1. FEBUARY BENCHMARK REV IEW
Teachers please show slides to the students. Click on each, there are answers to the questions.

2. y = mx + b
slope

3. y = mx + b
y-intercept

4. (0, -1)
(0, 3)
(0, -11)
Y - intercept
(0, -93)
(0, 2)
(0, -9)
(0, 68)

5. UNIT
RATE
CONSTANT
PROPORTIONALITY OF
SLOPE M
CONSTANT OF
VARIATION

6. POSITIVE
SLOPE

7. NEGATIVE
SLOPE

8. RISE
RUN
SLOPE

9. Slope
Change of y
Change of x

10. 4 = 2 2 CONSTANT RATE OF CHANGE CHANGE OF Y CHANGE OF X X Y 2 4 8 6 1216 +4 +2 4 2
= 2 +2 +4 +2 +4

11. Determine the constant rate of change and interpret its meaning.
The constant rate of change is: -2 2
= -1 gallon of water leaks per hour -2 2

12. Interpret the unit rate and compare it to the slope.
The unit rate is:
-10
= -5 meters
per second
-10 2 2

13. Identify the constant of variation and interpret its meaning.15
= $15 per lawn 1 1 15

14. Rise
run 9 12 3 4 = =
SLOPE TRIANGLES

15. y2 – y1
x2 – x1
slope

16. Find the slope for the following points (4, 3) and (7, 8)5 3
8-3
7-4
y2 – y1
x2 – x1 = =

17. Write the equation for the graph.
1. Write the equation in y = mx + b
B = 1
2. Determine the y-intercept (b). Remember the Y-intercept is the point of the line that passes the y-axis. 4 1
3. Find the slope by using:
Rise
run 1 4
Y = 1 x + 1 4

18. Y = mx + b SLOPE INTERCEPT FORM m – SLOPE = -3/4 Y = -3/4 x + 3
b – Y Intercept = 3 ( 0 , 3 )
Goes through the Y- axis.
Y = -3/4 x + 3

19. Write an equation in slope-intercept (y = mx + b) form for the table.1 2 3 4 5 7 9 11
Find the slope using the formula
Pick 2 points from the table:
(0, 3) and (1, 5)
y2 – y1 = 5 – 3 = 2= 2
x x –
Find the
y-intercept (b):
The table has (0,3)
the y-intercept is 3
Answer:
Y = mx + b
Y = 2x + 3

20. y = kx
Direct variation
y = mx

21. domain x

22. range y

23. to exactly one member of
FUNCTION OR NON FUNCTION? F U N C T I O X Y 1 2 3 4 5 6
***Remember:
Each member of the
domain(x) is mapped
to exactly one member of
the range (y).

24. X Y 1 2 4 6 NON FUNCTION OR NON FUNCTION? F U N C T I O ***Oh LOOK!!!!
X is a cheater!!!
1 has too many partners.
WHAT A PLAYER!!!!!!
Definitely not a
Function.
There are members of the domain is mapped to more than one member of the range.
NON F U N C T I O X Y 1 2 4 6

25. Complete the function table.X
2x + 1 y -2 1 2
2(-2) + 1 -3
2 (0) + 1 1
2 (1) + 1 3
2 (2) + 1 5

26. Determine whether the relation is a function
A. No, there are members of the domain mapped to more than one member of the range.
B. No, each member of the domain is mapped to exactly one member of the range.
C. Yes, there are members of the domain mapped to more than one member of the range.
D. Yes, each member of the domain is mapped to exactly one member of the range.
ANSWER IS D

