n.Su)er^Xl'gebra 1 Part 1
, Date:
Period:
Chapter 1: Expressions and Equations.Packet
Lesson
1.1
1,2
1.3
1.4.
«
Goal; We are learning to:
evaluate algebraic expressionsand exponents;
apply the order of operations toevaluate expressions;
translate verbal phrases intoalgebraic expressions;
translate verbal sentences intoalgebraic equations orinequalities;
use formulas to solve real-lifesituations;
Chapter 1 Quiz
Block Date
1.1 Notes WALT: Evaluate expressions and use exponents
A js a letter used to represent a number. Examples: x, y, t, a
An £vOiS.DrCu'c €L>r press 10 K> consists of numbers and or variables and at least one
operation. An algebra-ic expression must contain a variable.
Algebraic Expression
5(n) 5 •«• 5n 5 *n
^ 2^y
a + b8 -y
Meaning5 times n
2 divided by y
a plus b8 minus y
OperationMultiplication
Division (In algebra we use thefraction bar to show division)
AdditionSubtraction
To •£\fg\Ua"Wi qUf^-CUC _
the variable, perform the operation(s) and simplify.
Evaluate the following expressions when y = 2:
1. 6y
P T. means to substitute a number for
y%- - da -t
3. y + 4 4. 11- y
is an expression that represents repeated multiplication of the same factor.
i27 is a power of 3 because 3 • 3 • 3 = 27
Read properly and then write as a product and then evaluate if possible:
A
24 =- . 10, 2.i 2- 2 - [b
3. z5 ^.
A power can be written in a form using two numbers, the base and the exponent:
^ L-L34 is a power. -J3 is the base. j is the exponent.
It means multiply the base by itself exponent times.
Evaluate:
3. O5 O
2. 10'
4. 33
s.|i -i- '4- , J^ ~ " —D O
7. s. r
9. xj Vv'henx-S
11. whend- —o
10. /:2 when k* 1.1
Exponents are used to find the area of a square snd the volume of a cube. The ares of a square is
and the volume of a cube is s3 where s Is the side length.
Find the area of the square: Find the volume of the cube:
a
Which is Correct? Circle your answer.
10 -2
5
3 - 2 + 4 ^ 2
18 -2
9
3 , 2 + 4 - 2
What do you recall about the Order of Operations?
O s
Use the Order of Operations to Evaluate these expressions. Show each step,
"~PrY on
1) 27- 32 * 2 -3 " n\S2J32-2 + 6
M-Vfc
3)15+ 6^ - 4
/^f-36 -f
SI -^
4) 36 -^ 3(4) Rewrite this expression. What does the parenthesis represent?
3
3
Lesson 1.2: imbedded Grouping Symbols C ( ) ]
Hint: start inside and work your way out. Inside > Out
Teacher Led Exarnpfe: 3 [ 25 - (3 * 2} (Show each step)
TRY (show each step): a)
©
A fraction bar acts as a grouping symbol. Remember groupings are performed firstin the order of operations.
When the numerator and/or denominator is an expression, -you must always simplify thenumerator and denominator before dividing. HINT; use parenthesis ( } around thenumerator and use ( ) around the denominator to remind you to simplify first
EXAMPLE:6+8 (6+8)
4-2 (4~
When you forget to simplify'.
- (6 + 8)
6+8
4-2
(4-2) - 14*2 = 7 YES!\\\ 4-2 = 6 + 2-2 = 6 NO!
TRY (show each step):
9+3 IX
3-1 - (o7-2
1+5
Lesson 1.2: EVALUATE each expression. Show each step.
1,
2.
3,
-9 + 4-3
( 5 - 3 )
2 (c2 + 4) when c =
4. c ^ - S • when g = 6
2g-5
*2- -7
5. - 8 when g = 2
2g +7
o
6. O.Sx + 4.49 when x = 26.5
±11n,7f
F
Name Date'.
Practice BFor use wjth psgss 8—13
•' Cci jJyaU- ^roilemSEvaluate the expression.
if 1 A . . Q . SI . JlO ^^ o ~> •
4. 13 ^ 6 4 - 4 - 3 '
• 7. 8(6-2)4-4
10. "(11 4- 15)-M3
c\_ s epo_m3%. -^'hee'Si-iOOO cvU
2, 72-24^3
S, 13-15^-54-9
8. 28-3(44-5)
11. -35 -32- 2
3. 5 -f- 1.2 -4- 03
2 T
9. L2 * 5 - 6 * 3
12. ~(3 -20)-H
20
Evaluate the expression. . .
