Summer Assignment Preparation for Algebra 2 H
Section 1
Evaluate the expression for the given value of the variable.
2. 7+x when x= -3
4. 3s2 when s = 7
5. 2x3 when x=4
7. x4 –7 when x=3
8. (x+2)2 when x=5
Evaluate the expression
10. 36 – 8 ÷ 4
11. 62÷9+3
12. 18+27÷9-6
14. 5  8  8  4
9  62
15.
4  72  1
13. 4  7 24  6

r
when r= -42
6
6. 3x5 when x= -2
1. 12 a when a=7
3.

9. (r-s)2 when r=3 and s=7
Check to see whether the given value of the variable is a solution or not.

 18. 5a≤15; a=3
16. y+11<23; y=12
17. 5n≥28; n=6
19. 3+x≥11; x=7
20. 36÷r<3; r=14
21. d-6> 3; d=9
Write the sentence as an equation or an inequality.
22. The product of a number and 6 is less than or equal to 48
23. 14 is the difference of 30 and a number.
24. Jon is a great bowler and you are a beginner. In the first game Jon’s score is 172. This is twice your score.
Write an algebra sentence to represent these facts.
For each of the following functions make an input output table using the inputs –2, -1, 0, 1, 2.
25. y=6-3x
26. y=4x+3
27. y=2(x-4)
28. y=x2+x+3
29. y=2(x-1)2+4
30. y=3x2-4x-1
Section 2


Write each pair of numbers on a number line and then write 2 different inequalities that compare the
numbers.
1. –4, 6
2. -8, -5
3. 0, -4
Evaluate the expression
2
4. 4
5.  6
6. 
3
Do the indicated operation
3 2
7. –6-4
8. 4.1-6.3
9.  

5 3

10. 6-(-4)
11. –5-(-11.2)-3
12. 3-6-(-14)
13. -4(-9)
14. 6(-14)
16. –43
17. (-7)2
18. –(-2)5
19. 18  6
20. 48  4
21.

15. 5(-8)4
21
1

4

22. Suppose an airplane is climbing
at a rate of 30 feet per second. Write an algebra expression for the altitude
of the airplane after one minute.

Use the distributive property to rewrite the expression without parentheses
23. 4(x=3)
24. 3(r-5)
25. (4x+2)3
26. –2(s-6)
27. –(3+r)
28. (c+4)(-5)
Simplify the expression by combining like terms if possible.
29. 3x+7x
30. 4f-f2
32. r+3r+6r-5
33. 4+5r-3-2r
35. 5(x-4)-2x+1
36. 6(3x+1)-(x-3)
31. 5+3b-2
34. t2+4t-3t2-t
37. 4(3x-7)-2(6-4x)
Section 3
Solve the equation
1. 5+a=-14
2. s-2=-6
3. –6=d-(-2)
4. –12a=-480
5. –6b=426
b
6.   16
7
d 4

3 7
8. 4x-7=17
9. 5c+3c-4=22
7.

1
(x 1)  3
4
10. 5x-2(x+3)=-3
11.
13. –4+6x=9x-2
14. 7d+2=32-5d

16. 4(x+2)=3(x+7)

17. 5(z-3)+4=3(z+2)
12.
3
g  2  7
4
15. 3x+10 = 5x-4x-16

18.
1
4a  12  2  3(6  a)
2
For the following equations round your solution to the nearest tenth.
19. –24x-47=233
20. 14.25f-16.5=8.75f

21. 3.2-3.6g=9.4g+8.2
For the following problems use the distance formula d=rt
22. Solve the formula for r
23. You drive 420 miles to LA in 7 hours. Use the formula to find your average speed.
Find the unit rate.
24. 52 ounces in 6 cartons of milk.
25. Earn $48.50 in 5 hours
Solve the percent problem
26. How much money is 30% of $420
27. 86 is what percent of 250?
Section 4
Plot and label the ordered pairs in the coordinate plane.
1. A(3,7); B(-2,6); C(4,-3)
2. A(-2,-4); B(6,-8); C(5,8)
3. A(7,-2); B(-3,-5); C(-8,0)
Make a T table for each equation and plot the graph
4. y=4x-2
5. y=6-3x
6. 3x+4y=6
Graph the equations without making a T table
7. y= -2
9. y 
8. x=7
2
3
Find the x intercept and y intercept of each line
10. 4x-y=-8
11. 6x+2y=18
12. y=8-2x
Find the slope of the line that passes through the two points 
13. (7,1) and (-3,1)
14. (1,1) and (-2,3)
15. (-5, 1) and (-4,-6)
In problems 16-18 x and y vary directly. Use the given values to write the equation
16. x=5 and y=15
17. x=8 and y=-3
18. x=7 and y=2
Write the equation in slope intercept form. Then graph the equation
19. x-y=2
20. -3x+2y=6
21. 4x-2y+3=12-3x
Determine whether each relation is a function or not. If it is a function, give the domain and range.
x
y
x
y
1
1
x
y
4
-2
3
2
0
3
0
0
5
3
1
3
4
2
7
3
2
4
2
4
3
5
3
Determine whether each graph represents a function
5
Section 5
Write the slope intercept form of the equation
1. slope=3 y intercept =2
2. slope =-4 y intercept= -3
3. slope= 
1
y intercept =0
3
Write a point slope equation for a line that passes through the given point with the given slope
2
4. (-2,0) slope=4
5. (4,-3) slope = -5
6. (-7,2) slope = 

