Dear Maverick Math Student; Entering Algebra 1 Summer ... · optional but suggested. summer assignment is attached. Mathematics requires good work habits, a willingness to think,

Dear Maverick Math Student; Entering Algebra 1 Summer Assignment June 2012

Research has found that students who periodically refresh their “math inventory” over the summer enter the fall school year with improved skills and a firmer command of the concepts. With this in mind, your optional but suggested summer assignment is attached. Mathematics requires good work habits, a willingness to think, and a good background of accumulated skills. It is necessary to “hit the ground running” immediately with this refresher material firmly fixed in your brain.

If you need resource materials, your old notebooks and workbooks are the best references. Websites are also available to help you recall important ideas. A calculator is a wonderful tool, but there is no substitute for good math skills. This assignment should be completed without a calculator (unless the problem is marked “with calculator”. Additional copies of this review packet can also be printed from Smart’s Mill Middle School website (in pdf form).

Have a restful summer. I hope you have an exciting 2012-2013 school year!

SuggestedPaceforstudentsenteringAlgebra1‐SummerAssignment

Lesson1:Monday,June18th1.1 and 1.2

Lesson2:Monday,June25th1.3 and 1.4

Lesson3:Monday,July2nd1.1‐1.4 Problem Solving and 1.5

Lesson4:Monday,July9th1.6 and 1.7

Lesson5:Monday,July16th2.1 and 2.2

Lesson6:Monday,July23rd 2.3 and 2.4

Lesson7:Monday,July30th Matrices and 2.5

Lesson8:Monday,August6th2.6 and 2.7

Lesson9:Monday,August13th3.1 and 3.2

Lesson10:Monday,August20nd3.3

Lesson11:Friday,August24thSelf –Test – Are you Ready for Algebra I????????????

1

Lesson 1:

1.1: Evaluating Expressions and 1.2:

A variable is a letter used to represent one or more numbers. The numbers are the values of the variable. An algebraic expression , or also known as a variable expression, consists of numbers, variables, and operations – but NO equality symbol!

A power is an expression that represents repeated multiplication of the same factor. For example – 81 is a power of 3 because 81 = 3 i3 3 i3. You can also write it as 34, where 3 is the base and 4 is the exponent or power. i

Practice Problems:

Evaluate the expression. Do I need to remind you that you MUST SHOW WORK!!!

1) 0.4x when x = 6 __________ 2) 0.8 + y when y = 12.5 _________

3) 24a

when a = 8 __________ 4) 1

y2

− when 5

y6

= __________

5) 1

k2

when 2

k3

= ________ 6) when 2x6

x7

= __________

Evaluate the power.

7) 23 = __________ 8) 2

14

⎛ ⎞⎜ ⎟⎝ ⎠

= __________ 9) __________ 53 =

10) 3

35⎛ ⎞⎜ ⎟⎝ ⎠

= __________ 11) 4

23

⎛ ⎞⎜ ⎟⎝ ⎠

= __________

12) Which expression has the greatest value when x = 10 and y = 0.5?

A) xy B) x – y C) xy D)

yx

13) Find the perimeter of a square with side length 7.5m . ______________

14) You can estimate the distance (in centimeters) that a leopard frog can jump using the expression 13l where l is the frog’s length (in centimeters). What distance can a leopard frog that is 12.5 centimeters long jump?

________________

2

1.2: Apply Order of Operations

P(lease) E(xcuse) M(y) D(ear) A(unt) S(ally)

P stands for parenthesis – evaluate expressions inside any grouping symbols E stands for exponents – evaluate powers M and D stand for – multiply and divide from left to right A and S stand for – add and subtract from left to right. Example: Evaluate 2[30 – (8 + 13)] – 2(30 – 21) = 2[30 – 21] – 2(30 – 21) Don’t perform too many operations at once! = 2(9) – 2(30 – 21) = 2(9) – 2(9) = 0 Practice Problems: Evaluate the expression. Do I need to remind you that you MUST SHOW WORK!!!

1) ________ 2) __________ 3) 35 2 7+i 21 6 3+ ÷ ( )28 20 9 5⎡ ⎤− −⎣ ⎦

__________

4) ( 2121 4

2+ ) __________ 5) ( ) 21

6 18 26

+ − __________ 6) ( )23 20 7 5⎡ ⎤− −⎣ ⎦

__________

Evaluate the expressions.

7) when x = 3 __________ 8) 22 3x+ 26t 13− when t = 2 __________

9) when m = 1.5 __________ 10) ( 23 m 2− )2k 1

k 3−+

when k = 5 __________

11) Insert grouping symbols in the expression so that the value of the expression is 14: 9 + 39 + 22 ÷ 11 – 9 + 3 3

Lesson 2:

1.3: Write Expressions

Translating Verbal Phrases Operation Verbal Phrase Expression

ADD: sum, plus, total, more than, increased by

The sum of 3 and a number 3 + x 10 more than a number x + 10

SUBTRACT: difference, less than, minus, decreased by

The difference of a number and 6 x – 6 5 less than a number x – 5 (CHANGES ORDER!!!!!)

