Black Tuesday – October 29 a stampede of selling hit the N.Y.S.E
Great Depression – worst period of economic decline in United States history, beginning in 1929 and lasted until World War II.
Reconstruction Finance Corporation – loaned money to railroads, banks, and insurance companies to help them stay in business.
Bonus Army – jobless veterans traveled to the capital as cheaply as possible.
Capital – money raised for a business venture.
Bankrupt – unable to pay debts.
Relief program – government program to help the needy.
Soup chicken – place where food is provided to the needy at little or no charge.
Public works – projects built by the government for public use.
Bonus – additional sum of money.
Franklin Roosevelt – Democrats New York governor; ran for president in 1932
Eleanor Roosevelt – married to FDR in 1905; a niece of Theodore Roosevelt.
Frances Perkins – first woman to hold a Cabinet post. She was secretary of labor.
Hundred Days – between Mar. 9 and Jun. 16, 1933, Congress passed 15 major new laws.
New Deal – program of FDR to end the Great Depression.
Works Progress Administration – put the jobless to work building hospitals, schools parks, playgrounds and airports.
Tennessee Valley Authority – boldest program of the Hundred Days. It set out to remake the Tennessee River valley.
Federal Deposit Insurance Corporation (FDIC) – insured savings accounts in banks approved by the government. If a bank insured by FDIC failed, the government would make sure depositors received their money.
Fireside chat – radio speeches given by President FDR.
Surplus – an extra amount, more than is needed.
Speculation – person who invests in a risky venture in the hope of marking a large profit.
Huey Long – Senator of Louisiana. He supported FDR, but soon he turned on him. He felt the New Deal of FDR didn’t go far enough.
Francis Townsend – A California doctor wanted the government to give older citizens over age of 60 to get a pension of $600 each month.
Charles Coughlin – a Roman Catholic priest also felt the New Deal didn’t go far enough.
Liberty League – Formed by conservative political and business leaders who felt FDR’s New Deal didn’t go enough.
Wagner Act – protected American workers from unfair management practices.
John L. Lewis – set up the Congress of Industrial Organization
Social Security Act – set up a system of pension for the elderly, unemployed and people with disabilities.
Pension – sum of money paid to people on a regular basis after they retire.
Collective bargaining – right of unions to negotiate with management for workers as a group.
Sitdown strike – work stoppage in which workers refuse to leave a factory.
Unemployment insurance – program that gives payments to people who have lost their jobs until they find work again.
Laissez faire – idea that government should play as small a role as possible in economic affairs.
Deficit spending – government practice of spending more than it takes in from taxes.
Dust Bowl – During 1930s states that suffered a severe drought.
Black Cabinet – Unofficial advisers who gave FDR advises.
Mary McLeod Bethune – A well-known Florida educator.
Indian New Deal – Gave Native American nations greater control over their own affairs.
John Steinbeck – A very famous writer during the Great Depression, told the heartbreaking story of the Okies.
Richard Wright – An African American writer, describe racial violence against black southerners.
Dorothea Lange – A photographer that was known for the despair of rural Americans during the depression.
Migrant worker – agricultural worker who moves with the seasons, planting or harvesting crops.
Civil rights – the constitutional rights due all citizens.
Repatriate – to send back to one’s own country.
Thursday, April 2, 2009
Monday, March 23, 2009
Ch 10 Quiz Study Sheet
Lesson 10 – 1 Exploring Quadratic Graph
Standard form – y = ax2 + bx + c
Quadratic parent function (simplest quadratic function) – y = x2 or f (x) = x2
The graph of a quadratic function is a U-shaped curve called a parabola. You can fold a parabola so that the two sides match exactly the same. The line that divides the parabola into two matching halves is called the axis of symmetry. The formula for the axis of symmetry is x = -b / 2a. Line of symmetry is the x-coordinate of the symmetry. The highest or lowest point of a parabola is its vertex. It is on the axis of symmetry.
y = ax2 + bx + c
If a is greater than zero; a > 0; the graph would turn out to be a regular U-shaped curve, and the vertex would be minimum.