13, 3x4 — 5 when* — 5 . 14, Sra3 -*• 6-when.Tn ~ 3
16, Sc2 - 2c when c = 9 17. 3-
= 10 20.
15. 200
4213. -- h TI when « = 6
a -6When a ~ 8 21. • when d = 3
22. Was the expression evaluated correctly using the order of operations? If not, find andcorrect the error. • ' -
23. Tournarnerit Dnriug a howling tonrnament, yon howled three games with scores* of 110, 130, and 129?respe<^ery,YonrayeragehowIJng score is given
25 = 55
hy- 130+129r. What is your average score?
Parntmg Three ?/eeks ago, an art.sirpply store started selling'apamtHtfor 75%of the original price. Now the Mt is 15% off of the sale price. The expression0.75;c — 0,'15(Q.75.r) represents the current price of the paint kit where x is the kit'soriginal price (in dollars). Find the cnrrent-price'of the kit if it originally cost $48.
Crnvfn. Molding Yon are decorating the perimeter of the ceiling of yonr living roomwith crown molding. The esgpression 2r 4- 2y represents the total amount.of moldingyon need where x is the width of the room (in feet) and}' is the length of the room(in feet): Find the total amount ofwoodyon need ifihe room is 11 feet wide and10.5 feet long.
Core Sample B efore a structure is bruit on a plot of land, it issometimes necessary to test the sorface beneath the plot of land todetermine its integrity. So, it may be necessary to take" a core sample-which is cyrrndrical in shape. End the volume of the core sampleshown by using the expression irp-h where r is the radios (in inches)and h is the height (mmches)' of the cylinder. Use 3.14 for IT.
1,10 2.41 3.9 4.15 5.19 6.1 7.36 8.1 9.4 10.2 11.13 12.31 13-187014.36 15. S 1G.387. 17.6 18.13 19.105 20.20 21.9
26.
22-. no,- SO - }(15): = SO - |(225) = SO 75 = 5 23.123 24. S30.60 25,43ft 26. 1017.36 in.3
Algebra 1Chapter 1 Resource Book
Do H.O
&*t
•ffl.
1-3 Variables and Expressions
Name Date
Operation Clue Words
•- !--
u sS u_ro
More
t -^ ftrt p
. \
Common mistakes when translating:
1. Order is important when writing subtraction and division expressions:
The difference of a number n and 6 is n - 6 not 6 - n
k - 2The/ quotient of a numb er k and' 2 is ~- not
2s K,
2. Difference between "less" and "less than":
5 less x is: 5 - x ;
5 less than x is: x-5 • L...I
'" ' 3. The words quantity, sum, difference sometimes mean you must use parentheses:
3 times the sum of 7 and a number n: 3 ( 7 + n)
'
The quotient when the quantity 10 plus a number x is divided by 2:* . Z-i
r
5 times the difference of x and 2: 5 (x - 2)
Common. xaistak&s when translating Ter bai pixrases-imu -mg
1, Order is important v&eax writing subtraction and division expressions:
Xhb difference of a number 71 and 6 is rt — 6 NOT 6 - n
k 2he quotient of a mmiber^: and 2 is ~ NOT ~
2-. CoS5sforTBetw&&D. " I s o i d "less fh.au":
51essri£z 5— x
5 less than x is: 2:— 5
S. Ike words "tke qu-a^iity" , * the sum?) j tctie difference-', sometmesmeaayounnistuseparenttiesis in 3Tour algebraic expression;
3 times tnfc 5iito of 7 and a number n is: 3 [ 7 4- 7-1)
(10-fx)Th3 quotient y/hen ite gnaatity 10plusajmmberxasdi-rf<3edby2is: —
5 times the difference of?; and 2 is: 5 ^ — 2
Translate each of the verbal expressions into Algebraic Expressions:
Word Phrases for ADDITION Algebraic Expression
1) 5 more than sorrie number
2j A n umber, "n", increased by 2
3} 3 plus-some number [rx"
4) The sum of a number, "y" and 4
5} A number add&d to S.
o ^—
1.3: WALT translate verbal phrases into algebraic expressions
Word Phrases for ADDITION Algebraic Expression
6} Sally is "m" years old. Her brother,Mike, is 2 years older than Sally.How old is
m
Word Phrases for SUBTRACTION Algebraic Expression
7) 3 less than some number, "y" 3
8) A number, "n"3 decreased by 7
9} 5 minus some number "x"
10} A number, "x" minus 5 X
11) The difference between 2 andsome number
12) The difference between a numberand 2
13) 9 less than some number
14) 9 less a number
1.3: WALT translate verbal phrases rnto algebraic expressions
Word Phrases for SUBTRACTION Algebraic Expression
15) Troy is "y" years old. His sisterDonna is 3 years younger thanTroy. How old is Donna?
