lesson 1 ~ order of operations - oregon focus challenge ws.pdf · lesson 1c ~ order of operations ....

Lesson 1C ~ Order of Operations Name__________________________________________ Period______ Date____________

Fill in the box with a number from 1 to 10 that makes the equation true. If there are two boxes in a problem, both boxes must contain the same number

1. 2. 14235 2 =×+− 44

)1(42

−=−−−

3. 74213402 =−+•

− 4.

24)7(6 3 −=+−

5. 27242

35 23 =+•−−

6. 4422)22( 432 =−++

Use the numbers 1, 2, 3, 4 and 5 once in each expression to create an answer that meets each criteria. Each expression must use at least one exponent and at least two different types of operations. You can make any of the values negative (e.g. −1, −2, etc).

©2010 SMC Curriculum Oregon Focus on Linear Equations

Example: Has an answer that is even. 45123 +−+

Uses each number once and equals 8,

which is even. 7. Has an answer that is odd. 8. Has an answer that is divisible by 3. 9. Has an answer less than 0. 10. Has an answer that is a prime number. 11. Has an answer that is between −10 and −20. 12. Has an answer equal to 24.

Lesson 2C ~ Evaluating Expressions Name__________________________________________ Period______ Date____________

Functions are used in most high school and college math courses. Function notation is a different way to show what value you are substituted into an expression.

For example: is read “f of x equals 3x + 1” 13)( += xxf When a number is in the parentheses, this number is substituted for the variable it replaced.

For example: ??)9( =f

Substitute 9 in for x in the equation above. 281)9(3)9( =+=f28)9( =f

Use the function . Find each of the following. 92)( −= xxf

1. 2. 3.

)2(f )7(f )3(−f

4. ( )2

1f 5. )8(−f 6. )0(f

Use the function . Find each of the following. 34)( 2 +−= xxxf

7. 8. )2(f )5(−f 9.

)7(f

Sometimes, you may put a value through multiple functions. Always start with the function inside the parentheses and then use the new value in the second (outside) function.

For example: Find when ))2(( fg xxf 3)( = and 7)( += xxg . First find . )2(f 6)2(3)2( ==fThen plug 6 into . )(xg 1376)6( =+=g

Answer: 13))2(( =fg Use the function and 1)( 2 += xxf xxg 310)( −= . Find each of the following. 10. 11. 12. ))2(( −fg ))5((gf ))1(( fg


Lesson 3C ~ The Distributive Property Name__________________________________________ Period______ Date____________ The Greatest Common Factor (GCF) is the largest number that divides a set of numbers. The GCF can be used when factoring. Factoring is a process in which an expression is broken into smaller parts. This is done by pulling out the GCF. Look at the example below. Example: 64 +x GCF between 4x and 6 is 2. Divide 2 from each term to get: )32(2 +x Check your work by distributing: 64)32(2 +=+ xx Factor each expression using the GCF. Check your work using the Distributive Property. 1. 2. 123 +x 106 +− x

3. 4. 1620 −x 8050 +− x

5. 6. x2277 + 1421 −x

7. 8. x369 + 10080 −x

Simplify each expression. Then factor the simplified expression using the GCF. 9. 10. 7212)8(4 −+−++ hhh 4)5(2 −++ yy

11. 12. 29)12(3 +++ pp 1)5(410 +++ xx


Lesson 4C ~ Solving One-Step Equations Name__________________________________________ Period______ Date____________

Solve each equation using inverse operations. Write a second equation using a different operation that has the same answer. The first one is done for you.

1. 2. 174 =+x4

8 y= 3. 7.42.3 −=−m

Answer: x = 13 New Equation: 262 =x

4. 65

32 1=+ k 5. 847 −=− x 6. 5.1

7=

p

7. 8. 3412 −=− w 85

43 2=x 9.

124

3=

h

Solve each equation using inverse operations. Write three more equations, each using a different operation, that has the same answer as the first. Each problem should have one equation for each operation ),,,( −+÷× .

10. 5

4−

=m 11. 212

1 =h

12. 13. 5241 −=−y 3

161 =−x

Write an algebraic equation for each problem. Solve each equation. 14. Kristina is four-fifths as old as her sister. Kristina is 12 years old. Write a multiplication equation and solve the equation to determine her sister’s age. 15. Keaton sold three-fourths as much as Jimmy during a fundraiser. Keaton sold 60 products. How many products did Jimmy sell?