MULTIPLY: times, product, multiplied by, of

12 of a number

12x

The product of 3 and a number 3x DIVISION: quotient, divided by, divide into

The quotient of a number and 2 x2

The quotient of 2 and a number 2x

GROUPING SYMOLS: quantity The product of a quantity 10 plus a number x and 2

2(10 + x)

Order is important when writing subtraction and division expressions! Unit Rates: A rate is a fraction that compares two quantities measured in different units. If the denominator of the fraction is 1, the rate is called a unit rate.

Example: A 16‐oz box of cereal costs $2.99. Find the unit rate. 2.9916 oz

= $0.19 per oz.

Practice Problems: Translate the verbal phrase into an expression. 1) 9 more than a number ___________ 2) The product of 6 and a number ___________ 3) The difference of 7 and a number __________ 4) The quotient of twice a number t and 12 __________ 5) Three less than the square of a number __________ 6) Seven less than twice a number __________ 7) The product of 15 and the quantity of 12 more than a number x __________ 8) Twice the quotient of 50 and the sum of a number y and 8 ________ Find the unit rate. 9) 32 students in 4 groups ___________________________ 10) 4.5 pints for 3 servings ______________________ 11) 12 runs in 5 innings _____________________________ 12) $136 for 20 shares _________________________

13) Which rate is greater: 1

14 miles in 2 minutes and 4 seconds or

31

16 miles in 1 minute and 55 seconds?

4

1.4: Write Equations and Inequalities Translating Verbal Sentences

Symbol Meaning Associated Words = Is equal to The same as, equals > Is greater than More than < Is less than Fewer than ≥ Is greater than or equal to At least, no less than ≤ Is less than or equal to At most, no more than

Practice Problems: Write an equation or an inequality. Do not solve. 1) The sum of 42 and a number n is equal to 51. ____________________

2) The difference of a number z and 11 is equal to 35. ____________________

3) The difference of 9 and the quotient of a number t and 6 is 5. __________

4) The product of 9 and the quantity 5 more than a number t is less than 6. __________

5) The product of 4 and a number x is at most 51. __________

6) The sum of a number n and 4 is no more than 13. ____________

7) The quotient of a number t and 4.2 is at least 15. ___________ 8) Which equation corresponds to the sentence “The product of a number b and 3 is no less than 12?

A) 3b < 12 B) 3b ≤ 12 C) 3b > 12 D) 3b 12 ≥ Write an equation or inequality to represent the following situation. Define a variable (let x = …).

9) You are talking part in a charity walk, and you have walked 12.5 miles so far. Your goal is to walk 20 miles. How many more miles do you need to walk to meet your goal.

10) You buy a storage rack that holds 40 CDs. You have 27 CDs. Write an inequality that describes how many more CDs you can buy and still have no more CDs than the rack can hold, You buy 15 CDs. Will they all still fit?

11) You are baking batches of cookies for a bake sale. Each batch takes 2.5 cups of flour. You have 18 cups of flour. Can you bake 8 batches? Why or why not?

12) Your friend takes a job cleaning up a neighbor’s yard and mowing grass, and asks you and two other friends to help. Your friend divides the amount the neighbor pays equally among all the members of the group. Each of you get $25. How much did the neighbor pay?

5

Lesson 3: Section 1.5 ‐ Problem Solving YOU MUST SHOW ALL WORK! 1) You are making a photo quilt by transferring photos to squares of fabric. Each square should be big enough so

that you can turn over an edge 58inch long on each side and have a finished square with a side length of

35

4

inches. a) What are the dimensions of each fabric square? ________

b) How many square inches of fabric do you need if you want to include 48 squares? __________ c) The fabric you buy is 36 inches wide. How long of a piece of fabric do you need? __________ d) You buy a piece of fabric that has the length you found in part c. Once you’ve cut all the squares, how many

square inches of fabric are left? __________

2) You pay $7.50 for 3 quarts of strawberries. You realize that you need more strawberries for your recipe. You return to the store with $4.50. Will you have enough money to buy 2 more quarts of strawberries? Why or why not.

3) You are comparing two dorm‐size refrigerators, both with cube shaped interiors. One model has an interior edge length of 14 inches. Another model has an interior edge length of 16 inches. How many more cubic inches of storage does the larger model have?

4) You collect miniature cars and display them on shelves that hold 20 cars each.

a. Which expression would you evaluate to find the number of shelves you need for x cars: 20x, x20

, or

20x

? Justify your choice!

b. Find the number of shelves you need to display 120 cars. 6

5) You are designing the layout for a newspaper about teen issues. The newspaper will be 1

222inches wide. You

plan to have 5 columns with 18‐inch gaps between them and

38‐inch margins on the left and right sides. How

wide will each column be?

6) What is the interest on $1200 invested for 2 years in an account that earns simple interest at a rate of 5% per year?

7) A car travels at an average speed of 55 miles per hour. How many miles does the car travel in 2.5 hours?

8) A builder lays sod on the lawns of new homes. The installed cost for sod is $0.38 per square foot. What is the cost of installing sod on a rectangular lawn that is 32 feet long and 18 feet wide?