3
Write a slope intercept equation for a line that passes through the given points.
7. (3,-2) (5,4)
8. (-2,1) (4,-4)
9. (5,2) (1,4)

Write a standard form equation of the line that passes through the given point with the given slope.
2
10. (4,-3) slope=5
11. (-2,7) slope = 
12. (4,5) slope=-5
3
Determine whether the lines are perpendicular or parallel or neither.
13. y=x-3; y=-x+7
14. y=2x+1
 2y-4x=5
16. y+4x=3; y=4x+3
1
17. y= x-2
3
y=6-3x
1
1
15. y= x+2; y= - x+6
4
4
3
18. 3y=-2x+10 y= x-7
2
 to the given
 line and passing through
Write in slope intercept form the equation of the line perpendicular
the given point.


2
19. (2,3) y=3x-7
20. (-2,4) y= x-3
21. (-5,7) y=3
3
For the following sets of points and lines determine if the point lies on the line.
22. Y=2(x+3)-1 (4,13)
23. Y= 18-3(x-2) (-2,18)
24. 7x-3y= 8
(2,-2)

Section 6


Solve the inequality and then graph the solution.
1. x  2  3
2. d  6  5
3. 2  y  7
4. 6  r  4
p
3
5. 9x  45
6. 4c  12
7.
8.  s  4
2
8
4
9. 2a+4>3 
10. –4y-7<5
11. 2x  6  3x
12.
–(x+3)<5x-10

2


 inequality for each statement and then graph it.
Write an algebra

13, F is greater then –3 and less than
7

14. x is greater than or equal to 5 and less than 10
15. x is less than or equal to 4 and greater than –2
16. x is less the 5 and greater than or equal to 0
Solve the inequality and graph the solution
17. 2  z  3  9
18. 4  3x  7 15


Solve the equation
20. w 16
21.
y  3

22.

4 x 12
Graph the inequality in the coordinate plane
24. y> -2
25. x  y  3
 5x-2y>9
27. 3y-4x<12
28.
Solve the inequality
30. x  5
31. 5  x 
7

19. 0  6  5n 10
23. 2x  4  6


33. 2x  7 12  2
32. 9  4 x 12

26. x  y  5
29. 2y-x<8

Section 7
Graph the system to find a solution
x  2

1. 

 y  3x  7
 x  y  10 
2. 

 x  y  2
3.
 2 x  4 y  12
5 x  2 y  10
Use the substitution method to solve the linear system
 y  2 x 
4. 

 x  y  10
2a  3b  6
5.
a  6b  6
5 x  8 y  17
6. 

3x  y  5

5r  s  4 
7. 

7r  5s  11
Use linear combination to solve each system. Then check your answer.
3x  3 y  6 
8. 

2 x  3 y  4
2 x  8 y  9
9. 

x  y  0 
2 x  3 y  15
10. 

3 y  5 x  12 
 4 x  15  5 y 
11. 

2 y  11  5 x 
Choose a method to solve each system. Justify your choice and solve the system.
 x  2 y  10
 y  2 x  6
2 x  y  8
 4 x  3 y  1 
12. 
13. 
14. 
15. 




3x  y  5 
 y  4

6 x  y  2
 8 x  4 y  4
16. You sell 20 tickets to admission for your school play and collect a total of $104. Admission prices are $6
for adults and $4 for students. How many of each type of ticket did you sell?
Use the graphing method to determine how many solutions each system has.
x  y  4 
17. 

2 x  3 y  9
x  y  6 
18. 

3x  3 y  9
2 x  3  3 y 
19. 

6 x  9 y  9
3x  8 y  4 
20. 

6 x  42  16 y 
Graph the system of linear inequalities
 y  x  1
21. 

 y  x  3
 y  2  x 
22. 

