Name
Assignment 14 - Function Operations and Composition
PreAP Algebra II Per_______ Date
FOR ALL PROBLEMS: Show all applicable work (formulas, equations, substitutions, etc.) for credit! NO WORK 
NO CREDIT! Assignment will be zeroed if there is missing or incomplete documentation (work). Assignment will be
zeroed if there is significant grading error. Round answers to three decimals when appropriate.
Let f ( x )  3 x 3  4 x 2 and g ( x )  5 x 2  4 x . Perform the indicated operations:
1. g ( x )  f ( x )
3.
2. g ( x )  g ( x )
g(x)  f (x)
4. g ( x )  g ( x )
Let f ( x )  4 x 3 and g ( x )  5 x 2 . Perform the indicated operations:
5.
f (x) g(x)
6..
7.
f (x)
g(x)
8.
Let f ( x )  3 x  2 and g ( x )   x 2 and h ( x ) 
9. f ( g ( 3))
11. h ( g (5))
x2
.
5
f (x) f (x)
f (x)
f (x)
Perform the indicated operations:
10.
h( f ( 9))
12. h(h( 4))
Let f ( x )  3 x and g ( x )  2 x  7 and h ( x ) 
x4
.
3
Perform the indicated operations:
13. f ( g ( x ))
14.
15. h ( g ( x ))
16. h (h ( x ))
h ( f ( x ))
17. The cost (in dollars) of producing x sneakers in a factory is given by C ( x )  60 x  750 . The number of sneakers
produced in t hours is given by x (t )  50t . Find C ( x (t )) . Evaluate C ( x (5)) and explain what this number
represents.
18. For a mammal that weighs w grams, the volume b (in milliliters) of air breathed in and the volume d (in millililters) of
“dead space” (the portion of the lungs not filled with air) can be modeled by:
b(w) = 0.007w
and
d(w) = 0.002w
The breathing rate r (in breaths per minute) of a mammal that weighs w grams can be modeled by:
1.1w 0.734
r (w ) 
b (w )  d (w )
Simplify r(w) and calculate the breathing rate for body weights of 6.5 grams, 300 grams, and 70,000 grams.
Name
Algebra II PreAP Period
Date
Assignment 15 – Systems Review
FOR ALL PROBLEMS: Show all applicable work (formulas, equations, substitutions, etc.) for credit! NO WORK 
NO CREDIT! Assignment will be zeroed if there is missing or incomplete documentation (work). Assignment will be
zeroed if there is significant grading error. Round answers to three decimals when appropriate.
Graph the linear system and estimate the solution. Then check the solution algebraically.
1. y = 5x + 2
y = 3x
2. y = -x + 3
-x – 3y = -1
3. x + 2y = 2
x – 4y = 14
4. y = 2x – 10
x – 4y = 5
5. -x + 6y = -12
x + 6y = 12
6. y = -3x -2
5x + 2y = -2
Solve the system using the substitution method.
7
2x + 5y = 7
x + 4y = 2
8. 3x + y = 16
2x – 3y = -4
9. 6x – 2y = 5
-3x + y = 7
10. x + 4y = 1
3x + 2y = -12
11. 3x – y = 2
6x + 3y = 14
12. 3x – 4y = -5
-x + 3y = -5
Solve the system using the elimination method.
13. 2x + 6y = 17
2x – 10y = 9
14. 4x – 2y = -16
-3x + 4y = 12
15. 3x – 4y = -10
6x + 3y = -42
16. 4x – 3y = 10
8x – 6y = 20
17. 5x – 3y = -3
2x + 6y = 0
18. 10x – 2y = 16
5x + 3y = -12
19-20: Identify each variable, write a system of equations illustrating the scenario, then solve the problem.
19. GUITAR SALES In one week, a music store sold 9 guitars for a total of $3611. Electric guitars sold for $479 each
and acoustic guitars sold for $339 each. How many of each type of guitar were sold?
20. COUNTY FAIR
An adult pass for a county fair costs $2 more than a children’s pass. When 378 adult and 214
children’s passes were sold, the total revenue was $2384. Find the cost of an adult pass.