7

Lesson 4: 1.6: Represent Functions as Rules and Tables

A function consists of

• a set called the domain containing numbers called inputs (also called the independent variable), and a set called the range containing numbers called outputs (also called the dependent variable).

• A pairing of inputs with outputs such that each input is paired with exactly one output.

In a function, every x value can be paired with one and only one y value.

Input 3 6 9 12 Output 1 2 2 1

Is an example of a function

Input 2 2 4 7 Output 0 1 2 3

Is not a function

Examples:

Identify the domain and range, and determine whether the pairing is a function or not.

1) 2) 3)

8

Input Output 0 7.5 1 9.5 2 11.5 3 13.5

4) The domain of the function y = 5x ‐1 is 1, 3, 4, 5, and 6. Find the range.

5) The domain of the function 1

y x2

= + 3 is 4, 6, 9, and 10. Find the range.

6) Write the rule for the function:

Input 0 1 2 3 Output 2.2 3.2 4.2 5.2

7) At a yard sale, you find 5 paperback books by your favorite author. Each book is priced at $0.75.

a) For each book you buy, you spend $0.75, so _______ is a function of _____________.

b) Write a rule for the amount of money (in dollars) you spend as a function of the number of books you buy.

c) Find the domain of the function.

d) Find the range of the function.

12 0

1 23

34

3 5

Input Output 7 13 11 8 21 13 35 20

1.7: Represent functions as Graphs

You can use a verbal rule, an equation, a table, or a graph to represent a function.

Verbal Rule Equation Table Graph

9

The output is 1 less than y = 2x – 1 Input Output1 1 2 3 3 5 4 7

twice the output

Graph the functions.

1) 1

y x 12

= + ; domain 0, 1, 2, 3, an 2) y = x + 2; domain 0, 1, 2, 3, and 4

rite the rule for the function represented by the graph. Identify the domain and the range of the function.

8

6

4

2

d 4

W

3) 4) 5)

5

Y

X

Y

X

Y

X

Y

X

Y

X

10

esson 5: 2.1: Integers and Real Numbers

ell whether each number in the list is a whole number, an integer, and/or a rational number. Then order the numbers from least to greatest.

) 3, ‐5, ‐2.4, 1 2) 16, ‐1.66,

L

T

53, ‐1.6 3)

35−

,1 ‐0.4, ‐1, ‐0.5

a .For the given value of a, find –a and

4) a = 6 5) a = ‐3 6) a = ‐6.1 7) a = 1

12

Evaluate the expression when x = ‐0.75.

) ‐x 9) 1 + x− 10) ‐x + x8 11) 3(‐x)

2) The change in value of a share of a stock was ‐$0.45 on Monday, ‐$1.32 on Tuesday, $0.27 on Wednesday, and s the absolute value of the change the greatest?

3) In golf, the goal is to have the least score among all the players. Which golf score, ‐8 or ‐12, is the better score?

1$1.03 on Thursday. On which day wa

1

2.2: Add Real Numbers and Properties of Real Numbers

11

To add numbers with the same sign, add the numbers and keep the sign. To subtract numbers with different signs, subtract the numbers and keep the sign of the larger number.

Examples:

Identify the property being illustrated:

) 9 + (‐1) = ‐1 + 9 4) ‐8 + 0 = ‐8

Simplify.

8) 0.47 + (‐1.8) + (‐3.8)

9)

1) ‐3 + 3 = 0 2) (‐6 + 1) + 7 = ‐6 + (1 + 7)

3

5) (x + 2) + 3 = x + (2 + 3) 6) y + (‐4) = ‐4 + y

7) ‐13 + 5 + (‐7)

1 2 3

3 7 92 5 1

⎛ ⎞ ⎛− + − + −⎜ ⎟ ⎜⎝ ⎠ ⎝ 0

⎞⎟⎠ 10)

2 38 6 3

3 5⎛ ⎞+ − +⎜ ⎟⎝ ⎠

14

11)

3 9

12 64 10

− + 12) 5 7

7 1312 8⎝ ⎠

⎛ ⎞− + −⎜ ⎟

13) Evaluate

1 3

x 3 74 1

⎛ ⎞+ − +⎜ ⎟⎝ ⎠

0

when 1

x 33

= −

14) The bottom level of a parking garage has an elevation of ‐45 feet. The top level of the garage is 100 feet higher. What is the elevation of the top level?

12

Lesson 6: 2.3 and 2.4

2.3: Subtract Real Numbers Two negatives become a positive!

xamples:

implify:

) 13 – (‐5) 2) 16 – 32 3) ‐11 – (‐3)

E

S

1

1 14) 14.7 – (‐2.3) 5) ‐18.2 – (‐15.4) 6)

2 4⎜ ⎟⎝ ⎠

⎛ ⎞− −

Evaluate the expression when x = 7.1 and y = ‐2.5.

7) x – (‐y) 8) y – x – 12 9) x – (‐6) + y

Evaluate the expression when x = 3.6, y = 6.6 and z = ‐11.