If a is less than zero; a <> 0; the graph opens up. If a is less than zero; a < y =" –10x2" y =" –0.9x2" y =" 9x2" y =" x2" y =" –7x2," y =" –" y =" –" y =" –" y =" –" y =" –7x2" y =" –7x2," y =" –" y =" –" y =" –" y =" –7x2," y =" –" y =" –" y =" –" y =" –7x2">
Lesson 10 – 2 Quadratic Function
Role of “b” affects the position of the symmetry. It also moves the graph left or right. The equation of the axis of symmetry is x = -b / 2a. When graphing in standard form (learned in lesson 10 – 1) it gives you the middle value of the table y = ax2 + bx + c.
Graphing inequality is very similar to graphing linear inequality.
Inequality with signs greater than or less than you would graph the inequality with dotted lines; < , > dotted lines - - -.
Inequality with signs greater than or equal to or less than or equal to you would graph the inequality with solid lines; ≤ , ≥ solid line ───.
Shading inequality graphs. Inequality with signs greater than or greater than or equal to you would shade the upper part of the graph; >, ≥.
Inequality with signs less than or less than or equal to you would shade the lower part of the graph; < , ≤. Sample Questions: 1. Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y = 2x2 – 13x + 18. x = ; vertex: ( , ) x = – ; vertex: (– , – ) x = – ; vertex: (– , 3) x = ; vertex: ( , – ) 2. Find the coordinates of the vertex of the graph of y = 4x2 + x + 3. ( , ) (–8, ) (– , ) (– , 3) 3. Match the graph with its function.
Standard form – y = ax2 + bx + c
Quadratic parent function (simplest quadratic function) – y = x2 or f (x) = x2
The graph of a quadratic function is a U-shaped curve called a parabola. You can fold a parabola so that the two sides match exactly the same. The line that divides the parabola into two matching halves is called the axis of symmetry. The formula for the axis of symmetry is x = -b / 2a. Line of symmetry is the x-coordinate of the symmetry. The highest or lowest point of a parabola is its vertex. It is on the axis of symmetry.
y = ax2 + bx + c
If a is greater than zero; a > 0; the graph would turn out to be a regular U-shaped curve, and the vertex would be minimum.
If a is less than zero; a <> 0; the graph opens up. If a is less than zero; a < y =" –10x2" y =" –0.9x2" y =" 9x2" y =" x2" y =" –7x2," y =" –" y =" –" y =" –" y =" –" y =" –7x2" y =" –7x2," y =" –" y =" –" y =" –" y =" –7x2," y =" –" y =" –" y =" –" y =" –7x2">
Lesson 10 – 2 Quadratic Function
Role of “b” affects the position of the symmetry. It also moves the graph left or right. The equation of the axis of symmetry is x = -b / 2a. When graphing in standard form (learned in lesson 10 – 1) it gives you the middle value of the table y = ax2 + bx + c.
Graphing inequality is very similar to graphing linear inequality.
Inequality with signs greater than or less than you would graph the inequality with dotted lines; < , > dotted lines - - -.
Inequality with signs greater than or equal to or less than or equal to you would graph the inequality with solid lines; ≤ , ≥ solid line ───.
Shading inequality graphs. Inequality with signs greater than or greater than or equal to you would shade the upper part of the graph; >, ≥.
Inequality with signs less than or less than or equal to you would shade the lower part of the graph; < , ≤. Sample Questions: 1. Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y = 2x2 – 13x + 18. x = ; vertex: ( , ) x = – ; vertex: (– , – ) x = – ; vertex: (– , 3) x = ; vertex: ( , – ) 2. Find the coordinates of the vertex of the graph of y = 4x2 + x + 3. ( , ) (–8, ) (– , ) (– , 3) 3. Match the graph with its function.
y = x2 + 5x
y = –x2 – 5
y = x2 + 5
y = –x2 – 5x
Lesson 10 – 3 Solving Quadratic Equations
Standard form of a quadratic equation; y = ax2 + bx + c; can have one, two or no-real number solution. The solution of a quadratic equation and the related x-intercept are often called roots of the equation.
When a quadratic equation doesn’t have a “b” value you use square roots to solve the equation. You solve the equation by finding the square roots of each side; y = ax2 , y = ax2 + c.
Sample Questions:
1. Solve a2 + 36 = 0 by finding square roots.
–8, 8
no solution
–12, 12
–6, 6
2. Find the side of a square with an area of 79 ft2. If necessary, round to the nearest tenth.
4.3 ft
8.9 ft
6,241 ft
39.5 ft
3. Solve x2 + 6 = 0.
–16, 16
–6, 6
–1, 1
no solution
Lesson 10 – 4 Factoring to Solve Quadratic Equation
Use factoring to solve a quadratic equation you will use one more step → tee off (use a T chart). You have to set the equation equal to zero, and make sure you set the standard form equation equal to zero.