2 y  4  3x 
y  x  4 
23. 

 y   x  1
3x  1  5 


24.  x  y  10 
 5 x  2  12


Section 8
Simplify the expression
1. 6364
5. (c4)3
2. (34)3
6. (5r)3r
3. (13a)2
7. (8v2)33v2
4. (-4xy)3
8. (2x)4(-3y)4
Rewrite the expression with positive exponents.
9. s-3
13.
10. 3y-2
3a
b 2
14.
2
x 4
3
16.
6 x 2
11. a-4b-3
4 y 4
x 2
12.
15. (3x-3)3
Graph the exponential function
17. y=3
x
1
19. y   
4
x
18. y=-2
x
1
20. y  3 
2
x
Simplify the quotient
211
21. 6
2
25.
 32
 33
3
23.  
4
1
22. x 3
x
7
4
27.  
7
r5
26. 7
r
3
 y
24.  
3
1
2
28.  
 x
2
4
Simplify the expression. Use only positive exponents.
6a 1b 3  3a 
33.
 
a 4 b 2  ab 
Write the number in decimal form
3a 2 b 2b 2
32.

2a a 2 b
35. 4.567  10 3
 4a 3 b 2
31. 
 5ab
24a 3b 5 a 3 s 2

30.
 3ab 2  4
3x 5 y 3 4 x 2 y 3
29.

xy
2x
36. 5.678  10 4
3



4
b 
b 
3 2
34.
37. 7.43  10 0
5 3
38. 2.345  10 6
Write the number in scientific notation
39. 393,356,000
40.
0.000000000567
41. 3457.671
42. 35.679
You deposit $1,200 in the bank at 6% interest compounded annually. Find the balance in your account at the
end of the given time period.
43. 1 year
44. 10 years
45. 25 years
46. A piece of machinery costs $240,000. It’s value decreases at a rate of 12% per year. Write a model to
represent the value of the machinery after n years.
Section 9
Evaluate the expression. Give the exact value if possible; if not round to the nearest hundredth.
1. 16
2. 625
3. 220
4.  100 5.  676 2+2
Solve the equation or write no solution Write the solutions as integers if possible otherwise write them as
radical expressions.
6. x2=36
7. 3x2-9=0
Simplify the radical expression.
8. 6x2+6=4
9. x2-4=-3
7
9
1
13. 2
14.
27
25
2
3
Sketch the graph of the function and label the coordinates of the vertex.
10.
88
11.
750
12.
15. y=2x2
16. y=x2-4
17. y= -x2-3x
18. y=x2-2x+3
Solve the equation algebraically. Check your solution by graphing.
20. x2-2x=-5x
21. x2+7x=-12
22. x2+3x=10
23. -2x2+4x+6=0
Write the quadratic equation in standard form, then solve using the quadratic formula.
24. x2-12=4x
25. 3x2+11x=4
26. –x2-5x=6
27. -2x2+4x=6
Determine whether the equation has two solutions one solution, or no solutions.
28. 3x2+14x-5=0 29. 4x2+12x+9=0
Sketch the graph of the inequality.
32. y>3x2
33. y< -x2+2
30. 5x2+125=0
34. y  5x2+10x
31. -3x2+5x-6=0
35y  -x2+3x+5
19. y=-3x2+12x-1
Section 10
Do the arithmetic
1. (5x2-3)+(x2+7)
2. (4x2-2)-(3x-8xx )
3. (9xx-2x+6)+(4xx-5x+2)
4. (-a2+4a)+(-2a2-3a-5)
5. (4x2-5x+3)-(3x2-4x)
6. (4r+2r3-3)-(r2+2r3+6r)
7. x(3x2-6x+2)
8. –4x(3x2-5x+3)
9. 3a3(2a2-4a+1)
10. (2a+3)(a+4)
11. (y+2)(y2-3y+4)
12. (2+4r-r2)(r-2)
Find the product
13. (z+4)2
14. .(3a-5)(2a+7)
15. (6r-3s)(6r+3s)
16. (3d+7)2
17. (-s-r)2
18. (4f-7g)2
Find the product
Solve the equation
20. (x+5)2=0
19. (x+3)(x-6)=0
21. x(x+3)=0
22. (4x-3)(2x+2)=0
Find the x intercepts and the vertex of the function, and then sketch the graph
23. y=(x-8)(x+6)
24. y=(x-3)(x+3)
25. y=(-x+3)(x-7)
26. y= -(x+1)(x-4)
Solve the equation by factoring
27. x2+4x+4=0
28. x2-12x=-36
29. –x2-4x=3
30. –x2+14x=48
33. 3x2-5=-14x
34. 12x2+46x-36=0
Solve the equation by factoring
31. 2x2+x-6=0
32. 9x2+24x=-16
Factor the expression
35. x2-9
36. 4x2-36
37.
144-x2
38. 64y2+48y+9
Factor the expression completely
39. x4-9x2
40. a4+4a3-45a2
41. x3-x2+4x+4
42. 8s3-3s2+16s-6
Section 11
Solve the equation and check your solution
9 15
x 16
1.
2.