10) (‐x – y) – z – 5 11) x + y – z + 12.9 12) x y z− −

13) ( )x y z− − − 14) x – y + z 15) ( )x z y+ −

r round. If he temperature outside the cave is ‐2.4 C, what is the change in temperature from outside to the cave?

16) The temperature inside Mammoth Cave in Kentucky is about 12.2 C yea t°inside°

13

.4: Multiply Real Numbers and Properties of Real Numbers

xamples:

ify the proper d

)

2

E

Ident ty illustrate .

2

0 05−

⋅ =1 2) 3) (3x)y = 3(xy)

4) (0.3)(‐3) = (‐3)(0.3) 5) 1(ab) = ab 6)

implify.

9) ‐9(‐10)

143 1 143− = −i

0 ( 76.3) 0⋅ − =

S

7) ‐4(7) 8) 5(‐7.2)

(132

2− −10) ) 1.9(3.3)(7)

valuate the expression when x = ‐2 and y = 3.6.

3) 2x + y 14) ‐x – 3y 15) xy – 5.4

6) 17)

11) ‐ 12) 0.5(‐20)(‐3)

E

1

2 2x y+ 2 2x y− 18) 1.5x y− − 1

In 1940 the surface area of the Dead Sea was about 980 square kilometers. From 1940 to 2001, the average rate of s per year. Find the surface area of the Dead Sea in 2001.

19)change in surface area was ‐5.7 square kilometer

14

.5: The Distributive Property

emember that 2(x – 4) = 2x – 8 and 4x + 3x = 7x (4x and 3x are called LIKE TERMS!)

xamples:

lify the

) 5(x + 11) 2) 3(x – 12) 3) ‐4(x + 8)

) 8) 2x(x – 1) 9) ‐x(5x + 2)

12x

3

6) 11x – (x + 7) 17) 9 – 2(x – 4) 18) 7x – 3(4 – 2x)

Lesson 7: 2.5

2

R

E

Simp expressions.

1

4) 9(2x + 1) 5) (‐10)(x – 7) 6) (4x + 3)5

7) x(4x – 1

10) 6 + 10x + 3 11) 2(3x + 1) + 4x 12) 6(5 – x) +

13) 7(x – 1) – 5 14) 8x + 3(2x – 1) 15) ‐2(x + 4) –

1


15

.6: Divide Real Numbers

ind the multiplicative inverse:

‐18 2)

2

F

12

− 3) 59 1)

Simplify the expression.

) ‐21 3 5) ‐18 ÷ ÷ (‐6) 6) ‐1 ÷ 72

⎛ ⎞−⎜ ⎟⎝ ⎠

4

7) 15 ÷ 34−⎛ ⎞

⎜ ⎟ ⎝ ⎠

8) 1 12 5

− ÷ 9) ( )42

7−

÷ −

numbers: 7, ‐4, 1, ‐9 and ‐6

implify the expression.

1)

10) Find the mean of the

S

6x 14

2−

12) 12y 8

4−

− 13)

20b 125

− +−

1

2y x

x−

14) Evaluate when x = 1 and y = ‐4.

5) Evaluate 2

9xy 1−−

1 when x = ‐3 and y = ‐2.

16

.7: Finding Square Roots and Compare Real Numbers 2

Evaluate the expression:

4 49 9− 3) −1) 2)

4) 121± 6) 1± 5) 225−

pproximate the square root to the nearest integer.

A

187) 10 8) − 9) 40

10)

200− 11) 86 12) 65−

or False?

All who

4) All real numbers are irrational numbers.

5) No perfect squares are whole numbers.

rder from least to greatest.

True

13) le numbers are real numbers.

1

1

16) No irrational numbers are whole numbers.

O

12, 3.7, 9,2.9− 16) −

17)

2

8, ,−

−1,0.6, 6 5

178.3, 80, , 8.25, 100

−− − − − 18)

2


17

.1: Solving One Step Equations

olve each equation. Show all work and check your solutions!

2) 11 = x + 6 3) t – 5 = 7

4) ‐2 = x – 6 5) 6 = 9 + x 6) ‐8 = d – 13

7) 5x = 20 8) ‐4t = 52 9)

3

S

1) X + 5 = 8

x

4= − 2

10) x

7 = 11) b – 0.4 = 3.1 12) ‐3.2 + z = ‐7−

7.4

13) ‐3.3x = 19.8 14) 3

x 18= 15) 2

x 167−

= 2

6) 4 2

x3 3−

= 17) y

0.120.5

− =−

18) 1

x 202

= 1

18

3.2: Solving Two Step Equations

Solve the equations. Show all work and check your solutions!