Sample Question:
1. Use the Zero-Product Property to solve –2x(2x + 5) = 0.
2, –
0, –
2,
0, –
2. Solve 16x = x2 by factoring.
0, 16
–4, 4
0, 4
1, 16
3. Solve 15 = 8x2 – 14x.
– ,
– ,
–3,
–5,
y = –x2 – 5
y = x2 + 5
y = –x2 – 5x
Lesson 10 – 3 Solving Quadratic Equations
Standard form of a quadratic equation; y = ax2 + bx + c; can have one, two or no-real number solution. The solution of a quadratic equation and the related x-intercept are often called roots of the equation.
When a quadratic equation doesn’t have a “b” value you use square roots to solve the equation. You solve the equation by finding the square roots of each side; y = ax2 , y = ax2 + c.
Sample Questions:
1. Solve a2 + 36 = 0 by finding square roots.
–8, 8
no solution
–12, 12
–6, 6
2. Find the side of a square with an area of 79 ft2. If necessary, round to the nearest tenth.
4.3 ft
8.9 ft
6,241 ft
39.5 ft
3. Solve x2 + 6 = 0.
–16, 16
–6, 6
–1, 1
no solution
Lesson 10 – 4 Factoring to Solve Quadratic Equation
Use factoring to solve a quadratic equation you will use one more step → tee off (use a T chart). You have to set the equation equal to zero, and make sure you set the standard form equation equal to zero.
Sample Question:
1. Use the Zero-Product Property to solve –2x(2x + 5) = 0.
2, –
0, –
2,
0, –
2. Solve 16x = x2 by factoring.
0, 16
–4, 4
0, 4
1, 16
3. Solve 15 = 8x2 – 14x.
– ,
– ,
–3,
–5,
Monday, March 16, 2009
S.S. Exit Project Information
The Research Paper:
Writing Strategy »»»»»»»»»»»»»» TELL THE STORY
- Exit Project Folder – info
1) Cover Sheet: Name, Class, Topic, Design
2) Introduction (What the paper is about & Research Questions)
3) Table of Contents
4) Research Paper (At least 5 pages)
5) Relevant Pictures (At least 5)
6) Maps, Charts, Diagrams & Graphs
7) Primary Source (Eyewitness account)
8) Creative Piece
*Interview (Optional)
9) Conclusion ________ Task
________ Understanding
________ Acknowledgments
- Must be typed
- Double Spaced
Writing Strategy »»»»»»»»»»»»»» TELL THE STORY
S.S. Handout:
(Click for a larger view)
Thursday, March 12, 2009
S.S. Chapter 25 Study Sheet w/ Diagrams
Want to Download this study sheet?
Click here:
http://www.megaupload.com/?d=L99X6U6K <-----Microsoft Word 1997-2003 http://www.megaupload.com/?d=SO0GN05T <----- Microsoft Word 2007
Highlights of the Roaring 20’s:
-Teapot Dome Scandal- when two oil executives bribed Albert Fall to give them government land in California and Teapot Dome, Wyoming.
-Kellogg Briand Act- a treaty that outlawed war.
-Prohibition
-Sacco and Vanzetti Trial => Prejudice in the Nation
-Farmers suffer because of the lack of other European countries buying crops.
-Clothing factories suffer because of the new short skirts (using less fabric).
-Labor unions have problems. Workers wanted higher pay, but since the government didn’t help out, workers felt betrayed by employers.
-Scopes Trial => Teachings about Evolution in the Classroom Becomes Illegal in Tennessee, Mississippi, and Arkansas
-KKK unties again. Terrorizes African Americans and Immigrants.
-Racism in the North – Lower paying jobs for African Americans and whites refuse apartments for blacks.
-Marcus Garvey – Universal Negro Improvement Association. “Back to Africa Movement”
-Limited Immigration (navitism)
-Hoover elected in 1928
Things to know:
recession- an economic slump.
installment buying- buying a credit.
stock- shares of ownership to investors.
bull market- a period of increased stock trading and rising stock prices.
on margin- when an investor would buy stocks with a 10% down payment.
communism- an economic system in which all wealth and property is owned by the community as a whole.
disarmament- reproduction of armed forces and weapons of war.
