Download Algebra I CORE 40

Algebra I Year End Review Packet
Name: __________________________
Due Dates: Part A is due: _______
Part B is due: _______
Part C is due: _______
Part D is due: _______
Part E is due: _______
Show all work for credit.
Part A
1. Solve for b: 8b – 9 = 5b – 12
2. Solve for p: 4(p – 9) + 3 = -29.
3. Solve for x. 3x – 5 = 3(x – 5) – 5(6 – 4x)
[A] ½
[B] 0
[C] 2
[D] -5
4. Zoe tried to solve the equation below. She made an error. Her work is shown below.
2(1 + 3x) – 10x = 14
2 + 6x – 10x = 14
2 – 4x = 14
-4x = 16
x = -4
Describe the error made by Zoe.
Answer____________________________
__________________________________
__________________________________
__________________________________
Solve 2(1 + 3x) – 10x = 14 for x.
Answer____________________
5. Solve for x: 11 – 6x = y
6. Solve for e: 15f 
e
3
6
7. The formula for the kinetic energy of an object is E 
[A] m 
Ev 2
2
[B] m 
1
mv 2 . Solve for m.
2
2E
v2
[C] m 
2v 2
E
[D] m 
v2
2E
8. You are driving to visit a friend in another state who lives 440 miles away. You are driving 55 miles per hour and
have already driven 275 miles. Write and solve an equation to find how much longer in hours you must drive to
reach your destination.
9. Solve for y: 7x – 14y = -28
10. Jamiyl has $33.75. He pays $9.25 to get into a movie. He can buy boxes of candy for $4.25 each.
Write a linear equation to find the maximum number of boxes of candy that he can purchase.
Answer____________________
Find the maximum number of boxes of candy that Jamiyl can purchase.
Answer____________________
PART B
1. Thomas solved the equation below. Explain the mistake that Thomas made when solving the equation and then
solve the equation
3 – 2(x – 5) = 21
3 – 2x – 10 = 21
-2x – 7 = 21
-2x = 28
x = -14
2. Solve -3 < 2x – 1< 5.
3. Solve for x: 14 – 5x = y
[A] x 
4. Solve for e:
y
9
[B] x  
1
7
 4e  .
2
2
6. Solve -2x + 7 < 37.
14 y

5 5
[C] x  9y  14
5. Solve for x:
y
5
[D] x   
14
5
x5 7
 .
x 1 4
7. Solve the equation for z:
8. The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46
centimeters, find the dimensions of the rectangle.
a. length = 5 cm; width = 18 cm
c.
length = 18 cm; width = 5 cm
b. length = 13 cm; width = 5 cm
d.
length = 13 cm; width = 8 cm
9. Danny goes for a bike ride on the weekend. The graph below shows his speed over time during his warm-up.
A
A
How many seconds after Danny started riding does his speed first begin to decrease?
Answer____________________
Describe Danny’s speed at point A.
Answer____________________
10. Below is the graph of a student walking from his house to the gas station and back. Which statement is true
about the student from t = 6 to t = 10?
PART C
1. Graph x  4y  8
2. What is the slope of the given line?
3. Write a linear equation that has the slope of -2 through (1, -4).
4. Write a linear equation in standard of a line that has the slope of 
5. What is the x-intercept of the graph of the line 4x + 6y = -12?
[A] (3,0)
[B] (0,3)
[C] (2,0)
[D] (0,2)
4
and a y –intercept of 2.
3
6. Graph y 
3
x  5.
2
7. Consider the statement: “All linear equations have a graph with one x-intercept.”
Which equation below shows that this statement is false?
[A] y = 3x + 2
[B] y = -1
[C] y = -½x – 8
[D] x = 4
8. TJ shovels driveways in the winter. He charges a base rate of $10 plus $7 per hour.
Write a linear equation that represents the cost, C, charged to a customer for h
hours.
Answer____________________
9. Write the equation of a line that passes through (0, 5) and (2, 3).
10. Write the equation of a line that has an x-intercept of -4 and a y-intercept of 3.
PART D
1.
The graph below shows the average professional baseball salary from 1989 through 1998.
Based on the graph, between which two years did the average salary have a negative rate of
change?
a.)1989 to 1990
2.
b.)1992 to 1993
c.)1993 to 1994
d.)1994 to 1995
The height of a triangle is x + 9 and the area is 48. Write an expression for the length of
the base of the triangle.
[A] l 
48
x9
[B] l 
48
2 ( x  9)
[C] l 
2(48)
x9
[D] l 
x9
48
3. What is the x-intercept of the graph of the line 4x - 6y = 12?
[A] (3,0)
4.
[B] (0,3)
[C] (2,0)
[D] (0,2)
Solve -5x + 4 < -3x + 12
[A] x < -4
[B] x > -4
[C] x < 2
[D] x > 2
5.
Solve the proportion:
[A] x = -17
6.
x3 2

2x  1 5
[B] x = 13
[C] x = 17
D] x = -13
Write the equation of the graph.
[A] y 
5
x4
4
5
[B] y   x  5
4
[C] y 
4
x5
5
[D] y 
4
x4
5
7.
You are driving to visit a friend in another state who lives 440 miles away. You are
driving 55 miles per hour and have already driven 275 miles. Write and solve an equation
to find how much longer in hours you must drive to reach your destination.
a.
;
c.
;
b.
;
d.
;
8.
Below is a graph of the temperature of a liquid over time (in minutes).
During what interval does the liquid remain constant in temperature?
[A] A to B
[B] B to C
[C] C to D
[D] both [A] and [C]
9.
Graph -2y = 6x
10. What is the domain and range of the relation shown in the table below?
x
y
-7
-5
-3
4
-2
4
-1
-2
Domain__________________
Range ___________________
Is the relation in the table above a function?
Answer __________________
PART E
1. Alice can buy 3 shorts and 9 t-shirts for $75.00. Justin can buy 6 shorts and 10 t-shirts for
$130.00. Assume that all shorts are the same price and all t-shirts are the same price.
Write a system of linear equations that can be used to find the cost of 1 pair of shorts (s)
and 1
t- shirt (t).
Answer____________________
What is the cost, in dollars, of one t-shirt?
Answer____________________
2. Solve for x.
4
2

x7 x5
3. What is the x-value of the solution to the system?
2 x  7 y  13

9 x  7 y  1
4. Solve 7x + 12 < -2x – 6
-2)}?
5. What is the domain of {(-1, 3), (-4, 4), (3, -5), (2,
6. Given the graph, find the rate of change and its meaning for the situation.
a. The balloon rises 15 ft every second.
b. The balloon rises 2000 ft every second.
2
ft every second.
3
d. The balloon rises 30 ft every second.
c. The balloon rises 66
7. Find the slope, the x-intercept and y-intercept of the equation 7x – 4y = 28.
slope = __________
x-int = ___________
y-int = ___________
8. Sara and Helen have each been selling boxes of cookies for 5 days. The number of boxes that
Sara sold (s) and the number of boxes that Helen sold (h) is shown in the table below.
Monday
Tuesday
Wednesday
Thursday
Friday
Sara (s)
1
2
4
6
7
Helen (h)
4
7
13
19
22
Write an equation that models the relationship between the number of boxes that Sara
sold (s) and the number of boxes that Helen sold (h).
Answer____________________
9. Solve for b: -8b – 9 = -5b + 12
[A] b = -1
[B] b = 1
[C] b = 7
[D] b = -7
10. Jem is older than Pearl. The difference between their ages is 6 years. The sum of their ages
is 44. How old is Jem?