Word Phrases for MULTIPLICATIOM Algebraic Expression
18) 7 times a number n
17} Twice a number
18} One fourth of some numberLL
19} The product of a number and 3
20) The square of some number n
21) One third of some number n M-or 3
1.3: WALT translate verbal phrases into algebraic expressions
Word Phrases for DIVISION Algebraic Expression
22} The quotient of 15 and somenumber n
23) The quotient of a number and 15
24) A number divided by 11
25) The ratio of six and some number
26) 20 divided by a number
r\) The ratio of some number and six
TWO Operations in Word Phrases Algebraic Expression
28) Three less thanlthe quotient of anumber and six\
29} Eight times/the sum of a numberand two\
30) [The product of a number and eightplus two -* -v-
I I
1.3: WALT translate verbal phrases into algebraic expressions
TWO Operations fn Word Phrases Algebraic Expression
31) Nine more than five times anumber n
32} Two degrees less than double atemperature
33} Six inches [ess than three fourthsof the length "x"
24} The difference between a numberand five divided by 2
35) 8 times the quantity of 4 plus x
36} The quotient of the square of anumber v/and 5
>oS
e 2OT N
OCDc_m
m
Ho
IImto
CD0)
5'5"e.
(Q
o'
I
Why Did the Cow Keep Jumping Over the Barrel?Translate each phrase below Into an algebraic expression and find your answer in the corresponding answer column.Write the letter of that exercise in the box that contains the number of the answer. '
E) 3 times a number
O) 3 more than a numberi^~*-
S) 3 decreased by a number'
3 less than a number
A) one third of a number
8 more than 3 times a number
N) 8 less than 3 times a number
(18) x + 3
(J5) 3x-8
19 x -3
3 3x
3-x
S) 5 times a number, increased by 8
5 times the sum ofa number and 8
H) 5 more than 8 times a number
8 times the sum of a number and 5
twice the sum of 5 times a numberand 8
T) 2 more than five eighths of anumber
8 times the sum of twice a numberand 5
2(5x
(20) 5(x + 8)
AJ 7 less than 4 times a numberr
7 decreased by 4 times a number
G 9 (ess th.an twice a number
9 decreased by twice a number
O) 9 less than half a number
J 7 times a number, increased by 4
R) 7 times a number, increased by 4times the number
7-4x
14
4x-7
7x + 4x
9-2X
T) 9 meters higher than altitude x
15 meters per second slower thanspeed x
15°C hotter than temperature x
9 meters shorter than twice length x
C) 9 years older than twice age x'- v
H) $9 cheaper than 4 times price x^ ..M) 9 centimeters less than three
fourths of length x
(7) x + 15
(28) x + 9
26 4x^9
2x-9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Name. Date
(~^ Prdctiee B
For use wiffi pages 14—20
Translate the verbal phrase trrto an expression,'
2, The quotient-ofarromBery and 22
7
1, .The difference of 9 and a number n
3, The sum of 57 and amtmber 6
5, IS less'thananrrmberc
7. The quotient of 8 and twice anumberz
Write an expression for the situation.
of a number x . •
6- 25 more than twice a ntnnberm:
S. The sum of 2 and the-square of a number r
10. The total height of al-foottan Drrdbathrf It is placed'on a base that is b feet fell
11, Eachperson's.share of baseball cards if 4-people share c cards equally
12., ISfumber of minutes in. Ti hours ._ :
Find the unit rate.
$755-video-games13. 14. 600stodents
8 classes15.
32 pencils4-"boxes
16. Candle. IVlaferjig Yon. are making candles for yo-ur friends, A. mold for the candlescosts $22'.5Q and was to make one candle costs $5. Write an algebraic expression, for
• tbetotal cost of roakingx candles, %umak:e 8 candles, Pind the total cost •
17. Baseball Last season, a baseball player scored 14 runs in. IS games. This season,the baseball player scored 12 runs in 15 games. Knd the number of runs scored pergame in each season, Hound your answers to the nearest hundredth- Then identifythe season in which the player scored more runs per game.