Harlem Renaissance is a time in the 1920’s, when many African Americans came to Harlem. The era was known for Jazz music, literature, dances, etc.
Prohibition – A ban of manufacturing, selling, and transportation of any liquor in the U.S.
League of Women – An organization that fought for equal rights for women.
Equal Rights Amendment – A right that the women should have the equal rights that men do.
Bootleggers – People that found ways to smuggle or make their own alcohol during the alcohol ban in the U.S.
Speakeasies – Bars that illegally sold alcohol to people.
Repeal – A cancellation.
Suburb – A community located outside of the city.
People to know:
Ana Roqué de Duprey – A woman that led the fight for women to vote in Puerto Rico.
Henry Ford – A person that introduce the assembly line to the car industry.
Charlie Chaplin – A very popular comedian during the 1920s.
Louis Armstrong – one of the brilliant young African American musicians who helped create jazz.
Ernest Hemingway – one of the most popular writers of the 1920’s; with a powerful style of writing that inspired many other writers.
F. Scott Fitzgerald – a writer in the 1920’s who wrote about the problems faced by the wealthy; usually about unhappiness.
Langston Hughes – one of the most well known poets of the Harlem Renaissance.
Zora Neele – a writer who wrote novels, essays, and short stories about how the African American folklore disappearing.
Babe Ruth – one of the most popular baseball players in the 1920’s. Raised in an orphanage, he worked hard and used his talent to become the star of the New York Yankees.
Charles A. Lindbergh – was known to be the first man to fly across the Atlantic without a map, parachute, and radio.
Diagrams: (Click the images for the full view!)
Click here:
http://www.megaupload.com/?d=L99X6U6K <-----Microsoft Word 1997-2003 http://www.megaupload.com/?d=SO0GN05T <----- Microsoft Word 2007
Highlights of the Roaring 20’s:
-Teapot Dome Scandal- when two oil executives bribed Albert Fall to give them government land in California and Teapot Dome, Wyoming.
-Kellogg Briand Act- a treaty that outlawed war.
-Prohibition
-Sacco and Vanzetti Trial => Prejudice in the Nation
-Farmers suffer because of the lack of other European countries buying crops.
-Clothing factories suffer because of the new short skirts (using less fabric).
-Labor unions have problems. Workers wanted higher pay, but since the government didn’t help out, workers felt betrayed by employers.
-Scopes Trial => Teachings about Evolution in the Classroom Becomes Illegal in Tennessee, Mississippi, and Arkansas
-KKK unties again. Terrorizes African Americans and Immigrants.
-Racism in the North – Lower paying jobs for African Americans and whites refuse apartments for blacks.
-Marcus Garvey – Universal Negro Improvement Association. “Back to Africa Movement”
-Limited Immigration (navitism)
-Hoover elected in 1928
Things to know:
recession- an economic slump.
installment buying- buying a credit.
stock- shares of ownership to investors.
bull market- a period of increased stock trading and rising stock prices.
on margin- when an investor would buy stocks with a 10% down payment.
communism- an economic system in which all wealth and property is owned by the community as a whole.
disarmament- reproduction of armed forces and weapons of war.
Harlem Renaissance is a time in the 1920’s, when many African Americans came to Harlem. The era was known for Jazz music, literature, dances, etc.
Prohibition – A ban of manufacturing, selling, and transportation of any liquor in the U.S.
League of Women – An organization that fought for equal rights for women.
Equal Rights Amendment – A right that the women should have the equal rights that men do.
Bootleggers – People that found ways to smuggle or make their own alcohol during the alcohol ban in the U.S.
Speakeasies – Bars that illegally sold alcohol to people.
Repeal – A cancellation.
Suburb – A community located outside of the city.
People to know:
Ana Roqué de Duprey – A woman that led the fight for women to vote in Puerto Rico.
Henry Ford – A person that introduce the assembly line to the car industry.
Charlie Chaplin – A very popular comedian during the 1920s.
Louis Armstrong – one of the brilliant young African American musicians who helped create jazz.
Ernest Hemingway – one of the most popular writers of the 1920’s; with a powerful style of writing that inspired many other writers.
F. Scott Fitzgerald – a writer in the 1920’s who wrote about the problems faced by the wealthy; usually about unhappiness.
Langston Hughes – one of the most well known poets of the Harlem Renaissance.
