10yd

9yd

15yd

7yd3yd 3yd

10yd

MLC MTH060 Review Problems for the Final Exam

This is not a sample test. These problems are designed to get you started on your review for the test. Study the homework and your textbook for a more complete review. Do your work on another sheet of paper.  Section  1.2 1. Find the perimeter of each figure. a) b) Section  1.3  2. Subtract. Show your work: a) 2,698 − 157 b) 367 from 543  Section  1.7  3.    Solve  each  equation  and  check  the  result.  Show  your  work  for  both  the  solution  and  the  check.     a)       b)     c)     d)    

 Section  1.9  4.    Write  exponential  notation.   a)     9 i 9 i 9 i 9 i 9   b)      

5.    Evaluate  each  expression.   a)       b)      

6.    Simplify.   a)       b)     c)      7. Find the average of the set of numbers. Show your work. 19, 2, 15, 3, 11  Section  2.1  8.    Place  an  <  or  an  >  symbol  between  the  numbers  to  make  a  true  statement.    a)    9 6   b)  −1 −9    

9. Find each absolute value. a) b) c)  

10.    Determine  whether  each  statement  is  true  or  false.    a)       b)         c)    

11.    Evaluate      when  x  is  each  of  the  following:      a)    6     b)    −6  

12.    Evaluate      when  x  is  each  of  the  following:      a)  −7     b)    7    Section  2.2  13.    Add.   a)       b)     c)     d)       e)      Section  2.3  14.    Rewrite  each  subtraction  as  addition  then  simplify.  Show  your  work.     a)       b)     c)     d)  −7 − 4 − 6 − (−3)    Section  2.4  15.    Multiply.   a)       b)     c)     d)      16.    Simplify.   a)       b)     c)     d)      Section  2.5  

17.    Divide.   a)       b)     c)     d)      

x +13= 35 15 + x = 27 5• y = 45 6• x = 42

(−2) i (−2) i (−2) i (−2)

(−2)5 (−2)4

13+ 2 i 5 52 + 3 i 4 2 i (9 − 7)2 − (4 +1)2

−5 − 6 − −6

−12 <12 −9 > 6 −5 > −5

−(−x)

− −x

−7 + (−4) 8 + (−3) −3+ 9 −8 + 8 −6 + 4 + (−9)+ 5

6 − (−4) −5 − 3 −10 − (−3)

−8 i 3 8 i (−3) −8 i (−3) −4 i (−1)

−42 (−4)2 −53 (−5)3

−18 ÷ (−3) 0−9

40

12 ÷ (−1)

2  

4/5 ft

3/5 ft

18.    Simplify.    Show  your  work.   a)       b)     c)    

Section  2.6 19.    Evaluate  each  expression  for  the  given  value  of  the  variable.     a)     b)     c)      20.    Use  the  distributive  law  to  write  an  equivalent  expression.     a)       b)     c)     d)     Section  2.7  21.    Combine  like  terms  to  form  an  equivalent  expression.     a)     b)     c)       d)        Section  2.8  22.    Solve  each  equation  and  check  the  result.  Show  all  your  steps  for  both  the  solution  and  the  check.     a)     b)     c)  

 d)    

 Section  3.1  23.    Determine  whether  5160  is:   a)  Divisible  by  3   b)    Divisible  by  5      Section  3.2  24.    Find  the  prime  factorization  of  each  number.     a)    150     b)    80    Section  3.6  

25.    Multiply  and  Simplify  if  possible.   a)     b)     c)    

 26.    Find  the  area.    Section  3.8  27.    Solve  each  equation  and  check  the  result.  Show  all  your  steps  for  both  the  solution  and  the  check.  

  a)     b)     c)      Section  4.1  28.    Find  the  LCM  of  each  set  of  numbers  or  expressions.  Show  your  work.     a)    40,  90   b)    24,  18,  90   c)       Section  4.2  

29.    Add,  simplify  if  possible.  Show  your  work.   a)     b)  

  c)    

Section  4.3  

30.    Subtract,  simplify  if  possible.  Show  your  work.   a)     b)      31.    Solve  each  equation  and  check  the  result.  Show  all  your  steps  for  both  the  solution  and  the  check.  

a) b) c)