Lesson 5C ~ Solving Two-Step Equations Name__________________________________________ Period______ Date____________

Write an equation for each situation. Solve the problem. Show your work and check your solution. 1. AJ started the day with $90. He bought three used video games and had $27 remaining. If each video game cost the same amount, what was the price of each game? 2. Sara took a large bag of flour and put the same amount into four different containers. She had 1.7 pounds of flour remaining. If she started with 16.1 pounds of flour, how much flour is in each container? 3. Maria is thinking of a number. If she divides her number by six and then subtracts 11, she gets 1. What is Maria’s number? 4. Ivan bought a new television. He was able to pay $120 at the time he received the television. He will pay $44 each month on the balance. The original cost of the television was $736. How many months will it take Ivan to pay off the television? 5. The zoo fed the large animals 1,023 pounds of food last week. Nine large animals each received the same amount while the elephant ate 195 pounds of the food. How much did each of the nine large animals receive? 6. Rick is 3 years older than half his brother’s age. Rick is 13 years old. How old is his brother? 7. Lucy ate eight more than three times as many pretzels as Matt. Lucy ate 56 pretzels. How many pretzels did Matt eat?

Lesson 6C ~ Solving Multi-Step Equations Name__________________________________________ Period______ Date____________

Solve each inequality. Graph the solution on a number line. See the Tic-Tac-Toe activity on page 37 in Oregon Focus on Linear Equations for examples of solving and graphing inequalities. 1. 123≤+x

0 5 10 33 −− 9≤x 2. 11542 −<+ ff

−5 0 5 3. 133)3(5 +>+ pp

−5 0 5 4. 19753 −≥+ yy

−5 0 5 5. 7)1(23 ++> mm


6. 13974 +≤− ww 7. 4510192 −<+ xx 8. 14)3(4)1(3 −+≥− hh

9. 134137 +>+ yy

0 105

−5 0 5

0 105

−5 0 5

0 105

Lesson 7C ~ The Coordinate Plane and Scatter Plots Name__________________________________________ Period______ Date____________ A reflection flips a point or figure over a line. The figures will be mirror images of each other. A translation is also called a slide. A translation moves a figure from one position to another on a coordinate plane without turning it. Find the coordinates of the point (1, 4) that has undergone each of the following. 1. Reflection over the y-axis. 2. Translation of 4 to the right. 3. Translation of 3 down. 4. Reflection over the x-axis. Graph the original figure and the image under the given transformation on a separate sheet of graph paper. Label the vertices correctly. 5. Triangle M(3, 4), N(−1, 2) and P(0, 5) A translation of 3 units to the left. 6. Square A(−1, 2), B(1, 2), C(1, 4) and D(−1, 4) A reflection over the x-axis. 7. Rectangle J(0, 1), K(0, 3), L(5, 3) and M(5, 1) A translation of 1 unit to the right and 2 units down. D

F

E

D’

F’

E’

8. Describe the translation that maps Δ DEF onto Δ D’E’F’. 9. Describe the reflection that maps HJK onto Δ Δ H’J’K’. J


10. What are the new coordinates of the point (3, −5) that has undergone a reflection over the y-axis followed by a translation of 4 units up?

K

H J’

K

H’

’

Lesson 8C ~ Recursive Routines Name__________________________________________ Period______ Date____________

Create a recursive routine that fits each description. List the start value, operation and first 6 terms. 1. Start value is a teen number and every other term is odd.