) 3x + 7 = 19 2) 5h + 4 = 19 3) 7d – 1 = 13

)

1

x

4 63+ = 5)

b9 11

2− = 6)

210 x 4

7= + 4

7) 2x + 7x = 54 8) 11x – 9x = 18 9) 6 = ‐7x + 4x

0) 5.6 = 1.1x + 1.2 11) 1.2x – 4.3 = 1.7 12) ‐5.3 = 2.2x – 8.6

3)

1

c

8.3 11.35.3

+ = 14) x

3.2 4.62.5

+ =1 15) 7.2y + 4.7 = 62.3

19

esson 10: Solving Multi‐Step Equations

LL K

) p + 2p – 3 = 6 2) 11w – 9 – 7w = 15 3) 23 = ‐4m + 2 + m

4) 3 + 4(x + 5) = 31 5) 14 + 2(4x – 3) = 40 6) ‐3 = 12y – 5(2y – 7)

7x – (6 – 2x) = 12 8)

L

Solve the equations. SHOW A WOR and check your solutions!

1

( )3x 5 6

2− = −7) 9) 27 = 3c – 3(6 – 2c)

0) 8.9 + 1.2(3a ‐1) = 14.9 11) 1.6 = 7.6 – 5(k + 1.1) 12) x + 1 = 3x – 1

3) 8x + 5 = 4x – 11 14) 3(x + 12) = 8 – 4x 15) 7(x + 7) = 5x + 59

1

1

20

esson 11

AST LESSON: ARE YOU READY FOR ALGEBRA 1?

o – you have worked through all the problems, and you have checked all of your answers. Take the following test and grade it yourself to see how well you understood everything. For any questions that are incorrect, please go back and x. GOOD LUCK!

L

L

S

fi

Expressions, Equations, and InequalitiesFor Exercises 1–3, evaluate the expression for the given value of the variable.

1. x2 1 5 when x 5 3 2.5}6 y when y 5 18

3. 20 2 a3 when a 5 2

For Exercises 4–6, evaluate the expression.

4. (5 1 2)2 5. 3[(4 1 6) 4 5]

6. 6 (27) 2 8 1 (52 2 4)

7. The diagram shows a box and a gift box.

14 cm15 cm

15 cm

15 cm

14 cm

14 cm

gift box box

a. What is the volume of the gift box?

b. When you put the box in the gift box, is there any empty space left? If so, what is the volume of the empty space?

8. Which is equivalent to the sum of four and the square of b?

A. 4b2 B. 4 1 b2

C. (4 1 b)2 D. 42 1 b2

9. Write an inequality: The quotient of 16 and b is at most 4.

A. 16}b

4 B. 16}b

4

C. b}16

4 D. b}16

4

10. At the hardware store, Maya buys n boxes of nails for $1.99 per box and b boxes of bolts for $2.49 per box. Which expression represents Maya’s purchase?

A. 1.99n 1 2.49b B. (1.99 1 n)(2.49 1 b)

C. (1.99 1 2.49)(n b) D. 1.99n 2.49b

Answers

1.

2.

3.

4.

5.

6.

7a.

7b.

8.

9.

10.

Benchmark Test 1

Name Date

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1Algebra 1

Benchmark Tests

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Answers

11.

12.

13.

14.

15.

16.

17.

18a.

18b.

18c.

19.

Benchmark Test 1 continued

11. Barry’s salary is $9.45 per hour. Which expression represents Barry’s earnings for h hours?

A. 9.45h B. h 2 9.45

C. 9.45 1 h D. h 4 9.45

Problem SolvingFor Exercises 12–15, state whether the given number is a solution of the equation or inequality.

12. 2x 1 4 5 10; 4 13. t 2 5 < 8; 11

14. 6c 5 42; 7 15. h}5 5 25; 5

For Exercises 16 and 17, read the following problem and answer the questions.

You make 100 refrigerator magnets to sell at a local crafts fair. Each magnet costs $.60 to make. In addition, you spend $50 for a booth and set up. Assuming that you sell half of your magnets, how much should you charge for each magnet to make a profi t of $100?

16. What do you know and what do you need to fi nd out?

17. Write and solve an equation to answer the question.

18. A restaurant charges $7 for a regular meal and $5 for a child’s meal. Both prices include tax.

a. Write an expression for the cost of a given number of regular and child’s meals.

b. A family has $35 to spend at the restaurant. Write an inequality to represent the maximum number of regular and child’s meals they can buy.

c. Does the family have enough money to buy two regular meals and three child’s meals? Explain.

Representations of Functions 19. The table shows how many newspapers Malcolm delivers and how

much money he collects from his customers.

Newspapers, n 12 15 18 21

Money, m $24 $30 $36 $42

Write a rule to describe how much Malcolm would collect for delivering n newspapers.

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Answers

20.

21.

22. See table.

23. See table.

20. The table shows amounts in U.S. dollars and the equivalent amounts of Mexican pesos on a certain day.

U.S. dollars, x 20 30 50 60

Mexican pesos, y 80 120 200 240

Write a rule to describe the relationship between dollars and pesos on that day.

21. Which is a rule for the function shown?

y

x

5

4

3

2

1

67

8

6 7 851 2 3 4

(3, 0)

(5, 2)

(7, 4) (8, 5)

A. y 5 23x B. y 5 3x

C. y 5 x 2 3 D. y 5 3 2 x

22. Make a table for the function shown.

26

y

x22

26

28

24

22

2

4

6

8

6 82428 42

(22, 25)

(0, 21)

(2, 3)

(4, 7)

x

y

23. Make a table for the function y 5 23x 1 4, with domain {22, 21, 1, 2}.

x

y

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Answers

24a. See graph.

