Chapters 1, 2, 3, 4, 5 Name Period 2 · 5 Simplify the following. When necessary, write answer in...
Transcript of Chapters 1, 2, 3, 4, 5 Name Period 2 · 5 Simplify the following. When necessary, write answer in...
Chapters 1, 2, 3, 4, 5, 6
Name ________________________
Period 2
Revised 2015
2
3
COMPARING RATIONAL NUMBERS Graph the following on a number line. 1) 0.01, 0.001, 0.1, and 0.0001 2) 2.25, 0.253, 0.2485, and 2.249 3) 0.38, 1.5, 0.475, and 2.249 4) 0.006, 5.02, 0.503, 0.1483 5) 0.98, 0.89, 0.934, and 0.9 6) 0.201, – 0.19, – 1.2, and – 0.21 7) 0.465, – 0.4053, – 0.47, and – 4.5 8) 0.51, – 0.583, 0.60, and – 0.5126 9) 0.04, –1.25, – 0.156, and – 2.3 10) 0.76, 07, – 0.076, and – 0.0710 11) 12) 13) 14) 15) 16)
17) 18) 19) 20)
21) –8.5, –9.62, –5.72, and –7.26 22)
23) 24)
25) 26) 4.5, 4.62, 4.72, and
27) – 5.3, – 6.3, – 5.27 and 28)
29) 30)
1 1 12 3 5, , and 5 32
8 3 5, , and
1 1 14 2 6, , and− − 31 2
2 5 10, , and− − −
5 31116 8 4, , and− − 52 11
3 12 6, , and− −
2 25 3, 1 , and 0.25− 7 2
8 52.41, 1 , and 2− − −
9 110 25.46, 5 , and 5 21
1000.34, 0.56, 0.13,− −
16 9, 37, 42
2, 27, 5.6, 1.43 − 12, − 3.75, − 37, − 6.3
24, 2 10, 8 3, 5 5 21
− 30 3 1 1 147 8 7 151 , 2 , 2 , and− − −
38 , 0.23, 5
9 , 12 , 0.55 1
22.53, 3.6, and 2− − −
4
Change the following repeating decimals to fraction: PACC Rational & Irrational Nos.
1. 6. 11. 16. 2. 7. 12. 17. 3. 8. 13. 18. 4. 9. 14. 19. 5. 10. 15. 20. Approximate the following radicals to the nearest whole number without using a calculator: 21. 26. 31. 36.
22. 27. 32. 37.
23. 28. 33. 38.
24. 29. 34. 39.
25. 30. 35. 40. Use the approximation method to place the following radicals in the correct position on the number line below: 41. , , , , , , , , , , , ,
1 2 3 4 5 6 7 8 9 10 11 12 13 14 42. , , , , , , , , , , , , 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.6 8.51 2.98 7.02
0.5 19.74 11.47 87.22
11.3 4.356 31.82 41.02
5.9 0.74 541.67 0.532
11.3 0.98 837.07 11.4532
8 17 138 288
24 39 199 293
1203 152 324 219
88 563 763
126
1253 370 603
69
200 563 87 111 1313
10 151 703 56 7 173 63
43
75 53 39 150 1403
22 123 253 5 90 533
119 15
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Simplify the following. When necessary, write answer in simplest radical form. Simplify Radicals 1 1. 361 2. 225 3. 1296 4. 2025 5. 3969 6. 4900 7. 8281 8. 12321 9. 5776 10. 2809 11. 28 � 28 12. 15 � 15 13. 8 � 8 14. ( 121 )2 15. 71 • 71 16. ( 26 )2 17. (136)2
18. (43)2 19. (88)2 20. (12)2 • (12)2 21. 56 22. 27 23. 60 24. 245 25. 132 26. 450 27. 108 28. 5415 29. 192 30. 392 31. 504 32. 2028
33. 4 • 3
34. 10 • 9
35. 16 • 5 36. 7 • 14 37. 18 • 9 38. 27 • 54 39. 8 • 6 40. 12 • 3 41. 33 • 22 42. 26 • 52 43. 70 • 125 44. 24 • 36 45. 48 • 28 46. 63 • 14 47. 162 • 8 48. 18 • 98
49. 9x2 50. − 49x2 51. 4x2y2
52. − 28x4 53. 16xy2 54. − 20xy2 55. 12x2 56. − 45x2 57. 25y4 58. 7x2y 59. 9x2y4 60. 24x4y2 61. a3 62. − 40a3 63. 54a3b2 64. 75a2b3 65. 144b6 66. − 1000a6