IS. Car Trip 15ra are getting ready to make a 640-mile car trip. ro. general, youx car candrive 1 SO miles on 5- gallons of gasoline. How many gallons of gasoline wnl you usefor the trip? You started out with 4 gallons of gasoline in yorrr car and gasoline is$2,29 per gallon. How much, money win you spend on gasoline o-n the trip1?
19. ' Plant Trellis Yon are braiding the wood trellis shown in thefigure so that you can grow a vine up me side of your home,
• Write an e-rpression. for the total ntrmber of feet of wood neededto buSd the trellis. Hmt; Write separate expressions for thenumber of feet of vertical pieces needed and the number "of feetof horizontal pieces needed. Then find the total number of feetof wood needed if the trellis is S feet tail and 2 feet wide.
* ' " ' * . •Lesson T.3
F.ractlce Level B
1 Q _-22 3-5'?-i-6 4-1; a. 40 - d
13. SIS/video game 14. 75 s^nte/dass is. S pencils/box
30 Chapter 1 Resource Book
ro
a?
* I >6t Wtl tktf Elwtrfcfei4 C <iy After Fi*% * LF0kt r ilfrEwpn* $t#te &trltlw<j?
|r Translate any phrase below into algebraic terms and find your answer in the corresponding answer column. Write the letter of theT, m exercise in the box that contains the numbercr 3D
|< F 5 more than 2 times a number'o 23 2 • H 7 less than 5 times a number
S E 5 times a number, decreased by 2N
te 1 2 diminished by 7 times a numberS 2 increased by 5 times a numberT twice a number, decreased by 7G 2 more than 7 times a number
A 9.. less than a number* '~• [ 4 times a number, plus 9T. 9 diminished by 4 times a number0 one-fourth of a number .S 9 times a number, decreased by 4E 4 more than 9 times a numberH 9 times a number, increased by
of the answer.
27
11
2219
6714
16
425
26
21
18
4 times the number
1 2 3 4 5 6 7 8 9 10 11 12 13
5x
7x
-2
+ 2
2 + 5x2x2x5x2-
9x
X"
9 -9x9x4xx4
14
+ 5- 7
-7- 7x
Keep working and you will discover the answer to the title question.
W 2 times a-number, increased by 8 8 3(x + 8)I 2 times the sum of a number and 8 28 3(2x + 8)
A 3 more than 8 times a number 10 2(x+8)G 8 times the sum of a number and 3 24 8x + 3 ,E 3 times the sum of a number and 8 3 2x+VH two-thirds of a number 15 8(x H- 3)R 3 times the sum of twice a number 20 JLy
and 8 3;
_v
-f 4x I 10 meters higher than height x 23 x - 50- 9- 4x- 4+ '4+ 9
15
••• £L 10 mph slower than speed x 1 x+ 10"'C 50 meters deeper than depth x 12 6x - 2H 50 mph faster than speed x 25 2x + 6
y T 6 meters less than twice length x 17 2x - 6R 6 years older than twice age x 13 x - 10H 2 years younger than 6 times age x 9 x + 50
•:.'
16 17 18 19 20 21 22 23 24 25 .26 27 28
Notes 1.4 Writing Equations and Inequalities A1P1
Symbol=<<>>
Meaningis equal tois less thanis less than or equal tois greater thanis greater than or equal to
Associated Wordsthe same asf ewer thanat most; no more thanmore thanat least,' no less than
Translate verbal sentence into equation:
1. The difference of twice a number lc and 8 is 12.
2. The product of 6 and a number n is at least 24.
3. y is no less than 5.
4. y isnomorethao.13
5. The quotient of a number p and 12, is at least 30.
6. The difference of a number z and 11 is equal to 35.
37. The sum of 12 and the quantity 5 more than a number t is less than. 6.
8, The product of 4 and a number w is at most 51.
9 The sum of a number n and 4 £ no more than 13.
" v. '• -.. sq-.-et - 13
Notes 1,4 Dayl Open Sentences A1P1
An open sentence in math is one whose truth value cannot be determined.
Is the following statement true or false? is a teletubby.