Name
Algebra II PreAP Period
Date
Assignment 16 – Graphing Inequalities
FOR ALL PROBLEMS: Show all applicable work (formulas, equations, substitutions, etc.) for credit! NO WORK 
NO CREDIT! Assignment will be zeroed if there is missing or incomplete documentation (work). Assignment will be
zeroed if there is significant grading error. Round answers to three decimals when appropriate.
Tell whether the given ordered pairs are solutions of the inequality. Show your work to justify your answer.
1. x  -7; (0, 10), (-8, -5)
2. y ≥ -2x + 4; (0, 4), (-1, 8)
Graph the inequality in a coordinate plane.
3. x  3
4. x ≥ 6
5. y  -2
6. -2y ≤ 8
7. y ≤ -2x – 1
8. y  3x + 3
9. y 
3
x+1
4
2
3
10. y ≥  x - 2
11. 2x + y  6
12. x + 4y  -12
13. 3x – y ≥ 1
14. 2x + 5y ≤ -10
What’s wrong with this picture?
15. y  2x + 3
16. y ≥ -3x - 2
17. Which ordered pair is a solution of 2x + 5y  9
a. (-4, -1)
b. (-2, 3)
c. (2, -4)
d. (6, -1)
18. Which ordered pair is not a solution of 3x – 5y  30?
a. (0, 0)
b. (-1, 7)
c. (1, -7)
d. (-5, -5)
Graph the inequality in a coordinate plane.
19. y  |x – 1|
20. y  |x| + 5
21. y  |x + 4| - 3
22. y ≤  |x – 2| + 1
23. y  3|x| + 2
24. y ≥ 2|x -1| - 4
1
2
25. The graph of which inequality is shown?
a. y ≤ -2|x + 1| + 3
b. y ≥ -2|x – 1| + 3
c. y  -2|x + 1| + 3
d. y ≥ -2|x + 1| + 3
26. The graph of which inequality is shown?
a. y ≥ 2|x – 3| + 5
b. y ≤ 2|x – 3| + 5
c. y  2|x – 3| - 5
d. y ≥ 2|x + 3| - 5
27. CALLING CARDS You have a $20 phone card. Calls made using the card cost $.03 per minute to destinations within
the United States and $0.06 per minute to destinations in Brazil. Write an inequality describing the numbers of minutes
you can use for calls to U.S. and Brazil destinations.
28. RESTAURANT MANAGEMENT
A pizza shop has 300 pounds (4800 ounces) of dough. A small pizza uses 12
ounces of dough and a large pizza uses 18 ounces of dough. Write an inequality describing the possible numbers of
small and large pizzas that can be made.
29. T-SHIRTS You sell t-shirts for $15 each and caps for $10 each. Write an inequality describing how many shirts and
caps you must sell to exceed $1800 in sales.
30. CRAFTS Cotton lace costs $1.50 per yard and linen lace costs $2.50 per yard. You plan to order at most $75 of lace
for crafts. Write an inequality describing how much of each type of lace you can order.
Name
Algebra II PreAP Period
Date
Assignment 17 – Systems Inequalities
FOR ALL PROBLEMS: Show all applicable work (formulas, equations, substitutions, etc.) for credit! NO WORK 
NO CREDIT! Assignment will be zeroed if there is missing or incomplete documentation (work). Assignment will be
zeroed if there is significant grading error. Round answers to three decimals when appropriate.
Graph the system of inequalities.
1. y  10
y  |x|
2. -x  y
-x + y ≥ -5
3. x + y ≥ -3
-6x + 4y  14
4. 3x – y  12
-x + 8y  -4
5. x  6
y  -1
yx
6. x ≥ -8
y ≤ -1
y  -2x - 4
7. x + y  5
2x – y  0
-x + 5y  -20
8. y ≥ x
x + 3y  5
2x + y ≥ -3
9. x + y  5
x + y  -5
x–y4
x – y  -2
10. x ≤ 10
x ≥ -2
3x + 2y  6
6x + 4y  -12
11. y  |x|
y  -|x|
12. y ≤ -|x – 3| + 2
y  |x – 3| - 1
Write a system of linear inequalities for the shaded region.