67. 18a6b2
68. 15a8b3
Holt McDougal, Larson Algebra 1, © 2011
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Simplify Radicals 2 Simplify the following. When necessary, write answer in simplest radical form. 69. a5b8 70. 2 50ab5 71. 8 300a4b6 72. 5 98a20b3 73. 5 • 3 74. 6 • 2 75. 3 • 6 76. 5 • 10 77. 27 • 3 78. 10 • 20 79. 90 • 40 80. 2x • 3x 81. 6x • 2x 82. 30x2 • 3x2 83. 3x • 8x3 84. 40x2 • 10x 85. − 6m3 • 4 18m3
86. 5 2 • 4 3 87. −7 3 • 2 10 88. 2 6 • 5 3 89. 4 10 • (−3 2) 90. 2 8 • 18 91. −10 3 • (−2 21) 92. − 6 • 7 10 93. 3 ab • 6 ab 94. 2ab2 • 14ab2 95. − 15a2b • (− 5a2 ) 96. 8ab2 • (− 10a3b4 ) 97. 2 18a2b • 6 3b2 98. 5 2a9b8 • 4 12a2 99. 8 8a4b3 • 7 14a5 100. 5 15c3 • 7 27c
101. 27
102. 95
103. 205
104. 142
105. 36
106. 410
107. 1111
108. 312
109. 3018
110. 820
111. 92 45
112. 73
113. 510
114. 3 62
115. 32 6
116. 5 2 710
• 313
117. 37
118. 512
119. 920
120. 827
121. 185
122. 23• 34
123. 103• 95
124. 56• 52
125. 35• 110
126. 37• 712
127. 2 23• 11
5
128. 118• 31
3
129. 2 524
130. 5 2 710
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Properties Closure
Take two numbers from a set and perform an operation. If the answer is always in the set, then the set is closed.
Identity Property: For all real numbers a, a + 0 = a and 0 + a = a
For all real numbers a, a • 1 = a and 1 • a = a Additive Inverse Property
For every real number, there is exactly one real number – a, such that a + (-a) = 0 and – a + a = 0.
Multiplicative Inverse Property For every non-zero real number a, there is exactly one number 1a , such that 1 1
a aa 1 and a 1• = • = .
The number 1a is called the reciprocal or multiplicative inverse of a. Multiplicative Property of Zero The product of any real number and zero is zero. a • 0= 0 Other Properties of Zero Zero divided by any nonzero real number is zero. 0
a 0= Division by zero is undefined. (Division by zero cannot be simplified.) Commutative Property. For all real numbers and b, a + b = b + a and a • b = b • a Associative Property For all real numbers a, b and c, (a + b) + c = a + (b + c) and (a • b) • c = a • (b • c). Distributive Property For all real numbers a, b and c, a(b + c) = ab + ac and a(b – c) = ab – ac. Properties of Equality For all real numbers a, b and c: Reflexive Property a = a (A number equals itself.)
Symmetric Property If a = b, then b = a.
Transitive Property If a = b and b = c, then a = c.
Substitution Property If a = b, then a can be replaced by b and b can be replaced by a. Additive Property of Equality: If a = b then a + c = b + c. Multiplicative Property of Equality: If a = b then a � c = b � c.
Underlined Properties are on the Keystone Algebra 1 Exam.
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Identify the properties displayed below: 1. 3 + ( 7 + 6 ) = ( 3 + 7 ) + 6 16. 25 = 25 2. If 5 + 3 = 8 and 8 = 2 + 6 then 5 + 3 = 2 + 6 17. 6 + 14 is a natural number.