Is the following equation true or false? x -f 2 ~ 5
If x —4., is the above true or false? If x = 3, is the above true or false '••
If you find a value that makes your equation or inequality true, it is a solution.
Is 6 a possible solution for the following inequality? t ,
x + 2<5
Check whether 3 is a solution to the following equations or inequalities:
a. 8~2x = 2
2
b. 4x-5 = 6
/- N —H" ( 3) ~3 - (Q
I 2^ - 5" - (p 7 '40 O
c. 2x + 5>12
- >
o
&- +- cf ~ 2°?
IN 7 less * '^) ~? C>
n
StudyFor use with pages 21—2$
f; Translate v&rbal sentences into equations or inequalities.
VocabularyAn open sentence is a mathematical statement that contains twoexpressions and a symbol mat compares them.
An equation is an open sentence that contains the symbol =,
An inequality is an open sentence that contains one of the symbols <
Y/hen you substitute a number for the variable in an open sentence, theresulting statement is either true or false, If me. statement is true, thenumber is a soltrQon of the equation, or a. solution of the inequality. -
=i|. J Write equations and Inequalities
Write an equation or an- inequality.
Verbal phrase.
! a. 3 times the quantity of 11 plus a number x is 112.
Equation
S(ll 4-x) = 112
b. The prodiicfc of 7 and. a. number y is nomors tfaan 31..
Wrrte an equation or an inequality.
1. Tae difference of 73 and a number x is 17.
2. The product of 8 and fee quantity of a number >f plus 6 is less thau^i
3. The-.quotient of a number W and 5 is at most 4.
Check possible solutions
Check whether 5 Is a solution of th& equation or inequality. \y Subrfitdte Conclusion j
-> -~j -i -3 /' S ^ T 7 1 O Q -Z- -)-^ Y ia. 3x — j — \2 j(:>) — J i 1-i b =F W A5 is nor a solufjon.
h. 9 -f 2(5) < 23
I 5 is a solution.
Check whether the given number'is a solution of t5e equation or'ineijuali^.1. 13+a-17:4 2. 75-3 = 10:2
7
Ves
3. 4c<15;3
K
Ansjver
II - 104. 21-3or>ll;2
1.73-x=17 2.
Name^^^^^^ss^^^^^^^^^^^m^^^^^^^^^^^^^^^^^^^^^^^s^^^s^^^^^^^^^^. = : D ate. - ' L__
Practice BFor use with pages 21-26
Write an equation or an inequality,
1. The difference of a number c and 17 is more than 3 3,
2. The product of 3 and a number x is at most 21.
3. The sum of 14 and twice a number 7 is equal.to 78.
4. The difference of 22 and the quotient of a number m and 4 is 54.
5. The sum of 7 and three times a number & is at least 12.
Check whether the given number is a solution of the equation or inequality,h
6. 6x +'7^ 25; 3- 3.. f- 7 = 1; 36
10. 4y~3>12;4 11. -f 14<33;9
Solve the equation using mental math.
12. x+ 9 = 11 " 13. 7-5 = 14. 8>v =
15. -r = 16. 2x - 1 = 15 17. + 2 = 20
.a
©
o*^>. f.= ^£-
X
Computers You are buying a new printer and a new scanner for your computer,and you cannot spend over $ 150. The printer you want costs $80. Write an inequalitythat describes the most thatyou can. spend on the scanner and still stay within yourbudget If you buy a scanner that costs $75, will you remain within your budget?
Go-Carts You and three of your friends are going to race go-carts. The last time youwent, you had a coupon for $3 off each admission and paid $48 for the 4 admissions.'What was the total price without the coupon? You pay the regular price this time andshare it equally. How much does each person pay?
Bracelets You are making beaded bracelets for your friends. You want to use3 0 beads for each bracelet and want to use no more than 145 beads. Write aninequality that models this situation. Can you make 4 bracelets?
Staircase When building a staircase, yon need to be concerned with the heightof the riser and the depth of the tread so that people can go up and down the stairs'comfortably. One rule of thumb used to determine proper riser height and treaddepth is that the sum of the-tread depth (in inches).and twice the riser height(in inches) should equal 26 inches. Write an equation that models this situation. •The riser height of a set of steps is 5 inches. What should the depth be?