13.
14.
Solving Systems of Equations using the Graphing Calculator - Graph each of the follow systems on a grapher. All
equations will first need to be re-written in slope-intercept form, then entered in "y = ". Sketch a rough graph of the two lines.
If fractions are “tidy”, such as
1
2
, it is easier to type 0.5. If fractions are not “tidy” such as y  x  1 , you need to type (2  3)x + 1.
2
3
To find the point of intersection using the graphing calculator use 2nd CALC. Choose INTERSECT (choice #5); ENTER. It
is not necessary to respond the FIRST CURVE, SECOND CURVE, or GUESS, just continue to hit ENTER until the grapher
calculates the intersection for you. Be sure to record your answer (3 decimal places if needed).
2x  y  8
15) 

3x  5y  35
x  5y  5y
16) 

8x   y  3
5x  4y  8
17) 
3x  6y  2
18) 
4x  5y  7
19) 
3x  2y  17
20) 

2x  4y  7

8x  3y  2
5x  2y  5

8  6x  4y
Name
Pre-AP Algebra II Period
Date
Assignment 18 - Word Problems Systems of Equations
FOR ALL PROBLEMS: Show all applicable work (formulas, equations, substitutions, etc.) for credit! NO WORK 
NO CREDIT! Assignment will be zeroed if there is missing or incomplete documentation (work). Assignment will be
zeroed if there is significant grading error. Round answers to three decimals when appropriate.
DO NOT solve #1-8:
Identify the variables, then write a system of equations or inequalities.
1. Twice the smaller of two numbers is one-half of the larger number. The larger number exceeds three times the smaller
number by 10. Find the larger number.
2. Tickets to a concert cost $18 for main floor seats and $14 for balcony seats. If 950 tickets were sold for a total of
$14,160, how many balcony seat tickets were sold?
3. The width of a rectangle is six less than three times the length of a rectangle. If the perimeter of the rectangle is 84 feet,
find the length and the width.
4. Luis has 28 coins, made up of nickels, dimes, and quarters. If he had 2 more nickels, he would have just as many
nickels as he has dimes and quarters put together. If the total value of Luis’ coins is $3.20, how many coins of each
kind does he have?
5. The sum of the ages of Mark, Laurie, and Peggy is 79 years. The sum of Mark’s and Peggy’s ages exceeds twice
Laurie’s age by one year. Five years ago, Mark was the same age as Peggy is now. Find their ages now.
6. You can work at most 20 hours next week. You need to earn at least $92 to cover your weekly expenses. Your dogwalking job pays $7.50 per hour and your job as a car wash attendant pays $6 per hour. Write a system of linear
inequalities to model the situation.
7. A chemist has an 18% salt solution and a 45% salt solution. How many ounces of each solution should be used to
make 24 ounces of a 36% salt solution?
8. Flying into a head wind, a plane traveled 6300 kilometers in 7 hours. On the return trip, the same wind decreased the
plane’s travel time by 1 hour. Find the speed of the plane in still air and the speed of the wind.
Write a system of equations/inequalities for each problem. Identify the variables, SOLVE the system of equations using
algebraic methods (substitution or elimination).
9. Twice the height of a rectangular box is 1 cm less than the width. The length of the box is 2 cm less than the sum of the
width and height. The sum of the length, width, and height is 18 cm. Find the length, width, and height of the box.
10. If Ann buys 6 apples, 5 bananas, and 2 pears, she will pay $4.15. If she buys 3 apples, 7 bananas, and 4 pears, she
will pay $4.10. If apples are $0.11 less expensive than twice the cost of pears, what is the cost of each item?
11. The perimeter of a triangle is 45 cm. The two shorter sides differ by 2 cm. The longest side is 7 cm less than the sum
of the other two sides. Find the length of each side.
12. The largest angle of a triangle is 15 degrees greater than the smallest. The sum of the two larger angles exceeds twice
the smaller by 24. Find the measurement of each angle.
