Special Messages & Answers

Last update 07/20/2005

 

Welcome back from vacation.  I hope that you had a wonderful
       and relaxing summer!   If this is the first time that you have visited my                          website, I hope that you enjoy the many screens that will provide you with some
pertinent information and math resources.  Many students do the practice tests at           the end of each chapter to prepare themselves for classroom chapter tests.  Please           also check out a great resource for all Algebra I students that provides PowerPoint presentations that teach Chapters 1 to 11 in the Houghton Mifflin Algebra I textbook.  These presentations were done by the incoming 10th grade students and each of these   individuals should be congratulated on the tremendous job that they did.  Also, as       before, the answers to practice tests and special problems/crossword puzzles are listed below.  A new feature this year, as you requested, is the problem numbers are now        included this year and are in red ink, and the answers as always are in green ink.  If        you have any suggestions, please do not hesitate to contact me.  As always, you can     reach me at home by telephone (before 9:00 pm please) or e-mail me at cgdyer@comcast.net with any questions or concerns.

Sincerely,

Mrs. Dyer

 

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Answers: Problem # is in red ink & Answer is in green ink

SUBJECT

 CHAPTER ANSWERS

Algebra I

Chapter 1

 1. 12, 2. 16, 3. 30, 4. 15, 5. 5, 6. 5, 7. 6, 8. 9.5, 9.  2, 10. 6, 11. any real #, 12. 2, 13. 1, 14. ±2,  15. Ø, 16. 25,  17. -6,  18. Sam has $34 & John has $39, 19. {-3,-1,5,7,},   20. 5>2,  21. 6<22, 22. 2x-3,     23. ¼ x,  24. x-4,  25. x £ 5
Algebra I Chapter 2 1. x-4, 2. -23+x, 3. -5x+3, 4. 5,    5. 2x+2, 6. 2x+2, 7. 6x+10,          8. -8x+32, 9. 30x-63, 10. -14x-22, 11. -2x-6, 12. 12x-30, 13. 10x-10, 14. 8x-5, 15. -6xy, 16. 0,            17. -5y-12, 18. x+3, 19. -3ab,    20. 14m-v, 21. -5x, 22. 3/2,        23. -¼, 24. 1st=21 & 2nd=22,  25. 1st=36 & 2nd=38 & 3rd=40 & 4th=42, EC. 18x-15, EC.13x+6
Algebra I Chapter 3 1. x = 4, 2. x =-5, 3. x =-7,           4. x = 4, 5. x =18, 6. x =±3,         7. x =Ø, 8. x =-75, 9. x =43,        10. 6 apples & 4 peaches
Algebra I Chapter 4 1. 6x²+xy+2y², 2. -3x³y+24x²y²-20xy³, 3. -12x³y4, 4. 10x-8x² ,       5. x5, 6. 4x²-9, 7. 4x³+6x²-17x+3, 8. 4x6
Algebra I Chapter 5 1. 5x(x+2), 2. 4abc²(2a-3b),          3. (y+3)², 4. (2x+11y)(2x-11y),     5. (x-5)(x+4), 6. (7x-5)(2x-1),      7. (3+b)(a+c), 8. [(x+2)-4y]• [(x+2)+4y], 9. x=-4 & x=3/2,      10. t=1 sec. & t=4 sec., 11. v=kt/p, 12. t=(v-u)/a, 13. 44 minutes
Algebra I Chapter 6 1. 5/8, 2. 3y/10x², 3. x6/y³,           4. 2x4y³z/9, 5. x/(x+2),                 6. (x-3)/2x, 7. (x-2)/(x-4),            8. -(x+1), 9. x, 10. (x-1)/(x+1),  11. 4/5x², 12. (x+2)/(x-2),          13. 3/2x, 14. x/2,                         15. (3x-2y)²/24x²y²
Algebra I Chapter 7 1. 12:1, 2. x³/27, 3. x = 4,             4. x = (cyd+c²y)/d, 5. 185 miles,     6. x = 8, 7. x = -2, 8. 1/121, 9. 216, 10. 1, 11. 1/8, 12. 9, 13. 5,950,  14. .0467, 15. 5.76 X 1010,        16. 6.5 X 10-12
Algebra I Chapter 8 see me for #'s 1 to 3,                     4. y =-x/2 + 4, 5. y =-4x+7,          6. y =5x+10,  7. y =-2x/3 + 8/3,       8. y =-5x/9 +19/9, 9. 7, 10. 1,     11. x² -1, 12. (x+2)²-3,               13. yes, it pass the vertical line test, 14. no, it fails the horizontal line test, 15. all real #'s, 16. y³-1/8,
17. (-5/4,-1/8), 18. x=-5/4,      19. graph not shown
Algebra I Chapter 9 #'s 1 to 4 x =2.5 & y =-2
Algebra I Chapter 10 1. is less than or equal to,               2. is greater than,  3. is greater than or equal to, 4. is less than, (see me for graphs) 5. x >3/2, 6. -2<x £ 3,  7. x >-5, 8. x £ -2, 9. x ³ -3,       10. x=Ø, 11. x=all real #'s,       12. -5< x ≤1, 13. x =3 & x =-13,  14. x ³ 5 &  x £ 1, 15. -3<x<1/3
Algebra I Chapter 11 1. 2/15, 5/27, 4/21, 2.  .58333..,   3. 1/6, 4. 5√6, 5. 28√2, 6. 11/25,  7. √7, 8. √(3)/3, 9. 10√2,           10. -6√6, 11. 14+6√5, 12. 3,      13. (3√2)/2,  14. (6 -3√5)/-1,            15. x = ±6, 16, x =14/3
Algebra I Chapter 12 1. ax²+bx+c=0,                             2. x =[-b±√(b²-4ac)]/2a,               3. x =1/2 & x =-5,                          4. x =-1 & x =-3,                           5. x =-7 & x =5,                            6. x =.29 &  x =-2.09,  7. x =±4
8. x² + 3x - 10 = 0, 9. b² - 4ac
10. 2 different real, rational roots,
11. 2 conjugate irrational roots,
12. 1 real, rational double root,
TOPIC CHAPTER