5 − (2 − 3 i 7) (6 − 4)(5 − 9)42 − 431− 52

3x − 2 for x = 6 5x2 − 3 for x = −4 −5x2 − 3y − 7 for x = −3 and y = −2

4(x + 3) −2(3x − 5) (−3x + 5)6 −(2x − 5)

4t + 7 + 3t 12x − 7 + 2x − 9 5x2 − 2x2 −6k2 + 3k − 5k2 − 7k

x − 4 = −21 9 − t = 7 −8x + 6 = −18 −13x − 5 = −31

310

i56

15 i13

−5t i 15t

12x = 3

5− 65x = −18

15 x i712

= 1410

12t 5, 8t 3

3−4

+ −14

58x + 1

8x −4x + 3

4x

− 37− 27

− 59− 712

t − 112

= 1312

x + 16= 78

− 34= y + 7

4

3  

0

2

4

6

8

10

12

14

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Inch

es

Month

St Louis Rainfall

0

5

10

15

20

25

30

35

40

45

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Car

s So

ld

Year

Bill's Car Lot

CourseMath 060

Writing 105Chem 102

PE 110

GradeCBCA

Credits4441

Section  4.4  32.    Solve  each  equation  and  check  the  result.  Show  all  your  steps  for  both  the  solution  and  the  check.  

a) b) c) Section  5.7  33. Solve each equation, check the result. Show your work. a) b)  Sections  6.1/6.2  34. The figure shows the average number of inches of rain in St Louis, Missouri each month.

a) Which month has the greatest average rainfall? b) Which month has the least average rainfall? c) What is the increase from April to July? d) What is the decrease from August to December?

   35.    Use  theline  graph  to  answer  the  questions.      

a) How many cars were sold in 2001?  

b) In which year were the most cars sold? Section  6.3  36.    Determine  whether  the  given  ordered  pair  is  a  solution  of  the  given  equation.     a)    (8,  2);        ?     b)    (−5,  −19);         ?    37.    Graph  (plot)  each  point  on  a  rectangular  coordinate  system.   a) (3,–2) b) (4, 3) c) (–5,–2) d) (–4, 5)  Section  6.4  38.  Graph  each  of  the  equations.   a)    y  =  4  −  2x   b)    y  =  −2     c)    x  =  3    Section  6.5  39. Find the mean, median, and mode of each set of values. a) 5, 9, 6, 4, 19, 8 b) 24, 39, 25, 15, 3, 70, 25  40.    Find  the  grade  point  average  for  a  student  that  received  the  following  grades.    Section  7.1  41.    Find  the  ratio  of  the  first  number  to  the  second  and  simplify.   a)    2  to  6   b)  0.3  to  2.4    Section  7.2  42.    Write  each  rate  as  a  fraction  in  simplest  form.   a)    18  pounds  in  9  seconds   b)    22  ft  in    4  seconds    43.    Find  the  unit  price  of  each  item.   a)    5  cases  for  $79.95   b)    $81.35  for  7  cartons  

12x − 2

3= 14

−2 + 16x = − 7

4− 59= − 1

6− 13x

x + 3.3= −8.7 5.2 + 3(x − 2.4) = −4.9

2x − 3y = 9 2x − 3y = 9

4  

4in

13in

9in

32.5in

T M

12ft

6ft30ft

3ft

3ft

8cm7cm3cm

6 m

8.5 m2 m

12ft

5 ft

44.    A  15-­‐pound  bag  of  chicken  feed  costs  $15.95  and  it  costs  $45.25  for  a  40-­‐pound  bag  of  the  same  feed  .  Which  bag  is  the  better  buy?    Section  7.3  45.    Determine  whether  each  proportion  is  true  or  false  by  finding  cross  products.  Show  your  work.  

  a)   58= 1016   b)   5

8= 11.518.4

  c)   4.28.6

= 9.218.4  

   

46.    Solve  each  proportion.  Check  your  result.   a)   43= 10x   b)   4.6

9.3= x27.4

  c)  38516

= t32    

Similar  Triangles  47.      Find  the  unknown  sides  of  the  triangles.    