13. An online media store is having a sale, as described in the add shown. Use the information in the ad to write and graph
a system of inequalities for the regular video game prices and possible sale prices. Then use the graph to estimate the
range of possibly sale prices for games that are regularly priced at $20. (See page 172, #35)
14. A book on the care of tropical fish states that the pH level of the water should be between 8.0 and 8.3 pH units and the
temperature of the water should be between 76F and 80F. Let x be the pH level and y be the temperature. Write and
graph a system of inequalities that describes the proper pH level and temperature of the water.
Solve the system using any algebraic method.
17. 4x + 5y + 3z = 15
x – 3y + 2z = -6
-x + 2y – z = 3
18. 6x + y – z = -2
x + 6y + 3z = 23
-x + y + 2z = 5
19. x + 2y = -1
3x – y + 4z = 17
-4x + 2y – 3z = -30
20. 2x – y + 2z = -21
x + 5y – z = 25
-3x + 2y + 4z = 6
Name
Period
Assignment 19 - Solving Systems of Linear Equations Using Matrices
Date
PreAP Algebra II
FOR ALL PROBLEMS: Show all applicable work (formulas, equations, substitutions, etc.) for credit! NO WORK 
NO CREDIT! Assignment will be zeroed if there is missing or incomplete documentation (work). Assignment will be
zeroed if there is significant grading error. Round answers to three decimals when appropriate.
 Write a system of equations for each problem. Be sure to identify your variables.
 Rewrite each system in matrix form and solve by using the inverse matrix. Show your calculator steps.
1. On a recent trip to the movies to see the Matrix, three students – Mark, Carly, and Rita – each spent some money at the
concession counter. Mark bought two candy bars, a small drink, and two bags of popcorn for a total of $5.35. Carly
spent $4.16 on a candy bar, two small drinks, and a bag of popcorn. Meanwhile, Rita spent $5.85. She didn’t buy any
candy, but she bought two small drinks and three bags of popcorn. If all the purchases included tax, what was the
purchase price for each item?
2. The sum of three numbers is 110. The second number is twice the first. The third number is equal to three times the
first minus one-half the first. Find the numbers.
3. One night Glen Rice of the NBA’s Miami Heat scored a total of 35 points against the Los Angeles Clippers. In
basketball, it is possible to make a 3-point field goal, a 2-point field goal, or a 1-point free throw. He made as many 2pointers as 3-pointers and free throws combined. He scored one point more with 2-pointers than he did with 3pointers and free throws combined. How many of each did he score?
4. The sum of four numbers is 22. The first number is twice the difference of the second and the fourth. The second
number is 5 times the difference of the third and the fourth. The third number is twice the difference of the first and
the fourth. What are the four numbers? (Assume that “first through fourth” are positive integers listed smallest to
largest.)
5. At the high flying amusement park there are three kinds of rides: Jolly rides, Adventure rides, and Thrill rides. Admission
is free when you buy a book of tickets, which includes ten tickets for each type of ride. Or you can pay $5.00 for
admission and then buy tickets for each of the rides individually. Shalin, Lauren, and Jennifer decide to pay the
admission price and buy individual tickets. Shalin pays $19.55 for 7 Jolly rides, 3 Adventure rides, and 9 Thrill rides.
Lauren pays $13.00 for 9 Jolly rides, 10 Adventure rides, and no Thrill rides. Jennifer pays $24.95 for 8 Jolly rides, 7
Adventure rides and 10 Thrill rides. (The prices above do NOT include the admission price only ticket cost.)
a. How much does each type of ride cost?
b. What is the total cost of a 30-ride book of tickets?
c. Would Shalin, Lauren, or Jennifer have been better off purchasing a ticket book? Explain.
6. A family invested a portion of $5000 in an account at 6% annual interest and the rest in an account at 7.5% annual
interest. The total interest they earned in the first year was $340.50. How much did they invest in each account?
7. The midsize angle of a triangle is 30 greater than the smallest angle. The largest angle is 10 more than twice the
midsize angle. What are the measures of the three angles?