x 5
2 x
12 5  t
x2  9 x  3
4.
5.


x3
2
8 t3


6 x2

10
12
z  15
9
6.

16
z 10
3.


The variables a and b vary directly. Use the given values for a and b to write an equation relating a and
b.
 b=10
7. a=3; b=15
8. a=5;
9. a=20; b=5  10. a=24; b=8
The variables a and b vary inversely. Use the given values for a and b to write an equation relating a and
b.
1
11. a=2; b=5
12. a=8; b=1
13. a=8; b=
14. a=4.7; b=6
4
Simplify the expression. If already simplified write simplest form.
x5
16x 5
6x 2 18x 3
15.
16.
17. 2

x  7x  10
42x
12x


18.
x 2  6x  8
x4

19.
5a
a 2  25
Write the product in simplest form
4 x 15
x 2  5x  6 x
21.
22.



x2  x
x3
3 24 x


20.
x 2  9x  18
x 2  4 x 12
23.
6x 2
 x  4 
x 2 16
26.
x 2  5x  36
 x 2 16
x 2  81
29.
6 3

x2 x
32.
4 x 1
3x

3x  2 x  4
35.
5
4
1 2
x 1
x  3x  4
Write the quotient in simplest form.

24.
1 4x

6x 10

25.
5x
x

2
x  6x  9 x  3
28.
x
3x  2

x 1 x 1
31.
5x  3
5

2
x  25 x  5

Simplify the expression

27.
3x
4 x 1

2x  1 2x  1
30.
8 x2

3x 9x 2





Solve the equation and check your solution


33.
1
5

x3 x9


34.
2 4  x

3x
6


Section 12
Find the domain of the function. Sketch the graph and find the range.
1. y  5 x
2. y  5x  2
3. y  x  2
4. y  x  8
Simplify the expression
5. 8 7  15 7
20  45  80
6.
7.
4
8.
24
3
5 2
Solve the equation and check for extraneous solutions
9.
x 7  0
2x  1  4  7
10.
11. 4 x  5  21
12. x  4 x  3
Evaluate the expression
2
2
3
13. 5  5
7
3
 1 3
14.  64 2 