ANSWERS
Algebra II Chapter 1 1. -3, 2. -10, 3. 30, 4. -5k-8,        5. -600, 6. -5, 7. -105,  8. x = 5,    9. x = 6,  10. x = 2, 11. x = -8,    12. V=(x)(x-1)(x-2),                    13. Mike=$360 and Jim=$240,   14. # of Hamburgers=125 and # of Pizzas=165, 15. 1:40 PM
Algebra II Chapter 2  1. x <-3,  2. x <2,   3. Ø,               4. All Real #'s,  5. x <1,   6. x <-5,    7. x ³-2, 8. -5<x £ 2,  9. x =2 and x =-7,  10.  -13/3 £  x £ 5/3,      11. x <-3 or x >13
Algebra II Chapter 3 1. m=-3/4, 2. -5/7, 3. m=undefined therefore no slope, 4. m=0, 5. graph not shown, it is a vertical line that goes through the point +3 on the x axis, 6. graph not shown, it is a horizontal line that goes through the point -5 on the y axis, 7.  y=2x/3 + 3, make a table with the x values being -3, 0 and +3, the y values would be 1, 3, and 5, so plot the points (-3,1), (0,3) and (3,5) and connect the points, 8. m=2/3, b=3, start at the ordered pair (0,3) and rise +2 and run +3, 9. enter y=2x/3 + 3 into the y= key screen and hit graph, 10. y=-5x/7 -18/7,            11. y =5x-8, 12. y =-2x+10,       13. y =2x-1, 14. m=-1, so              y = -x+3, 15. y = x +3. 16. x =-2 & y =-2 for all four methods, 17. graph not shown, 18. 3, 19. -17, 20. -252, 21. -65, 22. -9x² + 24x - 12,        23. -3x² +12x -2, 24. all real #'s,  25. x ³ -3, 26. all real #'s except 0 & 5, 27. y=3x-1, 28. y=-x+5,    29. y=-3x/2+5,                          30. y=-4x/3+10/3, 31. 42,        32. 92,   33.  Domain is all real #'s, Range is all y ≤9, Graph is a parabola opening downward, Function is yes, 1 to 1 is no, relation is yes, and inverse is no, 34. Domain is all real #'s, Range is all y ≥0, Graph is a V which opens upward with the tip at -4 on the x axis, Function is yes, 1 to 1 is no, relation is yes, and inverse is no, 35. see me for the answers.   
Algebra II Chapter 4 1. 6x²+xy+2y², 2. -3x³y+24x²y²-20xy³,3. -12x³y4, 4. 10x-8x², 5. x5, 6. 4x²-9, 7. 4x³+6x²-17x+3, 8. 4x6, 9. 5x(x+2), 10. 4abc²(2a-3b),     11. (y+3)(y+3) or (y + 3)²,          12. (2x+11y)(2x-11y),                13. (x-5)(x+4), 14. (7x-5)(2x-1), 15. (3+b)(a+c),                            16. [(x+2)+4y][(x+2)-4y],           17.  x =3/2 & x = -4, 18. t = 1 sec. & t = 4 sec.
Algebra II Chapter 5 1. 3y/5x, 2. (y4z5)/x³, 3. 1/xy³,       4. 7.92 X 106, 5. 4.1 X 10-7,         6. 2700,  7. .00618,  8. x/(x+2),  9. x(x+1), 10. -(2+x)/(x-6),        11. x(x-1)/(x+1)(2x²-x+1), 12. 4, 13. x=-4 (x = 2 is an extraneous root),          
Algebra II Chapter 6 1. 2√5, 2. √6/3, 3. .04, 4. -5,       5. 20√3, 6. 2x+2, 7. 9√2,             8. 2√3+3√2, 9. (2√15+√42)/3, 10. 2, 11. (4+√3)/13, 12. x=±5, 13. x=5, 14. x=1/6,                    15. 1172/495, 16. 5i√2, 17. -10,   18. -2i/3, 19. (3i√5+√10)/11,    20. x=±12i, 21. 3-2i,
Algebra II Chapter 7 1. x = [-b±√(b²-4ac)]/2a,              2. y-k=a(x-h)², 3. x²+3x-10,          4. x =-2 & x =-1,                          5. x = (2 ± i√ 6)/5,                       6. x =2±√15/3, 7. 2 different real rational roots, 8. 2 imaginary conjugate roots, 9. 1 real double rational root, 10. y + 5=3(x-2)², 11. point (2,-5), 12. line x =2,      13. minimum point, 14. 7,            15. ~3.29 & ~.71, 16. graph not shown, but opens upward, 17. yes, because it passes the vertical line test,  18. no, because it fails the horizontal line test 19. Domain is all real #'s, 20. Range is all y ³ -5,
