Pre-­‐Algebra  –  7th  grade  Standards  Review       Name:  

Section 1 – Integer and Rational Number operations

1. -3 + (-16)

2. -4.7 – 2.5

3. 0.5 - (-3.5)

4. !!

− !!

− !!

=

5. -7(-8) = ________

6. !!÷ −2 !

!

7. !!.!

.!"

8. −3 !!  ÷  1 !

!  

9. 1 + (−7 ) − (−2.5)

10. 7(−3) + 16

Section 2 – Proportional Relationships

1. A  shopper  bought  8  pounds  of  oranges  for  $16.80.    What  was  the  price  for  1  pound  of  oranges?        

   

2.  a. Find  the  rate  in  feet  per  second  for  each  animal  below:  

 Animal   Distance  (feet)   Time  (seconds)   Rate  (feet  per  second)  Lion   38   2    Tiger   84   6      

Bear   7  15  

 

   

           b.      Which  animal  is  the  fastest?  __________________    

   

3. The  table  below  shows  a  proportional  relationship  between  dollars  earned  (y)  and  the  number  of  hours  worked  (x).        

a. Complete  the  chart:  Dollars  

Earned  (y)   36   72     162  

Hours  Worked  (x)   2     7    

     

 b. What  is  the  rate  in  dollars  per  hour  (k)?  

           

c. Write  an  equation  to  show  the  relationship  between  dollars  earned  (y)  and  the  number  of  hours  worked  (x).  

       

4. Stephen  walks  0.75  mile  on  the  track  in  15  minutes.  Ben  walks  0.25  mile  on  the  track  in  6  minutes.  

Find  the  unit  rate  for  each  walker  in  miles  per  hour.  Who  is  the  faster  walker?      

a. Stephen’s  rate:                  

 b. Ben’s  rate:            

         

c. Faster  walker:                    

5. Write  an  equation  for  the  relationship  between  the  cost  of  apples  (y)  and  the  number  of  pounds  (x)  based  on  the  chart  below:    Number  of  Pounds   3   5.5   9  

Cost   $9.00   $16.50   $27.00        Equation:                

       

6. What  is  the  constant  rate  of  change  (k)  shown  in  the  table  below:              Number  of  Batteries  

(x)  Cost  (y)  

2   $2.38  

3   $3.57  

8   $9.52  

     

USE  THE  GRAPH  BELOW  FOR  QUESTIONS  8-­‐10  

     

7. What  is  the  cost  of  3  concert  tickets?            

8. Complete  the  chart  based  on  the  data  points  in  the  graph  above.    

Concert  Tickets   Total  Cost  

   

   

   

 9. Write  an  equation  for  the  graph  shown  above:          

     Section 3 – Proportions and Percents  

1.  You  told  your  parents  that  you  though  16  kids  would  show  up  at  your  birthday  party.    On  the  day  of  the  party,  you  realized  that  20  kids  actually  came.    Calculate  the  percent  error.  

             

2. A  garden  snail  moves  1/6  of  a  foot  in  1/3  of  an  hour.    What  is  the  snail’s  unit  rate  in  feet  per  hour?  

         

   

3. Alyssa  earned  $80  babysitting  in  October  and  $100  in  November.    What  is  the  percent  change?  (round  to  the  nearest  tenth  of  a  percent).  

                 

4. Shaylee’s  dog  weighs  60  pounds.    The  vet  suggests  its  weight  should  decrease  by  28%.    What  would  the  dog’s  new  weight  be?  

                   

5. I  want  to  buy  a  watch  that  is  $120.    It  is  on  sale  for  $96.    What  is  the  %  markdown  of  the  watch?                        

6.  Lucas  deposited  $200  in  an  account  that  pays  4.5%  interest.    If  he  leaves  the  money  in  the  account  for  5  years,  what  is  the  total  amount  in  the  account  at  the  end  of  the  5  years?  

                     

Section 4 – Expressions and Equations  Factor  Each  Expression    

1. 4𝑥 + 12              

2. 15𝑥 + 25              Simplify  Each  Expression    

3. −3(4𝑥 − 5)                    

4. 3+ 2(𝑥 − 5)                      

5. 0.2 10𝑎 − 20𝑏 + 4𝑏              

   Solve  Each  Equation    

6. −4𝑛 = −48                

7. !!𝑣 = −10  

               

8. 13− 𝑛 = 27                  

9. !!!"

= −5                    

10. 𝑥 + 3.9 = −5.9          

11. 𝑠 − !

!= !

!  

               

12. −3+ 5𝑗 = 22                  

13. 16 = 4𝑥 − 20                

14. 6 = 12− 8𝑚  

15. !!!+ 4 = 8  

           

16. 3 = !!!!!

                 

17. 15 = −5 2𝑥 + 3                  

18. 21− 3𝑓 = 15    

               Write  an  Equation  to  model  the  following  problems.    Solve.  ***Be  sure  to  define  your  variable***  

19. Alex  paid  $535  for  one-­‐year  of  cell  phone  service.    His  plan  included  a  $115  activation  fee  and  a  regular  monthly  payment?    Write  an  equation  to  find  the  amount  of  each  monthly  payment.  

                 

Section 5 – Inequalities Solve and graph the following inequalities

1. 5𝑥 − 3 ≤ 17

2. 12 ≤ 3 + 9𝑥

3. !!!≤ 2

4. −5𝑣 + 12 ≥ −18

5. !!− 29 ≤ −31

6. −7𝑥 + 10 > −32  

Section 6 – Geometric Applications    1. Find  the  surface  area  and  volume  of  the  figure:  

                     2. Find  the  area  of  the  shaded  region:  

                     3. Find  the  area  of  the  composite  shape:  

                   

4. The  area  of  a  circle  is  36𝜋  in2.    What  is  the  diameter?              

 

 

 

 

Section 7 – Statistics  1). What is the mode of the following data set?

34, 33, 28, 11, 34, 38, 27, 12, 28, 33, 34, 11, 34, 27, 33, 34, 27, 33, 34, 34

Use the following data to answer questions 2-4.

2, 5, 6, 7, 4, 5, 6, 5

2). What is the mode of the data?

3). What is the median of the data?

4). What is the mean of the data?

Tell if each sample is biased.

���5). A restaurant surveys customers one weekend morning and one weekday morning to determine what menu items they’d like to see.

6).Each student’s name is written on a slip of paper and placed in a box. One slip is selected to choose a homecoming king.

���7). A librarian randomly chooses 100 books from the library’s database of classic novels to calculate the average length of a library book.

8). Make a box-and-whisker plot for the following data:

���Daniel’s points scored for 5 basketball games 15, 20, 12, 10, 8

LE/Min_________ LQ/Q1___________ UQ/Q3 __________

UE/Max___________ Med____________

9). Make a box-and-whisker plot for the following data:

���Adam’s points scored for 5 basketball games 2, 5, 7, 6, 5

LE/Min_________ LQ/Q1___________ UQ/Q3 __________

UE/Max___________ Med____________

10). Use the information from questions 8-9 to answer the following:

• Who has the greater median score? ___________ ���

• Who has the smaller interquartile range? _________ ���

• What does the interquartile range tell you about Daniel’s scores?

_________________________________________________________ ���

• What does the interquartile range tell you about Adam’s scores?

_________________________________________________________

• What does the range tell you about Adam’s scores?

_______________________________________________________ ���__

11). Using the basketball scores from questions 8-9, find the mean absolute deviation ���(MAD) for each student. Show your work below. ���

Adam

���Jessie

���12). What does the MAD tell you about Eric and Jessie’s scores? ���

Section 8 – Probability