Start Value: _________________ Operation: _________________

First Six Terms: ___________________________________________

2. Start value is a 40 and the fifth term is 25.


First Six Terms: ___________________________________________

3. Start value is divisible by 6 and the fourth term is divisible by 4..


First Six Terms: ___________________________________________

4. Start value is a positive even number and terms alternate between positive and negative numbers..


First Six Terms: ___________________________________________

5. Start value is a decimal number less than 1 and the fifth term is −2.


First Six Terms: ___________________________________________

6. Start value is a prime number which is four less than a multiple of nine. The third term is 35.


First Six Terms: ___________________________________________

7. Start value is a negative multiple of seven. The sixth term is 39.


First Six Terms: ___________________________________________

8. Start value is an odd number which is three more than one-half squared. The fourth term is 431 .


First Six Terms: ___________________________________________

9. Start value is the largest prime number less than one-hundred. The fifth term is 103.


First Six Terms: ___________________________________________


Lesson 9C ~ Linear Plots Name__________________________________________ Period______ Date____________ Determine the linear relationship shown by two points on the coordinate plane by stating the start value and operation. Create an input-output table for the x-values of 0 through 5. x y

0 1 2 3 4 5

x y

1. Start Value: ______ Operation: ________

2.


Start Value: ______ 0 1 Operation: ________

2 3 4 5

x y

x y

3. Start Value: ______ Operation: ________ 4. Create a linear relationship that includes the point on the coordinate plane below.

Start Value: ______ Operation: ________

Lesson 10C ~ Recursive Routine Applications Name__________________________________________ Period______ Date____________ 1. After three weeks on the market, the AdMi stock was at 22.5 points After five weeks on the market, it was at 19.5 points. Each of the first five weeks, it fell an equal amount. a. Create an input-output table that shows the value of the stock


over the first five weeks.

b. Write a recursive routine (start value and operation) that describes the value of the AdMi

Weeks x

Value y

0 1 2 3 4 5

stock based on the number of weeks it has been on the market. c. Create a scatter plot that shows the stock’s value over the

first five weeks. Label both axes. d. Assuming the stock continues to decrease at this rate, how many weeks until it is worth only 3 points? 2. When Suzi finished her 6-week exercise program, she weighed 18 pounds less than when she started. After 2 weeks of the program, she weighed 152 pounds. Each week she lost the same amount. a. Create an input-output table that shows Suzi’s weight Weeks

x Weight

y 0 1 2 3 4 5 6

over the six weeks using the table at the right. b. Write a recursive routine that describes Suzi’s weight

based on the number of weeks she has been participating in the program.

c. Create a scatter plot that shows Suzi’s weight over the six weeks. Label both axes. d. How many more weeks should she continue with the

program if she would like to weigh 125 pounds?

Lesson 11C ~ Rate of Change Name__________________________________________ Period______ Date____________

Each table shows three terms in a recursive routine. Determine the rate of change and start value for each table. Find two more terms in the routine. 1. 2. 3.


Rate of Change: _____ Rate of Change: _____ Rate of Change: _____ Start Value: _____ Start Value: _____ Start Value: _____ . 4. 5. 6. Rate of Change: _____ Rate of Change: _____ Rate of Change: _____ Start Value: _____ Start Value: _____ Start Value: _____ . Complete each table using the rate of change and the start value for each problem. 7. 8. 9. Rate of Change: 4 Rate of Change: 4

1− Rate of Change: 1.7 Start Value: −13 Start Value: 1 Start Value: −10.2

x y 0 −14 2 −2 4 10

x y 1 16 5 4 7 −2

x y 4 7.6 9 14.1 13 19.3

x y 1 −1 6 23

10 47

x y 1 2 0

431−

12 5−

x y −6.8 −1.7 0 5.1 11.9 51

x y 6 8

x y 4 11

x y −2 2

x y −4 10 −1 7 3 3

x y 8 3 13

215

20 9

x y −11 −9.2 −6 −3.2 −2 1.6

x y −1 6

x y 22 30

x y 5 9

Lesson 12C ~ Recursive Routines to Equations Name__________________________________________ Period______ Date____________

Determine the rate of change and the start value for each table. Write an equation in slope-intercept form. 1. 2. 3.