 1
15. 12 4 


8
16. 4 2  5 2 2
1
Simplify the variable expression
1
3
17. x  x
1
2
 
18. a
1
4 8
 1
19.  xy 3 


3
6
y
1 4


20.  x 2 x 3 


Solve the quadratic equation by completing the square
21. x2+10x=56
22. x2+6x+8=0
23. x2-12x=13
24. x2-10x-39=0
Find the distance between the two points. Round to the nearest hundredth if necessary.
25. (7,-6) and (-1,-6)
26. (12,11) and (9,15)
27. (12, -7) and (-4,29)
28. (5,8) and (0,-3)
Find the midpoint of the line segment connecting the two points.
29. (4,0) and (4,5)
30. (1,0) and (4,-4)
31. (6,2) and (4,10)
32. (4,-6) and (-8,3)
Section 13
1. Ima thief robs a bank and takes off in a get away car. Five minutes Polly Srule takes off after Ima.
Assign x and y to the variables in this situation and write an expression for the number of minutes Polly
has been driving.
a. How long has Polly been driving when Ima has been driving for 17 minutes?
b. How long has Ima been driving when Polly has been driving 29 minutes?
2. On the level ground a car can go a top speed of 132 kilometers per hour.(kph). For each degree of uphill
slope the car’s top speed is decreased by 11 kph.
a. Write an expression for the car’s top speed when the slope of the hill is x degrees.
b. How would you represent a downhill slope? What would be the car’s top speed on a 3 degree
downhill slope?
c. How steep would the hill be if the car’s top speed was 187 kph?
3. A missile tracking station in the Pacific ocean detects a missle coming toward it at 300 kilometers per
minute from a test site in the continental United States.
a. Let t be the number of minutes since the missile was detected. At t=0 the missile was 2800 kilometers
from the tracking station. Write an expression for the missile’s distance from the tracking station at
time t.
b. Where is the missile 7 minutes after it was detected? 5 minutes before it was detected?
c. At 7 minutes after detection the tracking station fires an interceptor directly toward the oncoming
missile. The interceptor travels at 431 kpm. Write an expression for the inteceptor’s distance from the
tracking station.
d. Write an equation that is true at the time the interceptor meets the missile. At what time do they meet?
How far are they from the tracking station?
4. If an object is thrown into the air with an initial upward velocity of r, then its distance above its starting
height at t seconds after it was thrown is approximately d=rt-5rt2 meters. Homer Un, the famous
baseball player hit a a fly ball to the infield with an initial upward velocity of 30 meters per second.
a. What is its height after 2 seconds?
b. When is it 25 meters above where it was hit (Homer’s bat is about 4 feet off the ground).
c. When does the ball hit the ground?
d. When is the ball at its highest point?
5. You are in a diving competition on the 3 meter spring board. You hit the water (3 meters below the
board) 1.6 seconds after you leave the board.
a. What was your initial upward velocity?
b. When do you pass the board again on the way down?
c. How high above the board did you go?
d. If another diver steps off the 10 meter platform at the same time as you jup for your dive, who hits the
water first? How much sooner?
6. Jon can paint the backyard fence in 14 hours. Tom can paint the same fence in 12 hours. Mrs. Smith
would require 18 hours to paint the same fence. If all three work together how long will it take the three
of them to paint the fence?
7. Old silver coins contain 90% silver. Silver solder contains 63% silver. If you wanted to make 200 grams
of an alloy (silver mixture) which was 82% silver, how many grams of silver coins and how many grams
of solder would you need?
8. Ace Flyer flies his plane from Tampa to Orlando, a distance of 80 miles flying against a head wind and the
trip takes32 minutes. Later he returns to Tampa with the wind and the trip back takes 20 minutes. How fast
does he fly through the air? How fast is the wind blowing?
9. A normal calculator can handle numbers as big as 9.99 x 1099. To see how big this number is, answer the
following questions.
a. The volume of the earth is 2.59 x 1011 cubic miles. One cubic mile is 52803 cubic feet. What is the volume
of the earth in cubic feet?
b. One grain of sand has a volume of 1.3 x 10-9 cubic feet. How many grains of sand would it take to fill up a
sphere the size of the earth?
c. Which is larger, your answer to part b or the largest number a calculator can handle?
10. The units digit of a two digit number is 40% of the tens digit. If the digits were reversed the new number
would be 27 less than the original number. What is the original number?
11. Ten sandwiches are purchased at a total cost of $55.50. Some of the sandwiches are tuna which cost $6.00
and some of the sandwiches are roast beef which cost $4.50. How many of each kind of sandwich were
purchased?
12 K and L start 400 km apart and approach each other at constant but different rates. It takes 12 hours for them
to meet. If K goes 10 km per hour faster then L what are their rates?
13. Earl Wells leases a rectangular tract of land. 5.3 km by 4.1 km. He can drill for oil on the inner 70% of the
land, but must leave a strip of uniform width around the edge with no wells. What is the width of the strip?
14. Researchers are trying to determine the amount of blood a particular animal has in its body without killing
the animal. They withdraw a 100ml blood sample and replace it with 100 ml of slightly radioactive blood.
They later withdraw a second sample and note that the ratio of radioactive blood to nonradioactive blood is
2:34. How much blood does the animal have?
15. Toby Rich has $10,000 to invest. He can put part of it inot a certificate of deposit (CD) paying 8% and part
of it in a savings account paying 5%.
a. How much interest will Toby earn if he puts 70% of the money into savings and the rest into a CD?
b. How much interest will Toby earn if he puts 70% of the money into a CD and the rest into savings?
c. What is the range of amounts Toby could invest in savings and still be sure of a return of at least $750 in
interest?
16. The number of pounds of food you take on a camping trip varies directly with the number of days of the
trip. Suppose on a 10 day trip, you take 17 pounds of food.
a. Write the particular equation relating the amount of food you take to the length of the trip in days.
b. How much food should you pack for a 28 day trip?
c. How many days can you camp with 51 pounds of food?
17. Vi Olin estimates that the number of mistakes that she makes in plays a piece of music is inversely related
to the total number of minutes she practices the piece. After 20 minutes of practicing a piece she averages 4
mistakes.
a. Write the equation relating the number of mistakes to number of minutes of practice.
b. Vi wants to practice her current piece long enough that she will only make one mistake. How long is this?
c. If Vi had only practiced 5 minutes, how many mistakes would you expect her to make?