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

5

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

6

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

7

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.

8

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

9

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

10

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

11

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

13

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

16

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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