TVUSD& & & & & & Name& & Algebra&1& Year%EndRe ... & & & & & Name&_____ & Algebra&1& Year%EndRe*Engagement% Functions’ & For’each’relation’represented,’state’the’domain’and’range’of’each,’they2intercept,&and

TVUSD Name __________________________________________ Algebra 1

Year End Re-‐Engagement Number & Equations

1-‐2) Solve for the indicated variable. 1) a) 3x – 7 = -‐5(x – 5) b) 2(h – 1) = -‐(h – 6) c) 10 = a(-‐1 + 4)2 -‐ 22 2) a) 18 < -‐3(x – 2) b) -‐4(-‐2x + 3) > -‐28 c) 2x + 15 > 7x – 5 3) Which of the following values are solutions to the inequality: x < -‐3? -‐8, -‐3, 0, -‐1, 5, 10 4) Create a word problem (including a question and an answer) for each of the following:

a) 2x + 5 = 17 b) 10x + 20 < 170


Year End Re-‐Engagement Functions

For each relation represented, state the domain and range of each, the y-‐intercept, and whether or not the relation is a function. 1) a) y = x2 + 2 b) y = 2x + 1 c) y = 2x – 3 {x | {x | {x | {y | {y | {y | yes or no ? yes or no ? yes or no ? (0, ) (0, ) (0, ) 2) a) b) c)

{x | {x | {x | {y | {y | {y | yes or no ? yes or no ? yes or no ? (0, ) (0, ) (0, ) 3) Jordan weighs 160 lbs. By lifting weights each month for a year, he continually gains weight

until he is 200 lbs. 4) a) b) c)

{x | {x | {x |

{y | {y | {y | yes or no ? yes or no ? yes or no ?

y-‐int: y-‐int: y-‐int:

x -2 -1 0 1 2 y 1/4 1/2 1 2 4

x -2 -1 0 1 2 y 4 1 0 1 4

x -2 -1 0 1 2 y 0 2 4 6 8


Year End Re-‐Engagement Functions (cont’d)

5) Find the slope determined by the two points.

a) (-‐3, -‐6) & (9, -‐3) b) (-‐2, 8) & (-‐5, 2) c) (2, -‐4) & (-‐5, 10) 6) Write the equation of the line passing through each pair of points.

a) (5, 2) & (9, 6) b) (2, 4) & (8, 1) c) ) (3, 1) & (4, 7) 7) Graph the following equations.

a) 𝑦 = !!𝑥 − 4

b) 𝑦 = !!

!𝑥 + 2

c) 𝑦 = !

!𝑥 + 4

8) Duffy arrives at your house with a certain number of jelly beans in his stomach, and immediately begins to binge on more. After 1 minute he has 100 jelly beans in his stomach, and after 3 minutes he has 180.

a) How many jelly beans is Duffy consuming per minute? b) How many jelly beans did he have in his belly when he arrived in your house? c) It is scientifically proven that a person will vomit when 600 jelly beans are in the stomach. How long will it take for Duffy to throw up all over your living room carpet?


Year End Re-‐Engagement

{ { {

Systems 1) Solve the following systems of equations.

a) 2x + y = 4 b) 3x + y = 5 c) x + y = 6 6x + 3y = 12 6x + 2y = 15 4x + 2y = 14

2) Sally got the following solutions when three different systems of linear equations. Tell which indicates one solution, no solution, and infinitely many solutions.

System #1 System #2 System #3 x = 13 0 = 13 0 = 0

3) For the system of equations represented by each table, determine the solution. a) b) c)

4) What is the meaning of the solution of a system of equations?

5) The sum of two numbers is 7; their difference is 5. What are the two numbers?

x y1 y2 0 7 3 1 6 4 2 5 5 3 4 6 4 3 7

x y3 y4 0 2 2 1 3 3 2 4 4 3 5 5 4 6 6

x y5 y6 0 1 -‐1 1 2 0 2 3 1 3 4 2 4 5 3


Year End Re-‐Engagement Systems (cont’d)

6-‐7) Solve for the indicated variable. 6) Given system of inequality, place points A, B, C so that they meet the following conditions.

a) Point A is a solution of both inequalities. b) Point B is a solution of neither inequality. c) Point C is a solution of one inequality, but not the other.

7) Write the system of inequalities graphed above.

8) Is point P a solution to the system? Why or why not?

P


Year End Re-‐Engagement Exponential Functions

1) Which of the following is a possible graph of 𝑦 = 4(!

!)! . Why?

a) b) c)

2) a) Place a next to all the equations below that are an example of exponential growth.

Then, create your own example. _______________________________

𝑔 𝑥 = 6𝑥 + 5 𝐶(𝑟) = 20,000(.6)! ℎ(𝑠) = !

!"(4)!

𝑓(𝑥) = 3(2.5)

!! 𝑡 𝑥 = !

!𝑥! − 4 𝑝(𝑑) = 100(!

!)!

b) Place a next to all the equations above that are an example of exponential decay. Then, create your own example.

