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

y = mx + b slope

y = mx + b y-intercept

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

UNIT RATE CONSTANT PROPORTIONALITY OF SLOPE M CONSTANT OF VARIATION

POSITIVE SLOPE

NEGATIVE SLOPE

RISE RUN SLOPE

Slope Change of y Change of x

4 = 2 2 CONSTANT RATE OF CHANGE CHANGE OF Y CHANGE OF X X Y 2 4 8 6 12 16 +4 +2 4 2 = 2 +2 +4 +2 +4

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

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

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

Rise run 9 12 3 4 = = SLOPE TRIANGLES

y2 – y1 x2 – x1 slope

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

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

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

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 x2 - x1 1 – 0 1 Find the y-intercept (b): The table has (0,3) the y-intercept is 3 Answer: Y = mx + b Y = 2x + 3

y = kx Direct variation y = mx

domain x

range y

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).

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

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

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

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

Lines are parallel No solution Null set

SAME LINES INFINITE SOLUTIONS ∞ ALL NUMBERS

NON PROPORTIONAL

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

PROPORTIONAL

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

GREATER THAN

LESS THAN

GREATER THAN OR EQUAL TO

LESS THAN OR EQUAL TO

add Plus Sum Increased by total

subtraction Difference Subtracted from Minus Decreased by

Product Times Twice Double of multiply

Quotient Divided by Half Separated into over division

Is Results in Is the same as Equivalent to Equal

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

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

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

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

Formula for Scale Factor? New Old

Formula for new perimeter? 1 K x old

Formula for new area? 2 K x old

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

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

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

Keyword for Corresponding Matching

Keyword for Congruent Same Equal

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

What do you call the red line? Transversal

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 °

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 °

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

What is this axis? x-axis

What is this axis? y-axis

What is the y-intercept of the graph 5

What is the slope of the graph? -1

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

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

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

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

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

What are these called? Legs of a Triangle

What is this called? Hypotenuse

Which side is always the biggest? Hypotenuse

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

Convert to standard decimal Notation 6.38 x 10-5 0.0000638

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

Convert to standard decimal Notation 3.56 x 10-4 0.000356

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

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

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

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

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

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

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

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

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

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

COLORS IN A RAINBOW VS. SHOE SIZE

Perimeter of the Base (P) Perimeter of the Base (Rectangle) P = 2 ( l + w ) P = 2 ( 3 + 2 ) P = 2 ( 5 ) P = 10 ft

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

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

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

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 + 2 * 6 S = 60 + 2 * 6 S = 60 + 12 S = 72 ft2 B = b * h B = 3 * 2 B = 6ft2 P = 2 ( l + w ) P = 2 ( 3 + 2 ) P = 2 ( 5 ) P = 10 ft

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

Volume = Sphere V = 4/3 𝜋 r³ r = 7cm V = 4/3 x 𝜋 x 7³ V = 1436.76 cm³

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 = 376.99 cm²

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

Perimeter of the Base (P) Perimeter of the Base (Rectangle) P = s1 + s2 + s3 + s4 P = 2 + 2 + 3 + 3 P = 4 + 3 + 3 P = 7 + 3 P = 10 ft

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

Lateral Surface Area S = P * h S = 10 * 6 S = 60 ft2 P = s1 + s2 + s3 + s4 P = 2 + 2 + 3 + 3 P = 4 + 3 + 3 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

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 + 2 * 6 S = 60 + 2 * 6 S = 60 + 12 S = 72 ft2 B = b * h B = 3 * 2 B = 6ft2 P = s1 + s2 + s3 + s4 P = 2 + 2 + 3 + 3 P = 4 + 3 + 3 P = 7 + 3 P = 10 ft

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

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

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 = 2 1 x 32 New = 2 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 = 2 2 x old 3 1 = 3 16 = 4 x old The perimeter will increase by 3. 4 in2 = old

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

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:

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.

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

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

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.)

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

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.

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

This rotation is 90 degrees counterclockwise.                                              Clockwise           Counterclockwise

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.

              Line reflections are FLIPS!!!

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!

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?

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.

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

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

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

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

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.

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.

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

Simple Interest

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.

Formula I = P r t

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

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

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

Examples Susan deposits $2000 into her savings account. What is her balance after she earns 7% simple interest for 6 years? I = ? Interest 980.00 P = $2000 + Principal + 2000.00 r = 7% total balance $2980.00 t = 6 years I = P r t I = 2000 X .07 X 7

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.

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) .038 t = 5 years A = p(1 + r)t A = 1200(1 + .038)5

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) .067 t = 3 years A = p(1 + r)t A = 3500(1 + .067)5