3. 6 + 0 = 6 18.
3x7
+ −3x7
= 0
4. 9 – ( 2 + 3 ) = 9 – 5 19. 18 + 3 � 6 = 18 + 6 � 3 5. 11 ( x + y) = 11x + 11y 20. a ( x y ) = ( a x ) y
6. 0 �12 = 0 21. 09= 0
7. 15
• 47
is a rational number. 22. 9 + (16 + 15) = 9 + 31
8. 1y = y 23. a � 0 = 0 9. 6x – 3y = -3y + 6x 24. 2y + x = 2y + 1x 10. 2 � 1 = 2 � 1 25. 6 + 8 = 14 so 14 = 6 +
11. (7 – 4) y = 3y 26. −59
• 9−5
= 1
12. 15
• 5 = 1 27. 4(a + 3) = 4(3 + a)
13. 6 + ( 2h + 3h ) = 6 + (2 + 3)h 28. – 7 – 3 is an integer.
14. −34
+ 34
= 0 29. (4 + 9)x = 13x
15. 10 + 1 = 11 so 11 = 10 + 1 30. 5c + 2c = (5 + 2)c
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Name the property used in each step. Algebraic Proofs 1. 2.
3. 4.
5.
Show all the steps and name the properties used to simplify each expression below: 6. 5 + 8 � 1 – 4 � 2 7. 5(16 – 24) + 7 � 1 8. 9 / 32 + 6(8 � 4 – 25) 9. 26 � 1 – 6 + 5(12 / 4 – 3) 10. –2(–6)(–5x) 11. 12. 9x(2.8)(–5) 13. 5x + 23 = 38 14. 6 + 8x = 10x + 12
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Solve the following equations showing all the work. Equations Review 15 1. x + 7 = 21 2. 3 + x = – 11 3. 17 = x – 12 4. 9 – 14 = 8 + x 5. 19 = 5 – x 6. 14 – x = – 21 7. 4 + x + 16 = 9 8. 25 = 30 – x – 6 9. 5x + 12 – 4x = 9
10.
34 x = 9
11. −76 x = 28
12. 13 =
49 x
13. 12x = 36 14. 11 = 9x 15. –8x = –64 16.
611 = –2x
17.
3x= 7
5
18.
12x
= 35
19.
511
= x5
20.
37= x
6
21.
6x= 15
4
22.
2x3
= 618
23. 9x + 2 = 29 24. 5 + 8x = 21 25. 5 = 4x – 11
26. 17 = 12x – 7 27. 7 – 5x = 22 28. –31 = 6c – 11 29. 42 – 9x = 21 30. 77 = 7x – 7 31. 9x + 3 + 4x = 16 32. 5x + 6 – 3x = 14 33. 8 = 6x – 2 – 8x 34. 12 = 35 – 4x + 6 35. 6(2x – 3) = 2 36. 8(5x + 4) = 19 37. 51 = 3(6x – 11) 38. 42 = 9 + 5(x + 4) 39. 8(3x – 6) + 12 = 18 40. 9 + 2(5x – 6) = 4 41. 8 + 7(x – 1) = 6 42. 4x + 6 = 5x 43. 9x – 11 = 12x 44. 5x = 8x – 2 45. 11x = 3x + 5 46. 2x + 3 = 4x + 9 47. 9x – 1 = 6x – 13 48. 5x – 3 = 10 x – 28 49. 11x – 17 = 15 x + 29 50. 14x – 19 = 5x – 1 51. 7x + 2 = x – 4 52. 5x – 11 = 3x + 11 53. 17 – 4x = 11 – 6x 54. 22 + 6x = 31 – 7x
55. 5x + 7 + x = 8x – 2 56. 3x + 8 + 4x = 7x + 9 57. 6 + 8x + 2 = 17 + 5x – 1 58. 27 – 3x = 35 + 4x – 3 59. 4x – 16 = 18 – 4x – 9 60. 2x + 3x + x = 3x – 7 62. 3x – 8 – 5 = 42 + 9x 63. 8(4x + 6) = 5x + 1 64. 8x – 2 = 7(3x – 5) 65. 5(2x – 8) = 3(3x + 6) 66. 7(5x – 1) = 11(x – 4) 67. 8(4x + 2) = 12(2x + 4) 68. 6(2x – 3) = 8(9 – 8x) 69. 4(5x +6) + 3x = 13x – 1 70. 3(2x + 8) – 5 = x + 10 71. 4 + 5(6x + 4) = 6 + 2(3x + 5) 72. 9 + 4(3x – 1) = 5 + 8(9x +2) 73. 8 – 3(5x + 2) = 9 – 6(10x + 3) 74. 10 – 5(4x – 1) = 8 – 2(11x – 2) 75. 4(3x – 6) – 6(2x – 3) = 8 76. 8(2x – 1) – 7(5x + 6) = 10