8. A person’s theoretical maximum hear rate (in heartbeats per minute) is 220 – x where x is the person’s age in years
(20 ≤ x ≤ 65). When a person exercises, it is recommended that the person strive for a heart rate that is at least 50% of
the maximum and at most 75% of the maximum.
a. Write a system of linear inequalities that describes the give information.
b. Graph the system you wrote in part (a).
c. A 40-year old person has a heart rate of 158 heartbeats per minute when exercising. Is the person’s heart rate in
the target zone? Explain your answer.
Solve each system using matrices, rewrite each in matrix form and show your calculator steps.
9. 8x – 5y = 17
6x + 4y = 33
10. 4w + x + 2y – 3z = -11
-3w + 2x – y + 4z = 20
5w + 4x + 6y – z = -10
-2w + 3x + 5y + 7z = -45
11. 3x - 2 y = 15
4x + y = 9
12. 2x + 3y + 4z = 2
5x – 2y + 3z = 0
x – 5y – 2z = 4
13. 2x + y – 2z = 1
14.
6x + 2y – 4z = 3
4x – y + 3z = 5
1
x
4
3
x
8
2
y3
5
2
y2
5
Solve the system. Then classify the system as consistent and independent, “consistent and dependent, or inconsistent.
15. y = 3x + 2
y = 3x – 2
16. y = 2x – 1
-6x + 3y = -3
17. 4x – 5y = 0
3x – 5y = -5
18. 4x + 5y = 3
6x + 9y = 9
19.
1
x – 3y = 10
2
1
x + 2y = -2
4
20.
5
x – y = -4
2
1
5x – 2y =
4
Name
Assignment 20 – Review for TEST
Period
Date
PreAP Algebra II
FOR ALL PROBLEMS: Show all applicable work (formulas, equations, substitutions, etc.) for credit! NO WORK 
NO CREDIT! Assignment will be zeroed if there is missing or incomplete documentation (work). Assignment will be
zeroed if there is significant grading error. Round answers to three decimals when appropriate.
Given the four system of equations, one must solve in each of the following methods: elimination, graphing, matrices, or
substitution. You choose the method, but do not repeat any one method. For the graphing problem, attach the grid handed
out with this review. For the matrices, show the set of matrices that are set up on your calculator. In addition, classify each
system.
1.
1
xy4
2
x – 2y = 12
3. 4x – 2y = 6
y – 2x = 4
2. -5x + y = 37
2x – 3y = -20
4. 3y = 4x – 5
x – 5y = 15
5. You go to the Half-Price Book Store (where books aren’t really ½ price). The sale reads: 10%-75% off all books priced
between $3.99 and $18.99. If you find the latest Justin Bieber autobiography, priced at $12.99, misplaced in the
children’s section, how much might you spend. Identify the variables, inequalities necessary to solve your dilemma,
sketch the graph of this situation, then name the price(s).
6. You want to start kayaking and decide to try it out on Canyon Lake before trying to kayak a river. The lake is about 24
miles across and does not have a significant current. The day you choose to visit the lake, there is a slight wind. It
takes you and your friends 6 hours to travel across the lake with a headwind, but only 2 hours for the return trip. What
is your kayaking speed and what is the wind speed.
Graph the following inequalities, be sure to show only the overlapping shading.
7. 2x + y  5
y ≥ -2|x – 1| + 3
8. x ≥ -4
y3
3x – 2y  6
y
y
10
10
5
5
x
-10
-5
5
10
x
-10
-5
5
-5
-5
-10
-10
9. Using an algebraic method, solve the scenario: On a recent trip to the movies, three friends spent money on candy
bars, drinks, and popcorn. Dave bought three candy bars, two drinks, and three bags of popcorn for a total of $8.52.
Liz spent $7.33 on two candy bars, three drinks, and two bags of popcorn. Tom spent $5.85 on two drinks and three
bags of popcorn. What was the price of each item? Identify the variable, write the system of equations, then solve.
10. Using matrices, solve this following system: 5w + 2x + 3y – 2z = -67
-2w + 3x + 5z = 68
6w + 5x + 7y = -44
-w + 4x + 6y + 8z = 74
Find the value of each variable, include the calculator set-up (what the matrices look like on your screen).
10