arithmetic review 1...algebra(review(2( page1(algebra review 2 foil: 1. (6z-2)(3z+4) 2. (8b-3)(b+5)...

Arithmetic Review 1

Simplify: 1. -15 – (-6) 2. -3 * -7 3. |7 – 9| 4. 16 ÷ (-4) * 2 – 6 5. ( 49 * 6 – 3 * 16 ) ÷ 10 6. 170 = 7. 2 18 + 8 – 3 50 Solve

8. 151 +

32 =

9. 92 +275 =

10. 92 +53 =

11 21 -

31 =

Solve

12. 5.63 (2.1)=

13. 3.84 (2.8)=

14. 9 ÷31 =

15. 27 92

÷ =

Solve:

16. =+31

215

17. =+81

419

18. =•413

95

19. =•211

74

20. ( ) =239.

21. ( ) =267. Solve

22. =+103

157

23. =−812

417

24. =−915

618

25. ( )( )

=−−

−+

9393

26. ( )( )

=−−

−+

7575

27. 8 + .28 =

28. .3 + .43 =

29. 75.??=

30. 15.??=

31. =43 what decimal?

32. =53 what decimal?

33. 95.02 x 1.3

34. 99.99 x 4.11

Solve

35. =−+21

31

92

36. =+−21

31

51

37. 0 32.15. 38. 564.09.0

Answers to Arithmetic Review Check your answers.

If they do not match, try re-working the problem. Bring your work to the Math Center with specific questions.

1. -9 2. 21 3. 2 4. -14 5. 3 6. 1 7. -7 2

8. 1511

9. 2711

10. 4537

11. 61

12. 11.823 13. 10.752 14. 27 15. 121.5

16. 635

17. 9.375 or 875

18. 3665

19. 76

20. .1521 21. .4489

22. 3023

23. 841

24. 1855

25. -.5 or -21

26. -61

27. 8.28 28. .73

29. 43

30. 203

31. .75 32. .60 33. 123.526 34. 410.9589

35. 181

36. 3011

37. 2.64 38. 6.2666667

Arithmetic Review 2

1) 161*

2132

2) 163

415 −

3) 10

1542 n

+=

4) 61

31+

5) 41

21+

6) 125

41+

7) If a = 3, b = -5, then what does aba − equal?

8) 2)23( y 9) What percent is 12 of 30? 10) 104600 ÷

11) 31

92÷

12) 31

817

−

13) 85216 −

14) 21610

+

15) 85.357.423 × 16) 01.0801× 17) 2.6 (.001) 18) What is 82% of 704.50 ?

19) 31

87−

20) What percent is 3 of 20? 21) 40 = 20% of x

22) 8516 −

23) 7.2027.=

x

24) 01.0547 ÷

25) Write 214 as a decimal

26) 154110 ÷ 27) 12.003.0 × 28) 45.02.0 × 29) 25.0100×

Arithmetic Review 2 Answers

1. 3265

2. 81/16

3. n = 18

4. 21

5. 43

6. 32

7. 38

8. 18y

9. 40%

10. 460

11. 32

12. 2443

13. 8107

14. 821

15. 1630.7445

16. 8.01

17. .0026

18. 577.69

19. 2413

20. 15%

21. x = 200

22. 8123

23. x = .01

24. 54700

25. .19048

26. 274

27. .0036

28. .09

29. 25

Arithmetic Review 3

1. If the average of 6.2 and ‘n’ is 4.4, what is the number ‘n’?

2. What number divided by 3.8 is 1.9?

3. What is 16% of 30% of 24?

4. A shirt costing $16 is on sale for 15% off. If you were to apply a coupon for 10% off of the sale, what would you pay for the shirt?

5. Solve for ‘n’:

914

3923 =+

n

6. Solve for ‘t’:

810

43

216 =−

t

7. You have a rectangular yard that is 48 square feet in area in which you want to put a square garden surrounded by concrete. If the concrete takes up 12 square feet, what is the length of a side of a square garden?

8. If a cylinder has a volume of 96π centimeters cubed, and stands 6 centimeters tall, find its radius. ( V= πr2h)

9. If you ran around a rectangular park whose length is three times its width, and ran 1600 m total, what is the length and width of the park?