Zora Neele – a writer who wrote novels, essays, and short stories about how the African American folklore disappearing.
Babe Ruth – one of the most popular baseball players in the 1920’s. Raised in an orphanage, he worked hard and used his talent to become the star of the New York Yankees.
Charles A. Lindbergh – was known to be the first man to fly across the Atlantic without a map, parachute, and radio.
Diagrams: (Click the images for the full view!)
New York State Regents
Here's the site that contains the ACTUAL Science Regents!
Here:
http://www.nysedregents.org/testing/scire/regentlive.html
Be sure to download Adobe Reader! (It doesn't take up much space, not even half a gig)
http://get.adobe.com/reader/
Here:
http://www.nysedregents.org/testing/scire/regentlive.html
Be sure to download Adobe Reader! (It doesn't take up much space, not even half a gig)
http://get.adobe.com/reader/
Monday, March 9, 2009
Need More Help?
Here are some websites that will help you study for the Math State Exam
Book 1 of 2008 http://www.nysedregents.org/testing/mathei/08exams/m8bk1.pdf
Book 2 of 2008 http://www.nysedregents.org/testing/mathei/08exams/m8bk2.pdf
Book 3 of 2008 http://www.nysedregents.org/testing/mathei/08exams/m8bk3.pdf
*EVEN THOUGH THE LINK SAYS NYSEDREGENTS, IT IS NOT THE REGENTS*
DOWNLOAD THE STUDY SHEET NOW!:
http://www.megaupload.com/?d=N6UUFKL3
(Please do not steal this file and post it somewhere else. This took us HOURS to make)
Book 1 of 2008 http://www.nysedregents.org/testing/mathei/08exams/m8bk1.pdf
Book 2 of 2008 http://www.nysedregents.org/testing/mathei/08exams/m8bk2.pdf
Book 3 of 2008 http://www.nysedregents.org/testing/mathei/08exams/m8bk3.pdf
*EVEN THOUGH THE LINK SAYS NYSEDREGENTS, IT IS NOT THE REGENTS*
DOWNLOAD THE STUDY SHEET NOW!:
http://www.megaupload.com/?d=N6UUFKL3
(Please do not steal this file and post it somewhere else. This took us HOURS to make)
Math State Test Study Sheet!! with Free Download
For each topic I'll have sample questions and formula on the bottom.These are the topics that will be on the Math State Exam:
Angle pairs
Pythagorean Theorem
Transformation
Measurement
Equations / Inequalities
Sum of Interior Angles
Exponents
Percent
Polynomial
Unit Price
Map Scale
Convert Money
Angle Pairs
Complementary Angles - Angles that add up to 90° or a right triangle.
Example Of Complementary Angles:
Supplementary Angles - Angles that add up to 180° or a straight angle.
Example Of Supplementary Angles:
Vertical angles – The angles that are opposite of one another when two lines are formed. NOTE two angles equal each other.
Example Of Vertical Angles:
Adjacent Angles – two angles with a common side and vertex.
Example Of Adjacent Angles:
Corresponding Angles – angels that are equal. The angles are on the same side of the transversal one exterior and one interior. a, e are corresponding angles. Angles c, g are corresponding angles. b, f are corresponding angles. d, h are corresponding angles.
Example Of Corresponding Angles:
Transversal – A line that intersects two or more other lines to form eight or more angles.
Example Of Transversal:
Interior Angles – Angles formed inside a polygon. To find the sum of interior angles use: Sum of interior angles = 180(n-2); n = number of sides
Exterior Angles – Angles formed outside of a polygon.
Alternate Interior Angles – Angles that are created on the opposite sides of the transversal inside the parallel lines. d, e, and c, f are alternate interior angles.
Example Of Alternate Interior Angles:
Alternate Exterior Angles – Angles on the outside of the parallel lines. a, h, and b, g are alternate exterior angles.
Example Of Alternate Exterior Angles:
Pythagorean Theorem
If a and b are the measures of the legs of a right triangle and c is the measure of the hypotenuse, then a2 + b2 = c2.
Example Of Pythagorean Theorem:
Transformation *NOTE* Notation is normally not used in Math State Exam.
The image of a point, P, being transformed. P’ is P prime.
Reflection – mirror image. The line acts like a mirror. Notation is raxis.