Lesson 1.4practice Level B
1.'c-l7>33 2 -78 4 . 2 2 - = 5 4 . 6. yes
7. no S.no 9. yes 10. yes 11. yes 12.8 13.17 14.6 15.64 16.8 17.613. 80+ x< 150; no 19.$60;$15 20. 30* < 145; yes 21. t + 2r = 26; 16 in.
J>
Algebra 1Chapter 1 Resource Book 41
1,5 Formulas
Formulas to Memorize:
Perimeter of a rectangte: 2 ( L x W ) or 2L + 2Wwhere L = length of the rectangle
W - width of rectangle
Area of rectangle = L X Wwhere L = length of the rectangle
W - width of the rectangle
Area of a triangle: A — ~~bhjL*
where b = baseh - height
Area of a circle: A ~ 727-'where r = radius
Circumference of a circEe: C —where r = radius
Simple interest I = prtwhere I = interest earned or charged
,P..~ principle amount (amount invested or .borrowed)r = interest rate (as a decimal)t = time (years)
Distance Formula: d = rtwhere d - distance
r - ratet ~ time
Do not /rave to memorize- temperature formula
Temperature: C^~(^-32)
where F = temperature in Fahrenheit
1.5 Formulas
Hints to Memorize:
How well have your memorized the 1.5 formulas?
write each formula 5 times; say each formula out loud;flash cards; find an app; find a website;have someone test you; make up a matching game;
Are you ready? Without using your packet or text, fill in this chart. Check your answerson the next page: Reference 1.5 Formula. Any wrong, memorize those. Good Luck!
Name of formula
Perimeter of a rectangle
Perimeter of a square
Area of a rectangle
Area of a square
Area of a triangle
Area of a circle
Circumference of a circle
Simple Interest
Distance
Formula
P -o&*-;ux>
P = 3JUau3P - 4 sA- - U/V- Jtafr~Jfc"i
/y " 5
A _ bbrt - x
A ~TTr L
a - m-4C =• "rrr
r^g^_O ~ r-b
What does each variable in theformula represent?
Jt ^^enjfhU) — u)l ^
-s -^r^esb =- Uaseh K-eilck"f"
u
r-rct^i'u^
<£ =• tftrame-fe
p ; pn^i'piek ; V^f et^ , ^1-1 irv\
r
1. You are planning to build.arectangular ice skating rink in your town. The lengthof the ice skating rink is 125 feet and the width of-the rink is 70 feet What is theperimeter of the rink?
~P ~ ~^<Sl. 4- 2. > ~VFormula:
Substitution: 'K ^ 3-L 1 ^) t" ^-C ~/9
Simplify and label: Y — 2-^SO -f-
2. Find the area of the ice skating rink in problem number 1.
Formula: ' nr — . 0 ^OA X ' "\ N te^S*.
Substitution-: A vl 2-^}C "?o)
Simplify and label: A" ~ 2~7S~O
3. In the winter, the average temperature is 32° Fahrenheit. What is this indegrees Celsius? . j -- /•
C\ <^ ( JrFormula: V— J ^ -
Substitution:
Simplify and labef: Q
4. When you make a pot of pasta, the water boils at a temperature of 212°Fahrenheit What is the boiling point in degrees Celsius.
Formula: C, —x>
Substrtution: O — " -C ^-\ 3
•f ^Simplify and label: Q —
a = 00 "
5.' . Ms. Cardozo invested $1000 in a bank account that earns 5% interest eachyear. How much interestwill she have made after 7 years?
Formula: J_ 0
Substitution: J
Simplify and label:
x
6. In order to buy an x-box 360, Jamie put $400 into her savings account whichearns 3% interest per year. After 6 monthsj how much money will she have in
'all?
Formula:
Substitution:
Simplify and label: J
7. A car travels at an average speetravel in 2.5 hours?
Formula: ^ ^- Y~
Substitution: ^ r> (§
Simplify and label:
does it
m flying from Newark NJ to Orlando FL. If the flight takes 3 hours and theis traveling at 600 mph, how far apart are the two cities?
Formula:
Substitution: c| n.
Simplify and label: o\ [^ffljQ
Simplify and label:
9. Findtheareaof a triangle that has a base of 12 inches and a height of 9 inches.
AV"> U*\
— -1 £>
Substitution: A . ~
Simplify and label:
^-—— — crtL ^ "z"~*-^ O L K~\. Find the area of a triangle that has a height of 13 feet and a base of 2,5 feet
Formula:C** ^ -v, x-^ ^\ —-.