Rate of Change: ______ Rate of Change: ______ Rate of Change: ______ Start Value: _________ Start Value: _________ Start Value: _________ Equation: ___________ Equation: ___________ Equation: ___________ 4. 5. 6. Rate of Change: ______ Rate of Change: ______ Rate of Change: ______ Start Value: _________ Start Value: _________ Start Value: _________ Equation: ___________ Equation: ___________ Equation: __________ Use the given information to fill in the blanks in the each table and below the table. 7. 8. 9. Rate of Change: 2

1 Rate of Change: ______ Rate of Change: −1.3 Start Value: _________ Start Value: 4 Start Value: _________ Equation: xy 2

16 += Equation: xy 34 −= Equation: __________

x y −6 −2 −3 −1 −1

31−

4 311

9 3

x y −2 5 1 5 3 5 8 5 10 5

x y −10 −41 −8 −33 −6 −25 −3 −13 −1 −5

x y 0 −7 2 −3 5 3 7 7 10 13

x y −1 8 1 2 4 −7 6 −13 11 −28

x y −3 9.3 −1 5.1 2 −1.2 4 −5.4 7 −11.7

x y −3 2 5 −20

10

x y 0 10.6 4 0.2 9 −5

x y −2 1 3 6 8

Lesson 13C ~ Input-Output Tables from Equations

Name__________________________________________ Period______ Date____________

Complete the input-output tables for each equation. Graph the points on a separate sheet of graph paper to determine if the equation is linear (forms a straight line) or non-linear. 1. 2. 2)2( −= xy xy 5.03 −= 3. xy 2=


x y

Type: ________________ Type: ________________ Type: _______________ 4. 5. 6. 42 −= xy 12 += xy 43 −= xy

Type: ________________ Type: ________________ Type: _______________ 7. Write an equation for a non-linear curve (different than the ones above). Create a table of values including input-output pairs. Graph the curve. Equation: _______________

x 2)2( −= xy y 0 1 2 3 4

x xy 5.03 −= y −2 1 4 6 9

x xy 2= y −1 0 1 2

3

x 42 −= xy y −1 1 3 4 6

x 12 += xy y x 43 −= xy y −1 −2 0 −1 1 0 2 1 3 2

Lesson 14C ~ Calculating Slope from Graphs Name__________________________________________ Period______ Date____________


The line at the right has seven integer points shown. Use the graph to answer the questions. 1. List the seven ordered pairs. A ( , )

B ( , )

C ( , )

D ( , )

E ( , )

F ( , )

G( , )

2. Find the slope of the line using different slope triangles as designated below. Write each slope in simplest form. a. D and E b. B and D

AB C

D

E

F G

c. C and F d. A and G 3. Does it matter which two ordered pairs you choose to use on a line when determining the slope of the line? Support your answer with evidence. 4. Similar triangles are triangles that have the same shape but not necessarily the same size. Similar triangles have side lengths that are proportional. Two quantities are proportional if they have the same ratio. Are the four slope triangles you drew in Exercise #2 similar triangles? Why or why not?


Lesson 15C ~ The Slope Formula Name__________________________________________ Period______ Date____________

Determine the slope of the line that passes through each pair of points. Write in simplest form. Then use the slope to find three other points on the line formed by the given points.

Points on Line Slope Three Additional Points on the Line

1. (5, 4) and (1, 2)

2. (−1, 6) and (3, −2)

3. (0, 2) and (2, 5)

4. (3, 6) and (6, 5)

5. (−5, −1) and (−3, −4)

6. (−3, 0) and (−3, −7)

7. (6, −3) and (−3, 6)

8. (2, 5) and (6, 5)

9. Some lines are horizontal or vertical lines. You can determine this by finding the slope using the slope formula. You can also tell this by examining the ordered pairs on a line. How can you tell by looking at the ordered pairs for two points if… a. the line is a vertical line? b. the line is a horizontal line? c. Give an example of a set of ordered pairs for two points that form a vertical line.

Lesson 16C ~ Graphing Using Slope-Intercept Form Name__________________________________________ Period______ Date____________ Graph each set of equations on the same coordinate plane. Determine the point where the lines intersect. 1. 2. 52 −= xy 14

3 +−= xy 3. xy 38 −=

531 += xy 8+= xy 23

1 −= xy Intersection Point: ________ Intersection Point: ________ Intersection Point: ________ 4. 22

1 +−= xy 5. 43 −= xy 6. xy 22 +=

934 −= xy 52 −= xy xy 2

3= 42

1 −= xy 8−−= xy 6−=y

Intersection Point: ________ Intersection Point: ________ Intersection Point: ________ 7. Why would it be difficult to find the intersection point of a set of equations if the coordinate pairs were not integers?