24b.

24c.

25.

26.

27.

24. Jess puts 2 pennies on the fi rst square of a checkerboard. He stacks 4 pennies in the second square. In the third square, he stacks 6 pennies. Jess stacks 8 pennies in the fourth square.

a. Graph the function for the fi rst four squares.

1

2

3

4

5

6

7

8

4 5 6 7 8321

p

n

b. Write a rule to represent the number of pennies in the nth square.

c. What is the combined number of pennies that Jess puts in the 16th, 17th, 18th, and 19th squares?

25. What is the range of the function y 5 2x 1 2 with domain {3, 6, 8, 9}?

A. {23, 26, 28, 29} B. {21, 24, 26, 27}

C. {3, 6, 8, 9} D. {5, 8, 10, 11}

For Exercises 26 and 27, write the domain and range of the function on the coordinate plane.

26. y

x

5

4

3

2

1

67

8

6 7 851 2 3 4

(1, 2) (3, 3)

(2, 1)

(4, 4) (5, 4)

27. y

x

10

8

6

4

2

1214

16

12 14 16102 4 6 8

(2, 12) (6, 10)

(8, 2) (10, 2)

(12, 6)

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Test

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Answers

28a.

28b. See graph.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47a.

47b.

48.

49.


28. Each week, Nina saves $2.50 from the money she earns mowing lawns.

a. Write a rule to represent Nina’s total savings after w weeks.

b. Graph the function for the fi rst 4 weeks.

s

w

10

8

6

4

2

1214

16

6 7 851 2 3 4

Operations

For Exercises 29–31, given the value of a, fi nd 2a and |a |.

29. a 5 23 30. a 5 0.2 31. a 5 2Ï}

5

For Exercises 32–46, evaluate or simplify the expression.

32. 2 7}8 1

2}3

33. 8 1 (26.2) 34. 25 1 (212)

35. 22.4 2 9.3 36. 9 2 (23) 37. 2 1}3 2 12

1}2 2

38. a(2b)(21) 39. 4 7t 40.3}5 (210) (22)

41.3}5 4 (29) 42.

1}6

4 6 1}4 43. 3 4 12

1}9 2

44. Ï}

121 45. 2Ï}

144 46. 6Ï}

64

47. Given a 5 22 1}5 ,

a. What number multiplied by a equals 1?

b. Explain how you found your answer.

48. Petra rides her bicycle 4.5 miles on Monday, 1.6 miles on Wednesday, and 3.2 miles on Friday. What is the mean distance Petra rides?

A. 3.1 miles B. 1.6 miles C. 3.2 miles D. 9.3 miles

49. A weather report predicts that the temperature will drop 3°F per hour. If the temperature starts at 12°F, what is the temperature after 6 hours?

A. 218°F B. 26°F C. 3°F D. 9°F

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5Algebra 1

Benchmark Tests

Ben

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Answers

50.

51a.

51b.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

50. Evaluate the expression 2Ï}

36 1 Ï}

144 .

51. The lengths of two legs of a right triangle are 5 feet and 6 feet. By the Pythagorean Theorem, the length of the third side of the triangle

is Ï}

52 1 62 .

a. Approximate the length of the third side to the nearest whole foot.

b. Explain how you found your answer.

Properties of Real Numbers 52. Can a whole number also be considered a rational number? Explain.

53. Which is the most specifi c classifi cation of the number 2 5}8 ?

A. real B. integer C. rational D. irrational

For Exercises 54 and 55, write the numbers in order from least to greatest:

54. |27|, Ï}

50 , 26.9, 2 21}4 55. 2Ï

}

3 , 3}2 , 2|23.2|, 24

56. Which property is illustrated by the equation 25(3x 1 2) 5 215x 2 10?

A. inverse B. identity C. commutative D. distributive

57. Write a statement of the identity property of addition in terms of a

real number 1}3 m.

58. Which equation illustrates the commutative property of multiplication?

A. 5(x 1 2) 5 5x 1 10 B. 5(2x) 5 10x

C. 5(2x) 5 (2x)5 D. 5(2x) 1

}5(2x)

5 1

59. Jake writes the following:

2212 1}2 x 2

5 122 2 1}2 2x Step 1

5 x Step 2

List a property of real numbers to justify each of Jake’s steps.

For Exercises 60–62, use the distributive property to simplify the expression.

