Foundations of Common Core Math Final Exam Review Name: ______
Calc. inactive:
1. The floor of a rectangular cage has a length 4 feet greater than its width, w. James will increase both dimensions of the floor by 2 feet. Write an equation that represents the new area, N, of the floor of the cage?
2. A school purchases boxes of candy bars.
· Each box contains 50 candy bars.
· Each box costs the school $30 to purchase.
How much does the school have to charge for each candy bar to make a profit of $10 per box?
3. Energy and mass are related by the formula E = mc2. Solve this equation for “m”.
4. Write an expression equivalent to(x12)4
Minutes / 25 / 50 / 75 / 100 / 125Distance Traveled
(in miles) / 20 / 40 / 60 / 80 / 100
5. The table shows the distance a car has traveled. What is the meaning of the slope of the linear model for the data?
Number of Toppings (n) / Cost (C)1 / $12
2 / $13.50
3 / $15
4 / $16.50
6. The table shows the cost of a pizza based on the number of toppings. Write a function that represents the cost of a pizza with n toppings?
X / Y1 / 6
2 / 9
3 / 12
4 / 15
7. If f(x) = 3x2 + 2x + 9, evaluate f(-2).
8. What would be an equation for the function given in the table to the right?
Calculator active:
Time (weeks) / Weight (ounces)8 / 0.04
9 / 0.07
10 / 0.14
11 / 0.25
12 / 0.49
9. The table to the right shows the average weight of a type of plankton after several weeks. What is the average rate of change in weight of the plankton from week 8 to week 12?
10. Cell phone company Y charges a $10 start-up fee plus $0.10 per minute, x. Cell phone Company Z charges $0.20 per minute, x, with no start-up fee. Write a function that represents the difference in cost between Company Y and Company Z?
11. Mario compared the slope of the function graphed to the right
To the slope of the linear function that has an x-intercept of 43 and
a y-intercept of -2. What is the slope of the function with the smaller slope?
12. What is the perimeter of the figure below?
13. What is the area of the figure shown in question #12?
14. The area of a trapezoid is found using the formula A= 12 h (b1+ b2), where A is the area, h is the height, and b1 and b2 are the lengths of the bases. What is the area of the trapezoid to the right?
Lucy’s Savings / f(x) = 10x + 5Barbara’s Savings / g(x) = 7.5x + 25
15. Lucy and Barbara began saving money the same week. The table shows the models for the amount of money Lucy and Barbara had saved after x weeks. After how many weeks will Lucy and Barbara have the same amount of money saved?
16. Multiply: (3x – 4)(6x + 7)
17. The following sequence shows the number of trees a nursery plants each year: 2, 8, 14, 20,…
Write a formula using NEXT NOW that could be used to determine the number of trees the nursery will plant next year, NEXT, if the number of trees planted this year, NOW, is known?
18. There were originally 4 trees in an orchard. Each year the owner planted the same number of trees. In the 29th year, there were 178 trees in the orchard. Write a function, t(n), that can be used to determine the number of trees in the orchard in any year, n?
19. The following sequence shows the total number of days Francisco had used his gym membership at the end of weeks 1, 2, 3, and 4: 4, 9, 14, 19,… Assuming the pattern continued, write a function that could be used to find the total number of days Francisco had used his gym membership at the end of week n?
20. Dave correctly solved the equation below using 4 steps.
Given: 5(3x + 2) – 7x = 34
Step 1: 15x + 10 – 7x = 34
Step 2: 8x + 10 = 34
Step 3: 8x = 24
Step 4: x = 3
Between which 2 steps did Dave use the Division Property of Equality?
21. A function is given by h(x) = x – 4(x – 5)2. What is the value of h(8)?
22. What is the area of a square with sides of x2y3?
23. Simplify: a + 4(6a + 2b2) + (a2 – 6b2)
24. Use the set of equations below:
(a) y = 2x2 (b) y = 4x-1 (c) y = 2(x - 3) + 6
(d) y= 8x (e) y = 0.25(4x ) (f) y = 17 + x(x + 3)
Circle all equations that represent linear functions.
0 / 2
1 / 3
2 / 4
3 / 5
25. Dennis compared the y-intercept of the graph of the function f(x) = 3x + 7 to
the y-intercept of the graph of the linear function that includes the points in
the table. What is the difference when the y-intercept of f(x) is subtracted
from the y-intercept of g(x)?
26. Suppose that the function f(x) = 2x + 12 represents the cost to rent x movies a month from an internet movie club. Makayla now has $10. How many more dollars does Makayla need to rent 5 movies next month?
27. Alex walked 3 miles in 4 hours. Sally walked 3,520 yards in 4 hours. In miles per hour, how much faster did Sally walk than Alex? (Note: 1 mile = 1,760 yards)
28. Simplify: 5(2x + 1) – (x – 4)
29. Simplify using the order of operations:
For problems 30-31, use the following equation: 2x – 5(x – 1) = -4x + 3(-x + 2)
30. solve the equation using tables, include the table as part of your answer:
31. Solve the equation by graphing,
include the graph as part of your answer:
32. Solve the equation using algebra, clearly show each step in the solution and write which properties
you used to solve the equation.
For questions 33-35: A line in a coordinate plane goes through the points (-2, -3) and (-5, -1).
33. What is the slope of the line?
34. What is the y-intercept of the line?
35. Write the equation of the line.
36. Which of the following are nonlinear? Circle all that apply.
A. y = 3x
B. y = x2 + 1
C. y = -5
D. x + y ≤ 17 E. f.
37. In 2000 Jim planted a tree that was 434 feet tall. In 2005 the tree was 1558 feet tall. Assuming the growth of the tree is linear, what was the rate of growth of the tree?
38. A new singing group, The NC Divas, has just made a CD. They recorded it themselves at a cost of $6,000. They have been offered a contract by a recording company to produce and promote it. The company is offering them $4,000 and 15 percent of total sales. What will the minimum amount of sales need to be in order for the band to recover the expense of recording the CD?
Create a table, graph, and equation for the following scenario:
Marcus is going to start saving $20 every month to buy a stereo. His parents gave him $10 for his birthday to open his savings account.
a. Equation using function notation: ______
b. What is the rate of change and explain its meaning in the context of the problem.
c. What is the x-intercept and y-intercept and explain their meaning in the context of the problem.
Vocabulary:
Domain Range Independent variable Dependent variable
Slope Constant Rate of Change Coefficient
Slope-intercept form (y = mx + b) Standard form (ax + by = c)
Slope formula m = y2- y1x2- x1 arithmetic sequence an= a1+d(n-1)
a1 = 1st term
d = common difference
n = term number
area of rectangle: A = L*W area of a square: A = s2
perimeter of a rectangle: P = 2L + 2W or P = 2(L + W) perimeter of a square: P = 4s