Algebra II Chapter 8 1. 4, 2. 3 or 1, 3. 1, 4. 0 or 2, 5. ±1 & ±3 & ±9, 6. ±1 & ±2, 7. ±1  or ±3 or ±9 or ±1/2 or ±3/2 or ±9/2, 8. +3/2 and -3 both will work, 9. graph not shown, 10. -3 & 3/2 & ± i,
Algebra II Chapter 9 1. √52, 2. (-5,2), 3. circle,             4. (x+5)²+(y-2)² =8, 5. (-5,2),      6. 2√2, 7. N/A, 8. N/A, 9. N/A,  10. N/A, 11. N/A, 12. N/A,        13. N/A, 14. -3 & -7, 15. none,  16. no, 17. graph not shown, but it is a circle which has (-5,2) as the center and has a radius of ~2.83,       18. parabola, 19. y+1/2=1/2(x-1)², 20. N/A, 21. N/A, 22. minimum point, 23. (1,-1/2), 24. line x =1,  25. line y =-1, 26. c=1/2 so focus is the point (1,0), 27. N/A, 28. N/A, 29. x=0 and x=2, 30. y=0, 31. yes, 32. graph not shown, but it is a parabola w/vertex (1,-1/2) and it opens upward, 33. ellipse,           34. (x-2)²/9+(y+1)²/4=1, 35. point (2,-1), 36. N/A, 37. N/A, 38. N/A, 39. N/A, 40. N/A,41. c=±5      so (-.24,-1) & (4.24,-1), 42. line y=-1, 43. line x=2, 44. 4.6 & -.6, 45. .49 & -2.49, 46. no, 47. graph not shown but it is an ellipse centered at (2,-1), 48. hyperbola,              49. (x-3)²/25 - (y-1)²/4 =1, 50. N/A, but the center of the rectangle is (3,1), 51. N/A, 52. N/A, 53. N/A, 54. N/A, 55. N/A, 56. c=√29 which is ±5.39 so points (8.39,1) & (-2.39,1) 57. line y=1, 58. line x=3, 59. 8.59 & -2.59, 60. none, 61. no, 62. graph not shown, but it is a hyperbola that opens to the right and left.
Algebra II Chapter 10 1. 31/3x5/3, 2. 51/6, 3. 5¾ ,             4. 9√25/4, 5. x√x/8, 6. y=26,      7. 32, 8. 2√2, 9. x=1/3, 10. y=-2, 11. no inverse because it is not 1 to 1, 12. x=1/2, 13. x=3√7 which is 1.91, 14. 41/2=2,                    15. log2512=9, 16. 2log4A-1/2 log4B, 17. 4, 18. x=1/2, 19. -2/3, 20. 0, 21. x=2, 22. x=9.34,        23. x=10.46, 24. x=-.359,
Algebra II Chapter 11 1. arithmetic, 2. d=3, 3. 30, 4. 3n,  5. geometric, 6. r =3,                     7. 4.1178 X 1014, 8. 4·3n-1, 9. arithmetic, 10. d=-3, 11. t30=-82 & s30=115.5, 12. summation from n=1 to infinity of -3n+8, 13. geometric, 14. r =1/2, 15. 1.999...                16. summation from n=1 to infinity of .5n-1, 17. x6 + 6x5y + 15x4y² + 20x³y³ + 15x²y4 + 6xy5+y6,        18. 8568x13y5, 19. 1760,
Algebra II Chapter 12 Covered in Honors Pre-Calculus
Algebra II Chapter 13 Covered in Honors Pre-Calculus
Algebra II Chapter 14 Covered in Honors Pre-Calculus
Algebra II Chapter 15 Covered in Honors Pre-Calculus
Algebra II Chapter 16 The matrices are impossible to show and you must see me for the answers.  Sorry!
EXTRA PROBLEMS TOPIC

ANSWERS
Special Problems   Roman Numeral Problems

M=1,000  C=100   D=500   I=1   L=50   X=10   V=5  

Largest # LXVI=66,

2nd Largest # LXIV=64

Smallest # XLIV=44,

2nd Smallest # XLVI=46

XI=11, but IX=9     XC=90, but CX=110     VI=6, but IV=4

 
Special Problems Crossword Puzzle

Across:  trapezoid, Euclid, Descartes, Octagon, Meter, Hecht

Down:  circumference, pentagon, diameter, Halpert

 

 

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