77. x + 5
6= 3
7
78. 4x − 9
11= 3
8
79. x + 3
4+ 2x − 1
5= 11
2
80. 112+ 4x − 7
6= 5x + 1
3
81. 5.64x + 0.21 = 8.1x – 9 82. 9.543x – 7.2 = 0.4x + 5
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Functions A relation is a pairing between two sets of numbers. The first coordinate is called the domain. The second coordinate is called the range. A function is a special type of relation that pairs each x (domain value) with exactly one y (range value). Solve y = 4x if the domain is {–3, – 2, 0, 1, 2} Solve 8x + 4y = 24 if the domain is {-2, 0, 5, 8}
Use the graphing calculator to solve equations in two variables.
1. 2. 3. 4.
(x, y)
(Number of units, Predicted Value)
(Domain, Range)
(Input, Output)
(Input, Solution Set)
(Independent variable, Dependent Variable)
Domain X 4x Range
y (x, y)
–3
–2
0
1
2
Domain X Range
y (x, y)
–2
0
5
8
Method 2 1. Store domain values in L1. 2. On L2, rewrite equation, replacing L1 for x.
Method 1 1. Store domain values in L1. 2. On the home screen, rewrite equation, replacing L1 for x.
x y 0 0 3 6 6 12 9
12 15
x y 10 5 -2.5 0 0 -5 2.5
-10 5 -15
x y 0 1 5 2 6 3 7 4 8 5
x y -6 5 -4 -2 7 0 8 2 4
12
Find the missing values in this table:
x 0 1 2 3 4 y -9 -20 -31 -42 -53
Find the missing values in each of these tables and, if possible, find the equation for the table. 1. 3. 2. 4.
Write an Equation for a Function
• Find the first difference for x.
• Find the first difference for y.
• Find
• Find the y-intercept: the y-coordinate in (0, )
• Write equation in the form: y = x + original value
Changeiny yChangeinx x
Δ=Δ
yx
ΔΔ
Change in y Change in x
x -10 -7 -4 -1 0 2
y -19 -16 -13 -10 -7
x 0 1 2 3 4
y -15 -20 -25 -30
x –5 –4 –1 0 2 3
y 14 6 –3 –12 –15
x 0 1 2 3 4
y 17 24 31 38
Chapters 1 & 4
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Find the missing values in each of these tables and, if possible, find the equation for the table. 5. 9. 6. 10. 7. 11. 8. 12.
x -6 -4 -1 0 5
y 9 5 -1 -13
x 4 5 6 7 0
y 29 36 43 50
x 0 -10 -11 -12 -14
y 84 92 100 116
x 7 0 -5 -11 -15
y -29 31 61 81
x -8 -5 -3 0 9
y -31 -19 -11 37
x -1 0 4 8 12
y -6 9 21 33
x -13 -9 -6 0 8
y 19 11 5 -23
x -7 -1 0 6 8
y 12 6 -1 -3
14
Find the equation that corresponds to these tables. 13. 19.
x 8 6 4 2 0
y 15 13 11 9 7
14. 20.
x 0 -2 -3 -5 -9
y -5 -21 -29 -45 -77
15. 21.
x -4 -2 0 2 4
y 7 3 -1 -5 -9
16. 22.
x -6 -3 0 3 6
y 20 11 2 -7 -16
17. 23.