<a>£nu3Substitution: -£u
Simplify and label:A-
11. My bicycle's wheel has a 10 inch radius. What is the circumference of the v/heei?
Formula: Q ^
Substitution: CL —
Simplify and .label:
12. Rnd the area of a circular garden that has a diameter of 15 feet
Formula:
Substitution:
Simplify and label: /^ —(. 3,
13. You have a rectangular garden that is 8 feet wide and 4.5 feet long. What is ^~the perimeter of the garden? (
Formula; ( ~ 3, J^ \~
itution: 9 ^ 3- C ^ .Substitution: f-
Simplify and labei: P — °1 i~ j
14. Find the area of a rectangular garden that is 12 feet by 5 feet?
Formula: /T ~:=~ —^ '
Substitution:
Simplify and label: /V —
15. Atypical October day is 68° Fahrenheit. What temperature is this indegrees Celsius? *->
f~\ '"""o / '~^ "} ~v\: L_^ / ( t" O < -l
Substitution:
Simplify and label: / N x-«
C
16. The temperature in Austin Texas was 83°F. What is this in Celsius?
Formula: C'. = ^
Substitution: V-,' -- -, f o-<? ( O'
Simplify and label: p1' — 5^ jyf /" 7* '
17. What is the interest on $1200 invested for 2 years in an account that earnssimple interest at a rate of 5.% per year?
Formula: i
Substitution: 33 ^ ^- \y and label: tf> \O
13. Jenny is borrowing money from a friend at a simple interest rate of 4%. If sheborrows $2000 and plans to pay it back in 2 years, hov/ much interest will sheowe?
Formula:
Substitution:
Simplify and label:
19, 1 travel at a rate of 30 miles per hour. If 1 drive for 15 minutes, what distancewill I go?
Formula: Q
Substitution:
Simplify and label: ~f £
20. A cheetah runs at a rate of 85 miles per hour. At this rate, how far will it go in4 hours?
Substitution:
Simplify and label;
21. Find the circumference of a circle that has a diameter of 14 feet.
Formula: (—- -^ ' /J d
Substitution: C ~ C I V} L 3.- |
Simplify and label: £ ~ L ^
22. Find the area of a circular garden that has a radius of 9 feet.
r\Formula: ff *=-
Substitution:
Simplify and label: f\-
1.5 Formula Homework
For each problem, write a formula, substitute the values, simplify and label.
1. The temperature in Vancouver this July was 72 degrees F. What is that in
Celsius? C--CF-32)9
1
•o
2. If linvest$8QQ for 2 years at 5%; how much interest will I earn?
3. A car travels at 60 mph for 2.5 hours. How far did it go?
a ISO
. My garden is 11 feet by 7 feet What is the area and perimeter?
/V pII
ee.
5, I rode my bike at an average rate of 15 mph for 4.5 hours. How far did I go?
0 -
0 ~~
6. I invested $5000 for 3 years at 2%. How much interest did I make?
. 0 Z)
7. My yard is 2 5 yds by 2 8 yds. What is the area and p erimeter?
A-A- ¥
Find the temperature in Celsius for each of the following: C~ —(.F-32)
a. 38 degrees F b. 95 degrees F
-32)
y^
I ~- ~~~ ' /^\' 3 C-
-7 f^.3D
9. What is the area and circumference of a circle with a diameter of 12.2 inches?
3,
10. What is the area and circumference of a circle with a radius of 7.5 feet?
C. - 4-7^—-- i ( -
11. If a triangle has abase of 13 meters and a height of 21 meters. What is thearea?
TJ3Y2
6?
Station 1 before Unit 1 Quiz
Translate:
1 . Trie difference of 1 0 and x is at least 5 .
10 -X
2. 3 less -than twice a number an" is 12.
3. The product of 5 and a number "k" is no more than 30.
4. The quotient of 12 and eex" is at least 5.
5. The difference between "x" and 5 is at most 35.
X 3S
6. The quotient of 5 and x is at least 1.
5~ ^>
A
Evaluate
7. 24-4-2-^S
Ib * 4— 2-^8
8. !zi54-3 when b =
3 °/t
1.3 and 1,4 Study Guide- Station 3. -Ch 1 Quiz Review
Goal; Translate verbal phrases into algebraic expressions, equationsand inequalities.
« Review the 1 .3 "Operations Clue" table in your packet and associated exercises.• Review the vocabulary in 1.4.