27. One solution Lines intersect Y = 3x -2 3x -2 = -2/3x + 1.5

28. Lines are parallel
No solution
Null set

29. SAME LINES
INFINITE SOLUTIONS ∞
ALL NUMBERS

30. NON PROPORTIONAL

31. Y = 9x
Y = 2x
Linear Proportional
equations
Y = -6x
Y = -4x

32. PROPORTIONAL

33. Linear Non-Proportional
Y = 2x + 5
Y = 9x -7
Linear Non-Proportional
equations
Y = -4x +8
Y = -6x - 4

34. GREATER
THAN

35. LESS
THAN

36. GREATER THAN OR
EQUAL TO

37. LESS THAN OR
EQUAL TO

38. add
Plus
Sum
Increased by
total

39. subtraction
Difference
Subtracted from
Minus
Decreased by

40. Product
Times
Twice
Double of
multiply

41. Quotient
Divided by
Half
Separated into
over
division

42. Is
Results in
Is the same as
Equivalent to
Equal

43. Less than < Or
Less than or equal to ≤
At most
No more than
maximum

44. Greater than or equal to ≥
At least
No less than
minimum

45. What is scale factor?
When you make a shape bigger or smaller

46. When the scale factor is less than 1? Reduction or Enlargement?

47. Formula for Scale Factor?
New
Old

48. Formula for new perimeter?
K x old

49. Formula for new area?
K x old

50. What is the Algebraic Representation for k=5
(x, y) (5x, 5y)

51. What is the Algebraic Representation these two points: T (2 , 8) T’ (4, 16) ?
(x, y) (2x, 2y)

52. What is similar?
Same shape, not always the same size

53. Keyword for Corresponding
Matching

54. Keyword for Congruent
Same
Equal

55. Proportional Non-Proportional
Goes through origin
Has CROC
Constant Ratios
Has a y-intercept
Has CROC
No Constant Ratios

56. What do you call the red line?
Transversal

57. x ° x =132 ° 132° What is the value of x ?
ALTERNATE INTERIOR ANGLES are interior angles that lie on opposite sides of the transversal. When the lines are parallel their measures are equal.
132°
x °
What is the value of x ?
x =132 °

58. x ° x =62 ° 62° What is the value of x ?
ALTERNATE EXTERIOR ANGLES are exterior angles that lie on opposite sides of the transversal. When the lines are parallel, their measures are equal.
62°
x °
What is the value of x ?
x =62 °

59. Corresponding Angles
148°
x °
What is the value of x ?
x =148 °

60. What is this axis?
x-axis

61. What is this axis?
y-axis

62. What is the y-intercept
of the graph 5

63. What is the slope of the graph?-1

64. What is the slope formula?
Y2 – y1
X2 – x1

65. Find the slope for these
two points.
T (1,3) and O (4, 7)
m = 4/3

66. Unit Rate is the same as Slope
Unit Rate is the cost of 1

67. What is the slope intercept form
equation?
Y = mx + b

68. What is the formula for Pythagorean
Theorem?
a2 + b2 = c2

69. What are these called?
Legs of a Triangle

70. What is this called?
Hypotenuse

71. Which side is always the biggest?
Hypotenuse

72. When you see the word ladder, What concept do you apply?
Pythagorean Theorem
a2 + b2 = c2

73. Convert to standard decimal
Notation
6.38 x 10-5

74. Convert to Scientific Notation
2.3 x 106
2,300,000

75. Convert to standard decimal
Notation
3.56 x 10-4

76. Convert to Scientific Notation
6.4 x 107
64,000,000

77. Positive CPRT (Correlation, Pattern, Relationship, Trend)
Dots are
Above me,
So then it’s a
Positive CPRT
TOOL:
Box, Draw, Look

78. Negative CPRT (Correlation, Pattern, Relationship, Trend)
Dots are
Below me,
So then it’s a
Negative CPRT
TOOL:
Box, Draw, Look

79. Constant CPRT (Correlation, Pattern, Relationship, Trend)
Dots are
Next to me,
So then it’s a
Constant CPRT
…………………….
TOOL:
Box, Draw, Look

80. None CPRT (Correlation, Pattern, Relationship, Trend)
Dots are
CRAZY,
So then it’s a
None CPRT
TOOL:
Box, Draw, Look

81. FILL IN THE BLANKS: The _____ years of experience, the ______ income.
more
higher

82. HOURS STUDIED VS. QUIZ GRADE
FILL IN THE BLANKS:
The _______________ hours studied,
the _________quiz grades.
more
higher

83. HOURS OF VIDEO GAMES PLAYED VS. GRADE POINT AVERAGE
FILL IN THE BLANKS:
The _______ hours of playing video games,
the ________ grade point average.
more
lower

84. EXAM SCORE VS. NUMBER OF MISSED CLASSES
The __________ number of missed classes,
the ___________ exam score.
more
higher

85. SIZE OF TELEVISION VS. AVERAGE TIME SPENT WATCHING TV IN A WEEK.

86. COLORS IN A RAINBOW VS. SHOE SIZE

87. Perimeter of the Base (P)
Perimeter of the Base (Rectangle) P = 2 ( l + w ) P = 2 ( ) P = 2 ( 5 ) P = 10 ft

88. Find the area of the base (B)
Area of base (rectangle)
B= base x height
B= 5cm x 3cm
B= 15 cm²

89. Area of the Base (B) Area of the Base (Rectangle) B = base * height
B = 3ft * 2ft
B = 6ft2

90. Lateral Surface Area P = 2 ( l + w ) S = P * h S = 10 * 6 S = 60 ft2
P = 10 ft
S = P * h S = 10 * 6 S = 60 ft2
1. Draw
2. Label
3. Formula
4. Plug in
5. Show