18. 24.
x -6 -5 -4 -2 0
y -36 -31 -26 -16 -6
x -20 -15 -10 -5 5
y 39 29 19 9 -11
x 0 4 8 9 12
y 4 40 76 85 112
x 2 3 5 8 13
y 4 6 10 16 28
x -3 -2 -1 0 1
y -17 -13 -9 -5 -1
x -3 -2.5 -2 0 1
y -22 -18 -16 -8 -4
x -2 -1.5 -1 0 1
y 16 14.5 13 10 7
x 1 3 5 7 9
y 5 9 13 17 21
15
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Graphing Linear Equations
1. x + 3 = y 2. y = 3x + 2 3. 4x – y = 3 4. 4x + 3y = 6 5. 7x – 2y = 5 6. y = 5 and x = 5
1. Rewrite the equation in slope-intercept form. 2. Identify the slope. 3. Identify the y-intercept. 4. Graph the y-intercept. 5. Locate two other points on the line using the slope. 6. Draw a line through the points. 7. Label the line.
17
Intercepts are points where the graph crosses the axes. x-intercept = (a, 0) or a graph crosses the x-axis. y-intercept = (0, b) or b graph crosses the y-axis.
The STANDARD FORM of a linear equation is: Ax + By = C where A, B, C are integers and A ≥ 0 and A and B are both not equal to 0. A linear function is a linear equation were B ≠ 0 and whose domain is understood to be all real numbers. Graph using intercepts. 1. x-intercept is 2 2. 6x + 7y = 42 3. 3x + 4y = 6 y-intercept is 2.
SLOPE = m =
ΔyΔx
=y1 − y2x1 − x2
The SLOPE-INTERCEPT FORM of a linear equation is: y = mx + b where m = slope =
ΔyΔx
and b = y-intercept or (0, b)
The POINT-SLOPE FORM of a linear equation is: y – y1 = m(x – x1) given slope m and point (x1, y1).
18
Comparing Multiple Representations 1. Find and compare the slopes for the linear functions f and g. f(x) = ½ x – 4 Slope of f = ____________ Slope of g =____________ Compare: 2. Find and compare the y-intercepts for the linear functions f and g.
y-intercept of f ____________ y-intercept of g ____________ Compare: Connor and Sheila are in a rock-climbing club. They are climbing down a canyon wall. Connor starts from a cliff that is 200 feet above the canyon floor and climbs down at an average speed of 10 feet per minute. Sheila climbs down the canyon wall as shown in the table.
3. Interpret the rates of change and initial values of the linear functions in terms of the situations they model. Connor Sheila Initial value ____________ Initial value ____________ Rates of change ____________ Rates of change ____________ Compare:
x -4 0 4 8 g(x) -3 -3 -1 0
x -1 0 1 2 f(x) -7 -2 3 8
Time (min) 0 1 2 3
Sheila’s height (ft) 242 234 226 218
Holt McDougal , Course 3, 13.4A
19
Scatterplots & Line of Best Fit The 1990 earnings per share and dividends per share for 35 electric utility companies (in the central United States) are shown in the table. 1. Enter the data into L1 and L2. 2. Create a scatterplot. 3. 2ND 0 CATALOG D DiagnosticON ENTER ENTER CLEAR 4. STAT CALC 4: LinReg(ax+b) ENTER 5. Write the line of best fit in space to right. _______________________ 6. Write Correlation coefficient, r = _______
Earnings Dividend Earnings Dividend Earnings Dividend Earnings Dividend
1.67 1.73 1.99 1.67 2.55 2.35 3.32 2.62 1.73 1.46 2.00 1.72 2.56 2.00 3.38 2.51 1.77 1.48 2.00 1.65 2.58 1.80 3.45 2.81 1.79 1.42 2.00 1.86 2.69 2.46 3.54 2.28 1.84 1.63 2.23 1.74 2.74 2.10 3.70 2.50 1.90 1.60 2.23 1.56 2.77 1.74 3.79 2.76 1.92 1.83 2.25 1.80 2.79 2.30 4.12 2.40 1.97 1.46 2.38 2.20 3.02 1.90 4.40 2.96 1.99 1.56 2.48 1.60 3.26 1.78