10. What is 8456 divided by 100?

11. If you had a pole that extends out 10 times its original length of 14.3 feet, how long would the pole be if you fully extended it?

12. Find the equivalent values:

A. 681 B.

532

a. 850 b.

849 a. 5

62 b. 2

65

c. 648 d.

815 c. 6

52 d. 2

56

13. You have two pies, one cut into fourths and the other into eighths. If Jim eats 2

slices of the pie that is cut into eights, how many of the fourths would you have to eat in order to eat an equivalent amount of pie?

14. If you depart in an airplane from Philadelphia to Los Angeles ( 3 hour time difference) at 7:00 am (Phila. Time), and the trip takes 5 hours, what time is it in Los Angeles when you arrive?

15. Solve: 16. Solve: 17. Solve:

=+63

95 =−

32

97 =−

63

249

18. If your train leaves at 6:52 am, and you arrive at 9:23 am, how long was your trip?

19. Solve for ‘p’: 6 (p – 3) + p = 3p

20. If a club sells tickets to a show at $12 for adults and $6 for children, makes a total of $348 on 36 total tickets, how many of each type did they sell?

Answers

1. n = 2.6

2. 7.22

3. 1.152

4. $12.24

5. n = 8/3

6. t = 7

7. length = 6 feet

8. radius = 4 cm

9. width = 200 m, length

10. 84.56

11. 143 ft

12. 1: b. 849 2: c.6

52

13. 1 piece of pie.

14. 9:00 am

15. 1819 or 1

181

16. 91

17. -1/8

18. 2:31 minutes

19. p = 4.5

20. 22 adult tickets and 14

children’s tickets.

Algebra Review 1 Page 1

Algebra Review 1

1. (19t³ – 5t²) – (7t² – 3t)+(-15t³ – 8t) 2. (5y + 4)(3y – 8) 3. 2y²(2y – 7)(4y + 1) 4. Factor: 12d² – 6d 5. Factor: x² – 9 6. Factor: 3x² – 54x + 243 7. Factor: r² –18r + 72 8. Factor: 4s² – 4s – 15

9. Simplify:ssssrrnnmmm*********

10. 3

2

3

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−

cb

11. a-4 * a-3 12. (m5)-2

13. 8

4

−aa

14. 6

2

819wx

15. 5(x – 3) – 3 = 2x – 6(2 – x)


Answers to Algebra Review 1 Check your answers. If they do not match, try re-working the problem.

Tutorials are available for additional assistances. Bring your work to the Math Center with specific questions.

1. 4t3 – 12t2 –5t

• http://patrickjmt.com/polynomials-adding-subtracting-multiplying-and-simplifying-ex-1/



3. 16y4 – 52y3 – 14y2




5. (x – 3)(x + 3)

• http://www.youtube.com/user/yourteachermathhelp#p/search/5/AcCN_isD3PY

• http://www.youtube.com/watch?v=COCIk0irz14&feature=related

7. (r – 6)(r – 12)

• http://www.youtube.com/user/yourteachermathhelp#p/search/1/Nj9GgAM-dTQ

9. 42

23

srnm

• http://patrickjmt.com/exponents-applying-the-rules-of-exponents-basic-ex-1/



2. 15y2 – 28y – 32 • http://patrickjmt.com/polynomials-

adding-subtracting-multiplying-and-simplifying-ex-1/



• 4. 6d(2d – 1)

• http://www.youtube.com/user/yourteachermathhelp#p/search/5/AcCN_isD3PY

• http://www.youtube.com/watch?v=COCIk0irz14&feature=related

6. 3(x – 9)(x – 9) or 3(x – 9)2


8. (2s – 5)(2s + 3)


10. 9

6

bc





11. a-7 or 7

1a




13. a12




15. x = -2

• http://www.youtube.com/watch?v=9teKXGoWIQM&feature=relmfu

• http://www.youtube.com/watch?v=XfaWLVLfeJM&feature=relmfu

12. m-10 or 10

1m




14. 33wx

• http://patrickjmt.com/radicals-simplifying-radical-expressions-involving-variables-ex-1/


Algebra Review 2 Foil: 1. (6z-2)(3z+4)