91. Total Surface Area B = b * h P = 2 ( l + w ) B = 3 * 2 P = 2 ( 3 + 2 )
1. Draw
2. Label
3. Formula
4. Plug in
5. Show
S = Ph + 2B S = P * h + 2 * B S = 10 * * 6 S = * 6 S = S = 72 ft2
B = b * h
B = 3 * 2
B = 6ft2
P = 2 ( l + w )
P = 2 ( )
P = 2 ( 5 )
P = 10 ft

92. Find the volume
1. Draw
2. Label
3. Formula
4. Plug in
5. Show

93. Volume = Sphere
V = 4/3 𝜋 r³
r = 7cm
V = 4/3 x 𝜋 x 7³
V = cm³

94. Volume = Cone V = 1/3Bh V = 1/3(𝜋 𝑟 2 )ℎ V = 1/3(𝜋 x 6²) x 10
r = 6cm
V = 1/3(𝜋 𝑟 2 )ℎ
V = 1/3(𝜋 x 6²) x 10
h = 10cm
V = cm²

95. A . . B Find the distance between point A and B. C = ? a = 4 b = 5
1. Draw a line to connect the dots.
C = ?
a = 4
2. Complete the right triangle.
. B
3. Label what you know.
b = 5
4. Use Pythagorean Theorem
c = √(a² + b²)
c = √(4² + 5²)
c = 6.4 units

96. Perimeter of the Base (P)
Perimeter of the Base (Rectangle) P = s1 + s2 + s3 + s4 P = P = P = P = 10 ft

97. Area of the Base (B)
Area of the Base (Rectangle) B = b * h B = 3 * 2 B = 6 ft2

98. Lateral Surface Area S = P * h S = 10 * 6 S = 60 ft2
P = s1 + s2 + s3 + s4
P =
P =
P = 7 + 3
P = 10 ft
S = P * h S = 10 * 6 S = 60 ft2
1. Draw
2. Label
3. Formula
4. Plug in
5. Show

99. Total Surface Area B = b * h B = 3 * 2 B = 6ft2
1. Draw
2. Label
3. Formula
4. Plug in
5. Show
S = Ph + 2B S = P * h + 2 * B S = 10 * * 6 S = * 6 S = S = 72 ft2
B = b * h
B = 3 * 2
B = 6ft2
P = s1 + s2 + s3 + s4
P =
P =
P = 7 + 3
P = 10 ft

100. Find the area of the base (B)
Area of base (rectangle)
B= base x height
B= 5cm x 3cm
B= 15 cm²

101. Find the volume
1. Draw
2. Label
3. Formula
4. Plug in
5. Show

102. New = Change Units x Old New = 2 1 x 32 New = 2 x 32 NEW = 64 in.
Formula
A square has a perimeter of 32 inches. If the square is dilated by a scale factor of 2, what is the new perimeter?
NEW=CHANGE Units X OLD
CHANGE WORDS:
Doubled
Tripled
Dilate
Changed
Reduced
Enlarged
Increased
Decreased
UNITS
1 – PERIMETER
2 – AREA
3 - VOLUME
New = Change Units x Old
New = x 32
New = x 32
NEW = 64 in.
CHANGING
DIMENSIONS
A triangle has a new area of 16 square feet. If the triangle had a scale factor of 2, what was the old area?
The sides of an equilateral triangle is 5 cm. If the sides of the triangle is tripled, by what factor will the perimeter increase?
New = Change Units x Old
Change units
16 = x old
3 1 = 3
16 = 4 x old
The perimeter
will increase by 3.
4 in2 = old

104. To transform something is to change it
To transform something is to change it. In geometry, there are specific ways to describe how a figure is changed. The transformations you will learn about include:
Translation
Rotation
Reflection
Dilation

105. Renaming Transformations
It is common practice to name transformed shapes using the same letters with a “prime” symbol:
It is common practice to name shapes using capital letters:

106. Translations are SLIDES.
A translation "slides" an object a fixed distance in a given direction.  The original object and its translation have the same shape and size, and they face in the same direction.
Translations are
SLIDES.

107. Let's examine some translations related to coordinate geometry.
The example shows how each vertex moves the same distance in the same direction.