The data in the table shows the age in years and the number of hours slept in a day by 28 infants who are less than one year old. 1. Enter the data into L1 and L2. 2. Create a scatterplot. 3. 2ND 0 CATALOG D DiagnosticON ENTER ENTER CLEAR 4. STAT CALC 4: LinReg(ax+b) ENTER 5. Write the line of best fit in space to right. _______________________ 6. Write Correlation coefficient, r = _______
Age (yrs) Sleep (hrs) Age (yrs) Sleep
(hrs) Age (yrs) Sleep (hrs) Age (yrs) Sleep
(hrs) .03 15.0 .21 14.5 .52 14.4 .86 13.9 .05 15.8 .26 15.4 .69 13.2 .90 13.7 .05 16.4 .34 15.2 .70 14.1 .91 13.1 .08 16.2 .35 15.3 .75 14.2 .94 13.7 .10 14.9 .35 14.4 .80 13.4 .97 12.7 .11 14.8 .44 13.9 .82 14.3 .98 13.7 .19 14.7 .52 13.4 .82 13.2 .98 13.6
20
ALGEBRA 1 FORMULA SHEET
Linear Equations
Slope: m =
y2 − y1
x2 − x1
Point-Slope Formula: (y – y1) = m(x – x1) Slope-Intercept Formula: y = mx + b Standard Equation of a Line: Ax + By = C
Arithmetic Properties Additive Inverse: a + (– a) = 0 Multiplicative Inverse:
a • 1
a= 1
Commutative Property: a + b = b + a a � b = b � a Associative Property: (a + b) + c = a + (b + c)
(a � b) � c = a � (b � c) Identity Property: a + 0 = a a � 1 = a Distributive Property: a�(b + c) = a�b + a�c Multiplicative Property of Zero: a � 0 = 0 Additive Property of Equality: If a = b, then a + c = b + c Multiplicative Property of Equality: If a = b, then a � c = b � c
Formulas that you may need to solve questions on this exam are found below. You may use calculator π or the number 3.14
A=Lw
V=Lwh
21
Exponential Properties
am � an = am+n
(am)n = am�n
am
an = am−n
a−1 = 1
a
Algebraic Equations
Slope: m =
y2 − y1
x2 − x1
Slope-intercept Form: y = mx + b
Pythagorean Theorem
a2 + b2 = c2
Cone
V = 1
3π r2 h
Cylinder
V = π r2 h
Sphere
V = 4
3π r3
PSSA MATHEMATICS GRADE 8 REFERENCE
Formulas that you may need to work questions are found below. You may refer back to this age at any time during the mathematics test.
You may use calculator π or the number 3.14.
a
b
c
22
Addition add
addend
altogether
bigger than
greater than
in all
increased by
larger than
longer than
more
more than
older than
plus
sum
taller than
tally
together
the sum of
the tally of
the total of
total
Subtraction – amount of increase
decreased by
deduct
deducted from
difference
diminished by
fewer than
how many fewer
how many more
how much greater
less
less than
minus
shorter than
smaller than
subtract
subtracted from
take away
the difference between
younger than
Multiplication
of use
as many as
as much as
double use 2●
factor
multiply
product
times
the product of
thrice use 3●
triple use 3●
twice use 2●
Division
(any fraction)
average
divided by
divided into
dividend
divisor
out of
quotient
the average of
the quotient of
Variable
number
the number of ...
unknown
h, x, y, n
Exponent base
power
cubed (....)3
squared (....)2
the square of (....)2
square root of
Equality = any verb
equals
is
is the answer to
is the same as
Inequality
does not exceed
is at least
is at most
is between x
is greater than
is greater than or equal to
is larger than
is less than
is less than or equal to
is more than
is no less than
is no more than
is not equal to
Natural Numbers Whole Numbers Integers {1, 2, 3, …} {0, 1, 2, 3, …} {0, 1, 2, …}
Rational Numbers Any number that can be written as where a and b are Integers
and b 0. Includes all integers, fractions, terminating
decimals, repeating decimals, percents and perfect roots.