2. (8b-3)(b+5)

Simplify:

3. 252510

2

2

−

++

zzz

4. 14414424

2

2

−

++

bbb

5. zz 317

+

6. bb 5211

+

7. 2

69⎟⎠

⎞⎜⎝

⎛ z

8. 2

525

⎟⎠

⎞⎜⎝

⎛ b

Solve:

9. 7 (z - 5) + 2 = 3z

10. 3 (b – 4) + 10 = 7b

11. 364816 2 +− yy

Factor: 12. 49142 ++ yy

Solve:

13. -3y + 8 = 1 Factor:

14. 151416 2 −− yy Simplify:

15. 14b – 9z – 24b + 10z

16. 5x + 13y – x + 3y Solve

17. 5z + 3 = 9 Factor

18. 152912 2 +− yy Simplify

19. bx

xb 33

÷

20. ( )27+y

21. bb

3549−


Simplify:

22. zz

14460

23. ( )264 −y

24. ( )332 zb

25. ( )2539 yx

26. ⎟⎠

⎞⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

bz

zb

58

1625 2

27. ⎟⎠

⎞⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛22 12

81360

xy

yx

28. ( )232 zb +

29. ( )22yx +

30. 5(3x-1) = 12

31. 4(7b + 2) = 9

Solve:

32. ba

b+

2

if b = 6 a = 1

33. yx

x+

2

if x = -2 y = 3

Simplify:

34. 63

224 bbb

+−

35. 65

184

95 xxx

+−


Answers to Algebra Review 2 Check your answers. If they do not match, try re-working the problem.

Tutorials are available for additional assistances. Bring your work to the Math Center with specific questions.

1. 81818 2 −+ zz

• http://patrickjmt.com/solving-quadratic-equations-by-factoring-basic-examples/

• http://www.yourteacher.com/free-video-jwp.php?vid=7070

• http://www.youtube.com/watch?v=65BAsV0SK3k&feature=relmfu

3. 55

−

+

zz

• http://www.youtube.com/watch?v=jyJFGZUmUsg

5. z322


7. 49 2z




9. 433



11. 4(2y-3)(2y-3)


13. y = 37

• http://www.youtube.com/watch?v=Zj-9Zc9yKYU

2. 15378 2 −+ bb • http://patrickjmt.com/solving-quadratic-

equations-by-factoring-basic-examples/ • http://www.yourteacher.com/free-

video-jwp.php?vid=7070 • http://www.youtube.com/watch?v=65B

AsV0SK3k&feature=relmfu

4. 1212

−

+

bb


6. b557


8. 25b 2




10. b= -.5



12. (y+7)(y+7)


14. (8y + 5)(2y – 3)



15. -10b + z’ • http://patrickjmt.com/polynomials-




17. z = 6/5 http://www.youtube.com/watch?v=Zj-9Zc9yKYU

19. 2

2

9xb

• http://www.youtube.com/watch?v=Xdo4uQdbPWU&feature=related

21. -7/5

• http://www.youtube.com/watch?v=Ctdopjom3lI

23. 16 2y - 48y + 36




25. 10681 yx • http://patrickjmt.com/exponents-applying-

the-rules-of-exponents-basic-ex-1/ • http://patrickjmt.com/exponents-applying-


the-rules-of-exponents-basic-ex-3/ 27. 135/xy

• http://www.youtube.com/watch?v=4GHL2P6YMcc

16. 4x + 16 y • http://patrickjmt.com/polynomials-




18. (3y-5)(4y-3)


20. 2y + 14y + 49




22.125

• http://www.youtube.com/watch?v=Ctdopjom3lI

24. 398 zb




26. 5b/2

• http://www.youtube.com/watch?v=4GHL2P6YMcc

28. 6324 2 zzbb ++





29. 422 2 yxyx ++ • http://patrickjmt.com/exponents-applying-



the-rules-of-exponents-basic-ex-3/ 31. b = 1/28



• 33. 4

• http://www.youtube.com/watch?v=hmalVzYEbUU

35. 7x/6

• http://www.youtube.com/watch?v=aOajaL8bUjo

30. x = 17/15 • http://www.youtube.com/watch?v=9teK

XGoWIQM&feature=relmfu • http://www.youtube.com/watch?v=Xfa

WLVLfeJM&feature=relmfu 32. 36/7

• http://www.youtube.com/watch?v=hmalVzYEbUU

34. 3b/2

• http://www.youtube.com/watch?v=aOajaL8bUjo

APPLICATION REVIEW

1. Find the cost of the carpet needed to cover the floor of a room that is 14 yards long and 10

yards wide if the carpet costs $13.00 per square yard.

