Algebra 1 Final Review
Name _______________________
Hour ________
1.
Jamie starts filling a bathtub with water (the tub starts with no water inside). The water is entering the
tub at a constant rate of 3 gallons per minute. What quantity VARIES in this situation?
2.
If Chandler High School classes have 25 students for every one teacher. Let x represent the number of
students and y represent the number of teachers. Write a formula to represent the number of teachers in
terms of the number of students.
3.
Given the following formula, determine the value of y for the given value of x.
y = 2x + 3, when x = 4.2
Use the following to answer question 4.
Suppose a tank of water has a leak such that the water is draining out of the tank at a constant rate of
10 liters per hour. The tank originally has 160 liters of water inside.
4.
Determine the formula that represents the amount of water remaining in the tank (in liters) r in
terms of the amount of time that the tank has been leaking (in hours) t.
5.
How much larger is 7 than –19?
6.
Jack and John both go for a bike ride. Jack bikes 12 miles and John bikes 5 miles. How many times
longer is Jack’s bike ride than John’s?
7. Evaluate: (-12.4) (-5.8) =
8. Monique is making cookies and her recipe calls for 2 ½ cups of flour for one batch. How much flour
will Monique need if she is making 3 batches of cookies?
9. Use the Law of Exponents to rewrite the following expression.
45 a 2b3
4ab
10. Simplify the following expression into an equivalent form.
7x - 3(2x + 5) - 2x
11.
Sally and Bob both walk to school. Sally walks 1/3 mile to get to school and Bob walks 3 miles to get to
school. How many times longer is Bob’s walk to school than Sally’s?
12.
Write an expression to represent: The product of 4, and the quantity ‘3 more than x’
−9𝑥 5
13.
Simplify:
14.
Write an equation for the graph below by making an x, y table.
18𝑥 3
Use the following to solve # 15 and 16.
The function f defines the volume of water (in gallons) in a swimming pool in terms of the number of hours since
the swimming pool started filling. The maximum amount of water the pool can hold is 12,000 gallons. If the pool
fills at a constant rate of 300 gallons each hour the function f(t) = 300 t determines the number of gallons in the
pool after t hours of filling.
15.
Evaluate f(6) and explain what the answer represents in the context of this problem.
16.
What is the range of f?
17.
Circle the graphs below that represent a function.
Use the following to answer question 18.
A water tank is full of water when the plug is pulled to begin draining it. If w is the number of gallons of water in
the tank and t is the number of minutes elapsed since the plug was pulled, then the situation is represented by
the formula f (t) = 33 – 1.5t, where f (t) represents w (number of gallons).
18. Determine the horizontal intercept and explain its meaning in the context of the problem.
19. Determine the horizontal and vertical intercept of the function f(x) = 3x - 24.
20. Given the following graph of the function f, determine the horizontal and vertical intercepts of f.
Horizontal intercept: _____________
Vertical intercept: ___________
Use the following context to answer questions #21 and 22
Suppose the graph of f below represents the expected number of people n who will compete in a race for varying
values of the temperature t in degrees Fahrenheit at the start of the race.
21. Explain what the point (60, 40) represents in the context of the problem.
22. Determine the domain and range of the function.
23. Given the sequence –3, 6, –12, 24, …determine a7.
24. Circle the following sequences that are arithmetic.
I. 3, –1, –5, –9,…
II. –1, –3, –7, –13, …
III. 8, 15, 22, 28, …
25. Given g(x) = – 3(5 x – 20), evaluate g(7).
26. Amanda is a swimmer and is training for the Olympics. While swimming, she burns 455 calories per hour. She
usually swims 40 hours each week. As the number of hours Amanda swims increases from 17 hours to 22 hours,
what is the corresponding change in calories burned?
27. Alan was riding his bike at a constant speed of 64 feet in 8 seconds. How far did Alan travel in 7 seconds?
28. Mrs. Swartz rides her bike at 16 miles per hour. How far can she travel in 6.5 hours?
29. Mrs. Swartz rides her bike at 16 miles per hour. Write a formula representing the number of miles Mrs. Swartz
rides, m, in terms of the number of hours elapsed while Mrs. Swartz rides her bike, h.
30. Mrs. Baldwin charges $45 an hour for math tutoring. Chris only has $105, how long can he get tutoring?
31. Mrs. Baldwin charges $45 an hour for math tutoring. Mrs. Baldwin is saving up for a new bike that costs $270.
How long must she work to earn the money?
32. Miss Henry is hitting volleyballs at a rate of 12 per minute. As time increases from 3 to 7 minutes, how many
volleyballs does she hit?
33. Miss Henry is hitting volleyballs at a rate of 12 volleyballs per minute. Write a delta notation equation
representing the number of volleyballs Ms. Henry hits, h, in terms of the time elapsed hitting volleyballs, m.
34. Mr. Lowe is writing test questions at a rate of 14 questions per hour. What is the number of questions written in
any 3 hour time period?
35. Mr. Lowe is writing test questions at a rate of 14 questions per hour. How long will it take Mr. Lowe to write a
35 question final exam?
36. Suppose the changes in the values of 2 variables are related according to y = 3x. What is the change in x if we
start with x=2 and end at x=7?
37. According to problem number 36, what would be the y value for x = 7, if y = 2 when x = 2?
38. Write the formula for: y changes at a constant rate of 3.2 with respect to x, and (6, 4.5) is a point on the graph.
39. Write the formula for: y changes at a constant rate of -1.8 with respect to x, and (6, 8) is a point on the graph.
40. Write a formula that represents the values below:
x
y
-2
0
3
5
-5
-9
-15
-19
41. Write a formula that represents the values below:
x
y
1
2
3
-4
5
-10
8
-19
42. Write the equation for the relationship y changes at a constant rate of -4.2 with respect to x, and (-1, 7) is point
on the line.
43. Write the equation for the relationship y changes at a constant rate of 3.6 with respect to x, and (3, -9) is point
on the line.