥ 81
q ≥ 15
5(15) + 6 ≥ 81
75 + 6 ≥ 81
81 ≥ 81
16. Tim's phone service charges $27.42 plus an additional $0.18 for each text message sent per month. Tim's phone bill was $31.92. Write and solve an equation to determine how many text messages he sent this month. You will need to explain how you derived the equation and solved.
Equation: 0.18x +27.42 = 31.92
X= 25
0.18(25) + 27.42 = 31.92
4.5 + 27.42 = 31.92
31.92 = 31.92
17. Harper has $15.00 to spend at the grocery store. She is going to buy bags of fruit that cost $4.75 each and one box of crackers that costs $3.50. Solve and explain the process for solving.
Inequality Expression: 4.75b + 3.50 ≤ 15.00
b ≤ 2.42
4.75 (2.42) + 3.50 ≤ 15.00
11.50 +3.50 ≤ 15.00
15.00 ≤ 15.00
can buy 2 bags of fruit
18. Name the equation for finding the circumference of a circle or one of its equivalents.
What is C= diameter x PI ....(C=dPI)
19. Find the exact and approximate area of a circle whose diameter is 12.
A= PIr^2
d= 12 --> 12/2 r=6
Exact: PI(6)^2
PI(6 x 6)
Exact answer = 36PI units ^2
Approximate: 36(3.14)
Approximate Answer = 113.04 units^2
20. The base of John’s coffee cup has a circumference of 12πcm. Exactly how much space does the base of the coffee cup take up? Solve and explain the process for solving.
A= 36PI cm ^2
Exact Circumference: dPI
d= 12 --> 12/2 r=6
A= PIr^2
A=PI(6)^2
A= 36PIcm^2
21. The perimeter of a triangular lot is 72 meters. One side is 16 meters, the other side is twice the first side. Find the third side. You must explain how you solved.
Equation: x + 48 = 72
x= 24
24 + 48 = 72
72 = 72
22. Keith has a debt of $145.50 at the beginning of the summer. He wants to have at least $200 in the account at the end of the summer. If he plans to save $75.50 each week what is the minimum number of weeks he needs to save for in order to meet his goal? Solve and explain the process for solving.
Inequality Expression: 75.50x -145.50 ≥ 200
x ≥ 4.58
75.50 (4.58) - 145.50 ≥ 200
345.79 -145.50 ≥ 200
200.29 ≥ 200
5 weeks minimum
23. Name the formula for finding the area of a circle.
What is A= PIr^2 or PIr squared
24. Ms. Menardy bought a new tablecloth for her dining room table that approximately covers the table’s 28.26 square feet. What is the distance, in feet, around the outside of the table? Solve and explain the process for solving.
C= 18.84ft
C= 2PIr
C= 2PI(3)
C=6PI
C= 6(3.14)
C= 18.84
25. The distance around Sally’s front wheel of her bike is 75.36 inches. Sally wants to attach four decorative spokes to her front wheel that go from the center of the wheel to the edge of the tire. Approximately how many inches of the decorative spokes does she need to buy to complete the project?
48in decorative spokes
C= 75.36in
C= dPI
75.36 = 3.14(d)
d= 24 --> 24/2 =12 r=12
12x4= 48