Lesson 17C ~ Writing Slope-Intercept Equations for Graphs Name__________________________________________ Period______ Date____________ Three lines are given on each graph that intersect at one point. Find the slope-intercept equation of each line. Graph and write an equation for one additional line that intersects at the same point. Vertical and horizontal lines are not permitted. 1. Equation of Line a: ______________________

a

b

Equation of Line b: ______________________

c Equation of Line c: ______________________

Equation of New Line: ___________________


2. Equation of Line d: ______________________

Equation of Line e: ______________________

Equation of Line f: ______________________

Equation of New Line: ___________________

3. Write the slope-intercept equations of three lines that all intersect at a point in Quadrant 3.

f

d

e

Lesson 18C ~ Writing Linear Equations from Key Information Name__________________________________________ Period______ Date____________

Write the slope-intercept equations for the lines that form each side of the quadrilaterals below. Label each line with the line segment it corresponds to (i.e. 32: −= xyJK ).


1.

A

B C

D 2.

E

F

G

H

Lesson 19C ~ Different Forms of Linear Equations Name__________________________________________ Period______ Date____________

STANDARD FORM: where A and B are not both zero. CByAx =+

POINT-SLOPE FORM: 11 )( yxxmy +−= where m represents the slope and is a point on the line.

),( 11 yx

Find an equation in standard form that creates the same line as the slope-intercept equation given. The A and B values should be integers. 1. 2. 13 += xy 22

1 −= xy 3. 532 +−= xy

4. 45

7 +−= xy 5. 129 −= xy 6. xy 2

3= Find an equation in point-slope form that creates the same line as the slope-intercept equation given. 7. 8. 34 −= xy 52

1 += xy 9. xy 41−=

10. 11. 92 +−= xy 13

2 += xy 12. 323 −−= xy

Find two equations (one in point-slope form and the other in standard form) that create the same line as the slope-intercept equation given. 13. 14. 53 += xy 12

1 +−= xy 15. 241 −= xy


Lesson 20C ~ More Graphing Linear Equations Name__________________________________________ Period______ Date____________ Equations in standard form can be graphed using the intercept method. Find the x- and y-intercepts for each equation. Substitute 0 for x and solve for y to find the y-intercept. Substitute 0 for y and solve for x to find the x-intercept.

©2010 SM Curriculum Oregon Focus on Linear Equations C

1. 2. 842 =+ yx 1553 =+− yx 3. 993 =− yx 4. 5. 1052 −=+ yx 2044 −=− yx 6. 1682 =+ yx

7. 8. 20210 =+ yx 882 −=− yx 9. 124 −=x

Lesson 21C ~ Introduction to Non-Linear Functions Name__________________________________________ Period______ Date____________ Functions can be linear, non-linear or a combination of both. Sketch a graph for each situation and label the axes. Write a few sentences explaining each graph. In your explanations, use terms such as linear, nonlinear, continuous, discrete, increasing, and decreasing. (Look up the terms before starting the activity if you do not know their meanings.) 1. The temperature of water in ice cube trays from the time it is placed in a freezer. 2. The number of cars on the freeway and the level of pollution in the air. 3. The temperature of a kettle of water as it is heated. 4. The distance from a Ferris-wheel rider to the ground during two revolutions. Sketch a graph of a continuous function to fit each description. a. Linear and increasing, then linear and decreasing b. Neither increasing nor decreasing c. Increasing but non-linear d. Decreasing, discrete


Lesson 22C ~ Parallel, Intersecting or the Same Line Name__________________________________________ Period______ Date____________

Perpendicular lines cross at a angle. Two lines are perpendicular if they have slopes that are opposite reciprocals. A few examples are shown below.

°90

Examples of Slopes of Perpendicular Lines:

32 and

23

− and 4−41

35

− and 53

Determine if each pair of lines is perpendicular. Show your work.

1. 824

521

=+−

−−=

yxxy

2. 124510168=++=

yxxy

3. 664623

=+=−

yxyx

4. In geometry, some coordinate proofs use items such as slopes, distances and midpoints to prove that points form a specific type of quadrilateral.

a. Prove that quadrilateral ABCD is a parallelogram by using slopes.

A(2, 5) B(5, 7) C(6, 5) D(3, 3) b. Using slopes, determine if quadrilateral ABCD is a rectangle. Explain your reasoning.