108. Write the Points What are the coordinates for A, B, C?
How are they alike?
How are they different?

109. In this example, the "slide"  moves the figure 7 units to the left and 3 units down. (or 3 units down and 7 units to the left.)

110. Write the points What are the coordinates for A, B, C?
How did the transformation change the points?

111. A rotation is a transformation that turns a figure about a fixed point called the center of rotation.  An object and its rotation are the same shape and size, but the figures may be turned in different directions.

112. The concept of rotations can be seen in wallpaper designs, fabrics, and art work.
           
Rotations are TURNS!!!

113. This rotation is 90 degrees counterclockwise.
                                            
Clockwise
         
Counterclockwise

116. A reflection can be seen in water, in a mirror, in glass, or in a shiny surface.  An object and its reflection have the same shape and size, but the figures face in opposite directions.  In a mirror, for example, right and left are switched.

117.              
Line reflections are FLIPS!!!

118. The line (where a mirror may be placed) is called the line of reflection.  The distance from a point to the line of reflection is the same as the distance from the point's image to the line of reflection.
A reflection can be thought of as a "flipping" of an object over the line of reflection.
                             
   
                           
If you folded the two shapes together line of reflection the two shapes would overlap exactly!

119. What happens to points in a Reflection?
Name the points of the original triangle.
Name the points of the reflected triangle.
What is the line of reflection?
How did the points change from the original to the reflection?

120. A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
A dilation used to create an image larger than the original is called an enlargement.  A dilation used to create an image smaller than the original is called a reduction.

121. Dilations always involve a change in size.
                                              
Notice how EVERY coordinate of the original triangle has been multiplied by the scale factor (x2).

122. REVIEW: Answer each question………………………..
Does this picture show a translation, rotation, dilation, or reflection?
How do you know?
Rotation

123. Does this picture show a translation, rotation, dilation, or reflection?
How do you know?
Dilation

124. Does this picture show a translation, rotation, dilation, or reflection?
How do you know?
(Line) Reflection

125. Letters a, c, and e are translations of the purple arrow.
Which of the following lettered figures are translations of the shape of the purple arrow?  Name ALL that apply.
Explain your thinking.
Letters a, c, and e are translations of the purple arrow.

126. The birds were rotated clockwise and the fish counterclockwise.
Has each picture been rotated in a clockwise or counter-clockwise direction?
The birds were rotated clockwise and the fish counterclockwise.

127. Can you name examples in real life of each transformation?
Translation
Rotation
Reflection
Dilation

128. Simple Interest

129. Simple Interest
I = Prt; where p is Principal, r is the rate and t is the time in years.
Interest – The amount earned or paid for the use of money.
Principal – The amount of money borrowed or deposited.
Simple Interest – The amount paid only on the principal
Annual Interest Rate – The percent of the principal earned or paid per year.

130. Formula
I = P r t

131. Example
A $1000 bond earns 6% simple annual interest. What is the interest earned after 4 years?
I = ?
P = $1000
r = 6% (CHANGE TO DECIMAL) .06
t = 4 years
I = P r t
I = 1000 X .06 X 4

132. ANOTHER EXAMPLE
Find the simple interest earned on $500 after 5 years in a money market account paying 5%.
I = ?
P = $500
r = 5% (CHANGE TO DECIMAL) .05
t = 5 years
I = P r t
I = 500 X .05 X 5

133. Balance
The amount of an account that earns simple interest is the sum of the interest and the principal.
Figure out the interest
I = Prt
And then add interest to the principal

134. Examples
Susan deposits $2000 into her savings account. What is her balance after she earns 7% simple interest for 6 years?
I = ? Interest
P = $ Principal
r = 7% total balance $
t = 6 years
I = P r t
I = 2000 X .07 X 7

135. Compound Interest
The interest that is earned on both the principal and any interest that has been previously earned.
Formula A = p(1 + r)t
Example – You deposit $1200 into an account that earns 3.8% interest compounded annually. Find the balance after 5 years.

136. Examples
You deposit $1200 into an account that earns 3.8% interest compounded annually. Find the balance after 5 years.
A = ?
p = $1200
r = 3.8% (CHANGE TO DECIMAL)
t = 5 years
A = p(1 + r)t
A = 1200( )5

137. Another Example
Max borrows $3500 for a new car. The loan has 6.7% interest that will be compounded annually. How much money will he owe after 36 months?
A = ?
p = $3500
r = 6.7% (CHANGE TO DECIMAL)
t = 3 years
A = p(1 + r)t
A = 3500( )5