60. 2x(4x2 2 5x) 61. (4n 2 6) (23n) 62. x}2 (4 1 2x 2 4y)


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LESSON 1 LESSON 2 LESSON 3 LESSON 4 LESSON 5 Lesson 6 Section 1.1 1) 2.4 2) 13.3 3) 3

4) 13

5) 13

6) 3649

7) 8

8) 116

9) 243

10) 27125

11) 1681

12) C 13) 30 14) 162.5 cm Section 1.2 1) 47 2) 13 3) 32

4) 1

182

5) 0 6) 48 7) 29 8) 11 9) 0.75 10) 3 11) (9 + 39 + 22) ( 11 – 9 + 3)

÷

Section 1.3 1) 9+x 2) 6x 3) 7 – x

4) 2t12

5) 2x 3−6) 2x – 7 7) 15( x + 12)

8) 50

2y 8

⎛ ⎞⎜ +⎝

⎟⎠

9) 8 students per group 10) 1.5 pints per serving 11) 2.4 runs per innings 12) $6.80 per share

13) 3

116

miles

in 1 minute and 55 seconds Section 1.4 1) n+42=51 2) z‐11=35

3) t

9 56

− =

4) 9(t + 5) < 6 5) 4x 51 ≤6) n + 4 13 ≤

7) t

154.2

≥

8) D 9) x = more miles 12.5 + x = 20 10) x = more CDs x + 27 40 ≤11) x = # of batches No – you can make 7.2 batches or less 12) x=amount neighbor paid $100

Section 1.5 1) a) 7 in. by 7 in. b) 2,352 sq. in. c) 66 inches d) 24 sq. in 2) No – you

are $0.50 short

3) 1,352 cubic inches

4)a) x20

b) 6 shelves

5) 1

42inches

6) $120 7) 137.5 miles 8) $218.88

Section 1.6 1) D={0,1,2,3} R={7.5, 9.5, 11.5, 13.5} Function

2) D=1 2 3

, ,2 3 4

⎧ ⎫⎨ ⎬⎩ ⎭

R={0, 1, 3, 5} NOT a function 3) D={7,11,21,35} R={13,8,13,20} Function 4) R={4,14,19,24,29} 5) R={5,6,7.5,8} 6) y = x + 2.2 7) a) cost, #of books b) y = 5x c) D={0,1,2,3,4,5} d) R={0,5,10,15,20,25} Lesson 1.7 1) 2) 3) y = x D={0,1,2,3,4,5,6,7} R={0,1,2,3,4,5,6,7} 4) y = 2x – 2 D={1, 2, 3, 4} R={0, 2, 4, 6}

5) 1

y x2

2= +

D={0, 2, 4, 6} R={2, 3, 4, 5}

Section 2.1 1) 3:W, I, Rat ‐5: I, Rat ‐2.4: Rat 1: W, I, Rat ‐5, ‐2.4, 1, 3 2) 16: W, I, Rat ‐1.66: Rat 5

:3

Rat

‐1.6: Rat

‐1.66, ‐1.6, 53,16

3) 35−

: Rat

‐0.4: Rat ‐1: I, Rat ‐0.5: Rat

‐1, 35−

, ‐0.5, ‐0.4

4) ‐a = ‐6 a =6

5) ‐a = 3 a = 3

6) ‐a=6.1 a =6.1

7) ‐a=1

12

−1

a 12

=

8) 0.75 9) 1.75 10) 1.5 11) 2.25 12) Wednesday 13) ‐12 Section 2.2 1) Additive inverse 2) Assoc. Prop of Ad 3) Comm Prop of Ad 4) Additive identity 5) Assoc. Prop of Ad 6) Comm Prop of Ad 7) ‐15 8) ‐2.13

9) 1

205

− 10) 19

560

11)17

520

− 12)7

2124

−

13) 23

7 14) 145 feet 60

Section 2.3 1) 18 2) ‐16 3) ‐8 4) 17 5) ‐2.8

6) 35

7) 4.6 8) ‐21.6 9) 10.6 10) ‐4.2 11) 34.1 12) ‐14 13) 8 14) ‐14 15) ‐14 16) 12.2 ° C Lesson 2.4 1) Mult Prop of zero 2) Mult Identity 3) Assoc Prop of Mult 4) Comm Prop of Mult 5) Mult Identity 6) Mult Prop of zero 7) ‐28 8) ‐36 9) 90 10) 16 11) ‐43.89 12) 30 13) ‐0.4 14) ‐8.8 15) ‐12.6 16) 16.96 17) ‐8.96 18) ‐6.6 19) 632.2 square miles

Y

X

Y

X

21

LESSON 7 LESSON 8 LESSON 9 LESSON 10 MATRICES

1) 16 48 12

⎡ ⎤⎢ ⎥⎣ ⎦

2) 15 4 92 2 5

− − −⎡ ⎤⎢ ⎥− −⎣ ⎦

3) NOT POSSIBLE

4)

38 0

41

0 26

⎡−⎢ ⎥⎢⎢ ⎥−⎢⎣

⎤

⎥

⎥⎦

5) 28 491

3 42

− −⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

6)

1820.44.2

−⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

7)

79 13

81

10 13

−⎡−⎢ ⎥⎢⎢ −⎢ ⎥⎣ ⎦

⎤

⎥⎥

8)