Lesson 23C ~ Solving Systems by Graphing Name__________________________________________ Period______ Date____________

Create a system of equations that has the given solution. You may not use horizontal or vertical lines. Graph and record your equations. 1. SOLUTION: (4, 5) 2. SOLUTION: (–3, 1) 3. SOLUTION: (2, –8) EQUATIONS: EQUATIONS: EQUATIONS: 4. SOLUTION: (6, 0) 5. SOLUTION: (–7, –4) 6. SOLUTION: (1, –3) EQUATIONS: EQUATIONS: EQUATIONS:


Lesson 24C ~ Solving Systems Using Tables Name__________________________________________ Period______ Date____________ Each system of equations has a solution whose x-value is not an integer. Use input-output tables to determine what two integers the x-value of the solution lies between.


x y 0 1 2 3 4

x y 0 1 2 3 4

x y 0 1 2 3 4

x y 0 1 2 3 4

x y

x y

x y

x y

x y

x y

x y

x y

1. 2. 23 += xy 132 +−= xy 35= −xy 5.14 −= xy

32.0 += xy 4.3+= xy 14

Solution (x) between _____ and _____. Solution (x) between _____ and _____.

= − +xy 6.135.0 3. 4. = xy

85 +−= xy 6.22 +−= xy 4.13

+

Solution (x) between _____ and _____. Solution (x) between _____ and _____.

= − −xy 5 −= xy 5. 6. Solution (x) between _____ and _____. Solution (x) between _____ and _____. 7. How could you use the information in each of the above exercises to narrow in on the solution? Give an example using the information from one of the exercises above.

Lesson 25C ~ Solving Systems by Substitution Name__________________________________________ Period______ Date____________

Each set of three lines intersects to form a triangle. Use the substitution method to find the intersection point of each pair of lines in the set. List the three vertices of the triangle. Graph the triangle. 1. Line A: 2. Line D: 12 −= xy 42 += xy Line B: Line E: 42 =+− yx yx −= 4 Line C: Line F: 74 −−= xy 42 =− yx 3. Create a system of three equations that intersect to form a triangle with integer coordinates for the vertices. List the three equations and the three ordered pairs of the vertices.


Lesson 26C ~ Solving Systems Using Elimination Name__________________________________________ Period______ Date____________ Solve each system of equations using the elimination method. Both equations will need to be multiplied by a constant in order to solve. Check the solution.

1. 2. 1623232

=+=−

yxyx

1824 753−=+

=+−yxyx

3. 4. 1026

1534−=−

=+yxyx

44420 510 −=+−

=−yxyx

5. 6. yxyx

35 85226

+=+=

30 22375

=+=−

yxyx


Lesson 27C ~ Choosing the Best Method Name__________________________________________ Period______ Date____________

1. Solve the following system of equations using all four methods. Every method should provide the same solution.

244212=++=

yxxy

GRAPHING TABLES

x


y

x y

SUBSTITUTION ELIMINATION

2. Which method do you like best? ______________________ Why?

Lesson 28C ~ Applications of Systems of Equations Name__________________________________________ Period______ Date____________

Define the variables and develop a system of equations for each problem. Solve the system and check your solution. Write your answer in a complete sentence. 1. The Garrison’s minivan gets 14 miles per gallon for city driving and 19 miles per gallon for highway driving. At the beginning of the week, the 24-gallon tank was full. The family drove 421 miles before running out of gas. How many gallons were used for city driving and how many were used for highway driving? 2. A piggy bank contains dimes and quarters. There are a total of 64 coins in the bank with a total value of $10.30. How many of each type of coin are there in the piggy bank? 3. In triangle EFG the measure of angle E is four times the measure of angle F. The measure of angle G is less than the measure of angle E. What is the measure of each angle? (Hint: the °18 sum of the angles in a triangle is .) °180 4. Dave, Frank and Kathy can process 1,300 catalog orders per day when all three of them are working. Dave and Frank can do 780 orders per day and Frank and Kathy can do 850 orders per day. How many can each do in a day?


lesson 1 ~ order of operations - oregon focus challenge ws.pdf · lesson 1c ~ order of operations ....

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