2. A can of soup is in the shape of a right circular cylinder whose diameter is 3 inches and

whose height is 5 inches. (a) What is the volume of the can? (b) How much steel was used in

constructing the can? Use pi ≈ 3.14.

(

)

3

2

3. If a board is (2x + 6) feet long and a piece (x – 5) feet long is cut off, what is the length of the

remaining piece?

4. Find the area of the rectangle with length 5a – 7 and width 3a + 2.

5. Hans is renting a sofa for $12.75 per month. If a new sofa costs $306, how many months will

it take for the rental fees to equal the cost of a new sofa?

6. A high school boasts that three-fifths of its teachers have a master’s degree. If 45 teachers

have a master’s degree, how many teachers does the school have?

7. The charges for repairing a transmission were $255 including parts. If the mechanic worked

for 4 hours and the parts cost $75, how much down the mechanic charge per hour?

8. An office purchased 50 reams of paper for which it paid $260. There are two types of paper.

The lighter-weight paper cost $4.00 per ream and the heavier paper cost $7.00 per ream. How

many reams of each type of paper were purchased?

{

{

20 reams of the heavier paper

30 reams of the lighter-weight paper

9. To rent a small truck from U-haul in Orlando for local use, the cost is $19.99 per day plus 59

cents per mile. If x represents the number of miles driven and y is the cost of one day, then y =

19.99 + .59x.

a. Find the cost for one day if the truck was driven 25 miles.

b. If it cost $67.19 for one day’s rental, how many miles was the truck driven?

c. Find three ordered pairs and draw the graph.

(30,37.69), (80,67.19), (65,58.34)

d. From the graph, estimate the number of miles driven if the cost is $37.69. Verify

your answer from the equation.

30 miles

10. A company purchases a piece of machinery for $30,000. The value, V(x), of the machinery

as a function of the number of years after it was purchased, x, is given by V(x) = -1800x +

30,000.

a. Find the value of the machinery after 4 years.

V(x) = -1800x + 30,000 V(4) = -1800(4) + 30,000

V(4) = -7200 + 30,000 V(4) = 22,800

b. Find the value of the machinery after 10 years.

V(x) = -1800x + 30,000 V(10) = -1800(10) + 30,000

V(10) = -18000 + 30,000 V(10) = 12,000

c. What does V(8) = 15,600 mean?

After 8 years, the value of the machinery is $15,600.

11. The length of a rectangle is 5 less than twice the width.

If the area of the rectangle is 25 square centimeters, find the dimensions of the rectangle.

√

√

√

√

12. Find two consecutive odd integers whose product is 63.

{

{

√

√

√

13. Find the area of a triangle whose base is 3 5

3 inches and whose height is 4

3

2 inches.

in2

14. Find the quotient. Express answer reduced to lowest terms.

If a car used 12 10

8 gallons of gas on a trip of 416 miles, what was the average miles per gallon

for the trip?

15. Two numbers differ by 4. If 4

3 of the smaller number is increased by

2

1 of the larger

number, the sum is 2. Find the numbers.

{

{

16. A lawn mower uses 2 quarts of gasoline to mow 3

1 acre of grass. How many acres can be

mowed with 9 quarts of gasoline?

17. A machine can fill 3600 cans in 25 minutes. How many cans can be filled in 70 minutes?

18. Find the original price of a dining room suite that was discounted by $138 if the discount

rate was 30%.

19. Mark paid $664 for a suit that was discounted 20%. What was the original price of the suit?

20. The sum of the squares of two consecutive integers is 61. Find the integers.

{

{

√

√

√

arithmetic review 1...algebra(review(2( page1(algebra review 2 foil: 1. (6z-2)(3z+4) 2. (8b-3)(b+5)...

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