Complete all work on this sheet.
Translate the verbal phrase into an algebraic expression, equation orinequality,
1. 8 more than the product of 5 times a number w
v-%2. The quotient of 11 and the sum of 7 and a number x
\\X3. The square of a number y decreased by 13
4, The difference of 3 times a number m and 5
5. -of a numberp
ip6, 3 less than twice a number n is 12.
7. The product of 5 and a number A: is no more than 30.
s~i£ £-> **^r\? **v — ^ \J
{ 8. The product of 7 and the quantity 4 more than the number pis at most 65.
Station Q. Ch 1 Quiz Review continued
Translate,
9. The quotient of 12 and a number x is at least 5.
10. The number of nickels in cfdoilars
11. The amount of money you earn if you make 9 dollars^each hour for h hours
Check whether the given number is a solution of the equation orinequality.
12. 13 = 17; when a = 4I — l —1 "7
14. 4c < 15; when c= 3
16. 28-2x>10; when x
Evaluate.
18. 2 [(4 + 5) -5-3]
13. 7b~3 = 10; when 6 = 2
- 3 ^ ID
15. 21 -3c/>11; when d =
17. 4g + 6 < 1 4 ; when g= 3
19. 6 - 5
Ifr £(22 + 3 )
1,5 Study Guide Station 3' Ch 1 Quiz Review
Goal: Use formulas to solve real-Eife situations
Directions:
• Memorize all formulas covered in Lesson 1.5 sxcept the Temperature formula.• For each problem, write a formula, substitute the values, simplify and label.• Show all your work below.
1 . The average temperature in Seattle for the month of June was 77 degrees F. What is5
this temperature in Celsius?
^ _c-c-- 'S~ 5-
2. If 1 invest ?800 for 2 years at 5% how much interest will 1 earn?
— D ir-b
3. A car travels at 60 miles per hour (mph)for3.5 hours. How far did the car travel?
^ r
4. Evaluate:
a. b. 6.5+8-(2z+3)
-"7
c. 36-3(4)
Station 7> Oh 1 Quiz Review continued»__-'
5. My rectangular garden is 11 feet by 7 feet. What is the area and the perimeter?
A =£00
6. ! have a triangular window in my family room with a base of 4 feet and a height of 7feet. What is the area of my window?
CL
A =a 3-
7. The round rug in my living room has a radius of 3 feet. Find the circumference andarea of this rug.
C-
ANSWER KEY (check and correct, if needed)
Station 9,1 1 ', I P
1)8 + 5w 2) - SJy2 -13 4) 3m -5 5)-p or- 6)2n-3 =12/ "T" t O J>
7)5^<30 8) 7(4 + p) < 65 9) — < 5 10) 20d 11) 9/j%
12) yes 13) no 14) yes 15) yes 16) no 17) no 18) 6 19) 31 20) 48
Station 3,1)25DC 2) $80 3) 210 miles 4)a \ 5) p = 36 ft; a = 77ft2 6) 14ft27) c - 18.84 ft; a = 28.26ft2 ,N 0 ,
P.) 6 I
How to prepare for the Chapter 1 Quiz (Lessons 1.1 through 1.5)
• Read the goals on the cover of the Chapter 1 Packet* Review this packet and finish any problems you did not complete.
Review your graded ciasswork assignments and the types of errors you made (ifany).Make up your own problems for any goals that you are struggling with.Study with a friend, (remember to stay on task).For homework (copy each problem onto loose leaf and show your work):
o text page 20: "Quiz for Lessons 1.1-1.3 (#1 -10);o text page 33: "Quiz for Lessons 1.4-1.5 (#1 - 5);o check answers below and make any corrections;
Need more practice? classzone.com for online quizzes for each lesson.
ANSWER KEY (check and correct, if needed)
Text p. 20: "Quizfor Lessons 1.1 - 1.3" (#1 - 10);
1)53 2) 6 3)400 4) 19 5)49
7} y-7 8) f + 5 9) 2k 10)25 + 2p; $35.00
n6)2-
Text p. 33: "Quizfor Lessons 1.4-1.5" (#1 ~ 5);
1) 2n + 4 = 25 2) ^ < 9 ' 3) yes 4) yes 5) yes
Relax. Get a good night's sleep. Have a healthy breakfast. Believe m yourselfbecause I do.
"I will do well" "X will do well" "I will do well'