Irrational Numbers Any number that is not Rational. Includes non-terminating
non-repeating decimals, and non-perfect roots.
Real Numbers Includes all Rational and Irrational Numbers
Additive Inverse:
a + (– a) = 0
Multiplicative Inverse:
a = 1
Commutative Property:
a + b = b + a
a b = b a Associative Property:
(a + b) + c = a + (b + c)
(a b) c = a (b c)
Identity Property:
a + 0 = a AND a 1 = a
Distributive Property:
a (b + c) = a b + a c
Multiplicative Prop. of Zero:
a 0 = 0
Additive Prop of Equality: If a = b, then a + c = b + c.
Multiplicative Prop of Equality: If a = b, then a c = b c
TransformationType RuleTranslation Moverightorleftaunits Addaor–atoeachx-coor.
Moveupordownbunits Addbor–btoeachy-coor.
Reflection Acrossthey-axis Multipleeachx-coorby-1Acrossthex-axis Multiplyeachy-coorby-1
Rotation
180° Multiplybothcoorby-1.
90°clockwise Multiplyeachx-coorby-1,thenswitchx-&y-coor.
90° counterclockwise Multiplyeachy-coorby-1,thenswitchx-&y-coor.
Dilation ScaleFactor Multiplyeachcoor.byscalefactor.
23
TRIANGLE: Perimeter = side1 + side
2 + side
3
Area = base ● height
180 = Angle1 + Angle2 + Angle3
TRAPEZOID: Area = height (base1 + base
2)
Perimeter = side1 + side
2 + side
3 + side
4
PARALLELOGRAM: Area = base ● height
Perimeter = side1 + side
2 + side
3 + side
4
RECTANGLE: Area = length ● width
Perimeter = 2 length + 2 width
SQUARE: Area = side2
Perimeter = 4 side
CIRCLE: Area = radius2
Circumference = 2 radius
CUBE: Volume = side3
Surface Area = 6 side2
PRISM: Volume = length ● width ● height
CYLINDER: Volume = radius2 ● height
CONE: Volume = radius2 ● height
SPHERE: Volume = radius3
PYTHAGOREAN THEOREM: c2 = a
2 + b
2
ANGLE MEASURE:
Sum of angles = 180(n – 2)
180 (n – 2) = a1 + a2 + … + an
Angle = 180( n – 2 ) / n
FORMS OF LINEAR EQUATIONS: Slope Intercept Form: y = mx + b where m = slope and b = y-intercept. Standard Form: Ax + By = C where A, B, C are integers and A ≥
Point-Slope Form: (y – y1) = m(x – x1) where m = slope and point is (x1, y1).
DISTANCE = rate ● time
PREDICTED VALUE = Rate per Unit ● Number of Units
PREDICTED VALUE = Original Value + Rate per Unit ● Number of Units
PROPORTIONS: OR
SLOPE = m = for points (x1, y1) and (x2, y2)
SUM = first + second
TEMPERATURE (choose one): FAHRENHEIT = Celsius + 32 OR CELSIUS = (Fahrenheit – 32)
MEASUREMENT LABELS FOR WORD PROBLEMS
Perimeter, Circumference, Distance, Base, Height, Length, Radius, Side, Width
mm, cm, m, km, inches, feet, yards, miles
Area, Surface Area mm2, cm , m , km , inches , feet , yards , miles
Volume cm , m , km , inches , feet , yards , miles
Rate rate per unit, mph, mpg, cost per unit, % (percent)
EXPONENT RULES: am � an
= a m + n
(am)n = a
m�n a0 = 1
2 2 2 2 2 2 2
3 3 3 3 3 3 3
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