3135

⎡ ⎤⎢ ⎥−⎢ ⎥⎢ ⎥−⎣ ⎦

Section 2.5 1) 5x + 55 2) 3x – 36 3) ‐4x – 32 4) 18x + 9 5) ‐10x + 70 6) 20x + 15 7) 24x x−8) 22x 2x−9) 25x 2x− −10) 10x + 9 11) 10x + 2 12) 6x + 30 13) 7x – 12 14) 14x – 3 15) ‐2x – 11 16) 10x – 7 17) ‐2x + 17 18) 13x – 12

Section 2.6

1) 1

18−

2) ‐2

3) 4

15

4) ‐7 5) 3

6) 27

7) ‐20

8) 1

22

−

9) 27

10) ‐2.2 11) 3x – 7 12) ‐3y + 2

13) 4b ‐ 2

25

14) ‐9 15) 9 Section 2.7 1) 2 2) ‐7 3) ‐3 4) 11 ±5) ‐15 6) 1 ±7) 3 ≈8) ‐4 ≈9) 6 ≈10) ≈ ‐14 11) ≈9 12) ≈ ‐8 13) True 14) False 15) False 16) True

17) ‐3.7, 12− ,2.9, 9

18) 2

1, ,0.6, 6, 85−

−

19) 100− , 80− , 172−

,

‐8.3, ‐8.25

Section 3.1 1) x = 3 2) 5 = x 3) t = 12 4) 4 = x 5) ‐3 = x 6) 5 = d 7) x = 4 8) t = ‐13 9) x = ‐8 10) ‐49 = x 11) b = 3.5 12) z = ‐4.2 13) x = ‐6 14) x = 12 15) x = ‐56 16) ‐2 = x 17) 0.06 = y 18) x = 40 Section 3.2 1) x = 4 2) h = 3 3) d = 2 4) x = 6 5) b = 40 6) 21 = x 7) x = 6 8) x = 9 9) ‐2 = x 10) 4 = x 11) x = 5 12) 1.5 = x 13) c = 15.9 14) x = 3.5 15) y = 8

Section 3.3 1) p = 3 2) w = 6 3) ‐7 = m 4) x = 2 5) x = 4 6) ‐19 = y 7) x = ‐29 8) x = 1 9) 5 = c 10) a = 2 11) 0.1 = k 12) 1 = x 13) x = ‐4 14) x = ‐4 15) x = 5

22

Answer Key

Benchmark Test 11. 14 2. 15 3. 12 4. 49 5. 6 6. –29

7a. 3375 cm3 7b. 631 cm3 8. B 9. B 10. A

11. A 12. No 13. Yes 14. Yes 15. No

16. You know the number of magnets you have to sell, the cost per magnet, the amount you spend on the booth and set up, and the amount of profit you want to make; You want to find the price per magnet so that if you sell half themagnets you make a profit of $200.

17. 50p 2 [100(0.60) 1 50] 5 100; You should sell each magnet for $4.20.

18a. 7r 1 5c 18b. 7r 1 5c ≤ 35 18c. Yes; 7(2) 1 5(3) 5 29, which is ≥35.

19. m 5 2n 20. y 5 4x 21. C

22. x 22 0 2 4

y 25 21 3 7

23. x 22 21 1 2

y 10 7 1 22

24a. p

n

5

43

2

1

67

8

6 7 851 2 3 4

(1, 2)

(2, 4)

(3, 6)

(4, 8)

24b. p 5 2n 24c. 140 25. B 26. Domain: 1, 2, 3, 4, 5; Range: 1, 2, 3, 4 27. Domain: 2, 6, 8, 10, 12; Range: 2, 6, 10, 12 28a. s 5 2.5w

28b. s

w

10

86

4

2

1214

16

6 7 851 2 3 4

(1, 2.5) (2, 5)

(3, 7.5)

(4, 10)

29. 2a 5 3; | a | 5 3 30. 2a 5 20.2; | a | 5 0.2

31. 2a 5 Ï}

5 ; | a | 5 Ï}

5 32. 2 5 }

24 33. 1.8

34. 217 35. 211.7 36. 12 37. 1 }

6 38. ab

39. 28t 40. 12 41. 2 1 }

15 42.

2 }

75 43. 227

44. 11 45. 212 46. 68

47a. 2 5 }

11 47b. The inverse property of multiplication statesa p

1 } a 5 1. Since 22

1 }

5 5 2

11 }

5 ,

1 } a 5 2

5 }

11 .

48. A 49. B 50. 6

51a. 8 ft 51b. Ï}

61 is between Ï}

49 and Ï}

64 . So, it is between 7 and 8, and iscloser to 8.

52. Yes; Any whole number can be expressed as the quotient of itself divided by 1.

53. C 54. 26.9, 2 21

} 4 , |27 |, Ï

}

50

55. 24, 2|23.2|, 2 Ï}

3 , 3 }

2 56. D

57. 1 }

3 m 1 0 5

1 }

3 m 58. C

59. Associative property of multiplication; inverse property of multiplication

60. 8x3 2 10x2 61. 212n2 1 18n 62. 2x 1 x2 2 2xy

Answer Key

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Dear Maverick Math Student; Entering Algebra 1 Summer ... · optional but suggested. summer assignment is attached. Mathematics requires good work habits, a willingness to think,