Dimensional  Analysis  #1  48. Use dimensional analysis to perform the conversions. Show your procedure including unit fractions.

a) 19 oz to g b) 250 microns to cm c) 75 yd to m  Section  9.3  49. Find the circumference of each circle. Include correct units in your answers. Use 3.14 for π. a) A circle with a radius of 9 ft. b) 50. Find the perimeter of each figure. Include correct units in your answers. Use 3.14 for π. a) b)      51.    Find  the  area  of  each  parallelogram  or  trapezoid.  Include  the  correct  units  in  your  answers.     a)   b)            52.    Find  the  area  of  each  circle.  Include  correct  units  in  your  answers.  Use  3.14  for  π.       a)    A  circle  with  a  radius  of  4.5  yards.   b)      Section  9.4  53. Find the volume of each figure. Include correct units in your answers. Use 3.14 for π. a) b)

12 ft

12 ft

3 ft

5  

Scientific Notation

54.    Write  45,000  in  scientific  notation.   55.    Write    in  decimal  notation.    56.  Perform  each  of  the  calculations  using  a  scientific  calculator.  Leave  your  answer  in  scientific  notation.  

Round  decimals  to  three  places.    

    a)     b)    

Answers: 1. a) 44yd b) 26yd 2. a) 2541 b) 176 3. a) x = 22 b) x = 12 c) y = 9 d) x = 7 4. a) 95 b) (−2)4 5. a) −32 b) 16 6. a) 23 b) 37 c) −17 7. 10 8. a) 9 > 6 b) −1> −9 9. a) 5 b) −6 c) −6 10. a) true b) false c) false 11. a) 6 b) −6 12. a) −7 b) −7 13. a) − 11 b) 5 c) 6 d) 0 e) −6 14. a) 6 + 4 = 10 b) −5 + (−3) = −8 c) −10 + 3 = −7 d) −7 + (−4) + (−6) + 3 = −14 15. a) −24 b) −24 c) 24 d) 4 16. a) −16 b) 16 c) −125 d) −125 17. a) 6 b ) 0 c) undefined d) −12 18. a) 24 b) −8 c) 2 19. a) 16 b) 77 c) −46 20. a) 4x +12 b) −6x +10 c) −18x + 30 d) −2x + 5 21. a) 7t + 7 b) 14x −16 c) 3x2 d) −11k2 − 4k 22. a) x = −17 b) t = 2 c) x = 3 d) x = 2 23. a) yes. 5 +1+ 6 = 12 , which is divisible by 3 b) Yes. It ends in zero

24. a) 150 = 2 i 3 i 5 i 5 b) 80 = 2 i 2 i 2 i 2 i 5 25. a) 14

b) 5 c) −1 26. 625

ft 2

27. a) x = 65

b) x = 1 c) x =125 28. a) 360 b) 360 c) 24t 5

29. a) −1 b) 34x c) −13

4x 30. a) − 5

7 b) − 41

36

4.37 ×109

3.58 ×109( ) 3.25 ×1012( )4.3×105

1.2 ×1052

(3×1021)(2 ×105)

6  

y

xa)

d)

c)

b)

y

x

y

x

y

x

31. a) t = 76

b) x = 1724

c) − 52= y 32. a) x = 11

6 b) x = 3

2 c) x = 7

6

33. a) x = −12 b) x = −.96 34. a) June b) Jan c) 4in. d) 7in. 35. a) 20 b) 2000 36. a) no b) no 37. 38. a) b) c) 39. a) Mean: 8.5, med: 7 mode: none b) Mean: 28.71, med: 25 mode: 25      

40.    2.46   41.    a)    13   b)    

18   42.    a)    

2pounds1second   b)    

11 ft2sec  

43. a) $15.99 per case b) $11.62 per carton 44. The 15-pound bag @ $1.06 per pound 45. a) yes b) yes c) no 46. a) x = 7.5 b) x = 13.55 c) x = 9 5

47. M = 22.5 in., T = 10 in. 48. a)

19oz1

i28.35g1oz

= 538.65g

b)

250µ1

i1m

1000000µi100cm1m

= .025cm c)

75yd1

i3 ft1yd

i12in.1 ft

i1m

39.37in.= 65.58m

49. a) 56.52 ft b) 37.68 ft 50. a) 78.84 ft b) 15.42.ft 51. a) 38.5 cm2 b) 17m2 52. a) 63.585yd 2 b) 113.04 ft 2 53. a) 432 ft 3 b) 523.60 ft 3 54. 4.5 ×104 55. 4,370,000,000 56. a) 2.71×1016 b) 2 ×1025