_______________________________ 3) Write the equation of the function represented in the table. a) b)

4) You buy a car for $30,250 that depreciates each year. Write the function for the value of a car,

C(n), after n years, at the given rate. a) 15% b) 6% c) 10%

x 1 2 3 y 6 12 24

x 3 4 5 y 5,000 50,000 500,000


Year End Re-‐Engagement Exponential Functions (4 x 4)

5-‐8) You are given one of four representations for an exponential relation. Generate the

other three. 5) f(x) = 2x

____________________________________________

____________________________________________

____________________________________________

6) f(x) = ____________________________

____________________________________________

____________________________________________

____________________________________________ 7) f(x) = ____________________________

____________________________________________

____________________________________________

____________________________________________

8) f(x) = ____________________________

A colony of 100 bacteria doubles every hour.

x f(x)

x f(x)

0 1

1 3

2 9

x f(x)

x f(x)

0 1 5 10

Years

50 10 0

grams


Year End Re-‐Engagement Polynomials

1) Determine the degree of each polynomial.

a) 4x2 – 6x3 + 3x + 2 b) x2 + 3x – 5 c) 5x4 + 7x2

2) Subtract the polynomials a) (6x2 – 7x + 8) – (2x2 + 4x – 3) b) (x2 + 2x – 9) – (4x2 – 7x + 5)

3) Write a simplified polynomial that represents the perimeter of the given figure. a) Square b) Rectangle c) Concave Hexagon

4) Create your own rectangle with the dimensions given as algebraic expressions. Then show the

simplified polynomial that represents its perimeter.

x + 2 x2 +4x + 6

3x -‐ 1

2x + 4

x + 3

2x

x


Year End Re-‐Engagement Polynomials (Factoring)

5) Multiply

a) (3x + 2)(4x – 7) b) (8x – 3)(2x + 5) c) (x – 1)(x + 6)

6) Factor

a) x2 –7x + 12 b) x2 + 4x – 12 c) x2 + x – 20

7) Multiply

a) (x + 2)(x – 2) b) (x + 5)(x – 5) c) (x – 7)(x + 7)

8) Factor

a) x2 – 81 b) x2 – 100 c) 4x2 – 25

9) Multiply

a) (2x + 1)(3x – 1) b) (2x + 1)(x – 3) c) (7x – 1)(x -‐ 2)

10) Factor a) 2x2 + 11x + 5 b) 3x2 – 10x + 7 c) 7x2 – 2x – 5

11) Given the area of the rectangle what are its dimensions? 3x2 + 2x -‐ 5


Year End Re-‐Engagement Quadratics

1) a) Place a next to all the equations for which the graph has a minimum. Then, create your

own example. _______________________________

𝑔 ℎ = −ℎ! 𝐶(𝑟) = 3𝑟! ℎ(𝑠) = !

!"(4)!

𝑓(𝑥) = 3𝑥! 𝑡 𝑥 = !

!𝑥! − 4 𝑝 𝑑 = −2𝑑 − 5

b) Place a next to all the equations for which the graph has a maximum. Then, create

your own example. _______________________________

2) Write an equation for each graph below, in vertex form. Then convert to standard form. a) b)

3) a) y = -‐3(x + 1)2 – 7 vertex ( , ); Maximum or Minimum?

b) y = (x – 5)2 + 1 vertex ( , ); Maximum or Minimum?

c) y = 2(x + 6)2 – 2 vertex ( , ); Maximum or Minimum?


Year End Re-‐Engagement Quadratics (cont’d)

4) Find the solutions.

a) 2x2 – x – 1 = 0 b) 2x2 + x – 5 = 0 c) 3x2 + 7x + 2 = 0

5) Find the zeros of the function.

a) f(x) = x2 – 8x + 7 b) g(x) = x2 + x – 20 c) h(t) = t2 – 3t – 10 6) Graph each.

a) y = x2 – 3

b) y = (x + 3)2

c) y = (x – 3)2

d) y = -‐3x2


Year End Re-‐Engagement Modeling Types of Functions

1-‐4) Match one of the types of functions with each of the four examples given. Linear Quadratic Exponential Growth Exponential Decay 1) From Table

2) From Equation

f(x) = x2 – 2x + 2 g(x) = 2x + 2 B(x) = 100(!!)x P(x) = 2x

3) From Graphs

4) From Scenario.

a) Your parents give a penny on the first day of the month, two on the second, 4 on the third, doubling the number of pennies given each day.

b) The flight of the sponge rockets that we launched.

c) A given amount of radioactive material has a half-‐life of 50 years.

d) You make $6 an hour. 5) From Visual Pattern.

x 1 2 3 y 1 0 1

x 1 2 3 y 7 9 11

x 1 2 3 y 100 50 25

x 1 2 3 y 5 15 45


Year End Re-‐Engagement To Be Graded

Numbers & Equations 1a, 2b, 3 Functions 1c, 4b, 5a, 6a, 7c Systems 1a, 6a, 8 Exponential Functions 1b, 2b, 3b, 4a, 6, 7 Polynomials 1a, 2b, 3b, 5a, 6b, 8a, 10a, 11 Quadratics 1b, 2a & b, 3c, 4c, 5b, 6c Modeling 1a

Documents

TVUSD& & & & & & Name& & Algebra&1& Year%EndRe ... & & & & & Name&_____ & Algebra&1& Year%EndRe*Engagement% Functions’ & For’each’relation’represented,’state’the’domain’and’range’of’each,’they2intercept,&and