If the image reflect across the x-axis use (x,y) → (x, -y)
If the image reflect across the y-axis use (x,y) → (-x, y)
Rotation – turning the figure either 90o or 180o or 270o. Angles of rotation assume a figure is rotated counterclockwise. All formulas below are ONLY used when the figure is rotated counterclockwise. If the figure is rotated clockwise FIRST use 360o minus the rotated degree THEN follow the formula. Notation is Rdegree.
If the figure is rotated 90o counterclockwise use: (x, y) → (-y, x)
If the figure is rotated 180o counterclockwise use: (x, y) → (-x, -y)
If the figure is rotated 270o counterclockwise use: (x, y) → (y, -x)
If the figure is rotated 90o clockwise use: 360 – 90 = 270, then use the 270 degree counterclockwise formula: (x, y) → (y, -x).
If the figure is rotated 180o clockwise use: 360 – 180 = 180, then use the 180 degree counterclockwise formula: (x, y) → (-x, -y).
If the figure is rotated 270o clockwise use: 360 – 270 = 90, then use the 270 degree counterclockwise use: (x, y) → (y, -x).
Translation
Moving a figure a specific distance in a specific direction. After translating the figure will still have the same orientation. Notation is Ta,b
a is direction for left (negative) or right (positive); b is direction for up (positive) or down (negative).
Formula: Ta,b (x, y) → (x + a, y + b)
Example: The coordinates of the vertices of figure ABC are A (-3, 5), B (4, 6), C(0, 2). What would the coordinates of the vertices of figure ABC be under the translation T3,2 ?
We know a is 3, b is 2, and we know all the coordinates for figure ABC. So now we would plug everything into the formula, which is Ta,b (x, y) → (x + a, y + b).
A’ = (-3, 5) → (-3 + 3, 5 + 2) → (0, 7) that is the new coordinates for vertex A.
B’ = (4, 6) → (4 + 3, 6 + 2) → (7, 8) that is the new coordinates for vertex B.
C’ = (0, 2) → (0 + 3, 2 + 2) → (3, 4) that is the new coordinates for vertex C.
Dilation – When the figure gets larger or smaller. Dilation creates figures that are similar but nor necessarily congruent. Use a scale factor to dilate the figure. Notation is Dk.
Formula is: (x, y) → (xk, yk) k = the scale factor.
Example: Figure ABC has vertices whose coordinates are A (0, 4), B(-1, 1), and C(-3,2). Dilate figure ABC and find the new coordinates using the scale factor 2 (D2).
We know that the scale factor is 2, and we also know all the coordinates for figure ABC.
A’ = (0, 4) → (0*2, 4*2) → (0, 8)
B’ = (-1, 1) → (-1*2, 1*2) → (-2, 2)
C’ = (-3, 2) → (-3*2, 2*2) → (-6, 4)
Measurement
Geometry Formulas
Area (click the picture to get a better view) :
Area:
Square: A= s2
Circle: A= pi × r2
Rectangle: A= a × b
Triangle: Area = 1/2(b × h)
Parallelogram: A= b × h
Trapezoid: A= 1/2h(b1 + b2)
Volume (click the picture to get a better view) :
Volume
Cube: V= a3
Rectangular Prism: V= a × b × c
Pyramid: V= (1/3) × b × h
Cylinder: V= pi × r2 × h
Perimeter (click the picture to get a better view) :
Perimeter:
Square: P= 4a
Circle P= 2 × r × pi
Rectangle: P= 2 (a + b)
Parallelogram: P= 2a + 2b
Triangle: P= a + b + c
Trapezoid: P= a + b + c + d =2m + c + d
Exponents
Percent
Polynomial
Unit Price
Map Scale
Convert Money
Download this study sheet at (Only ofr Pc NOT for Mac):
http://www.megaupload.com/?d=N6UUFKL3
Angle pairs
Pythagorean Theorem
Transformation
Measurement
Equations / Inequalities
Sum of Interior Angles
Exponents
Percent
Polynomial
Unit Price
Map Scale
Convert Money
Angle Pairs
Complementary Angles - Angles that add up to 90° or a right triangle.
Example Of Complementary Angles:
Supplementary Angles - Angles that add up to 180° or a straight angle.
Example Of Supplementary Angles:
Vertical angles – The angles that are opposite of one another when two lines are formed. NOTE two angles equal each other.
Example Of Vertical Angles:
Adjacent Angles – two angles with a common side and vertex.
Example Of Adjacent Angles:
Corresponding Angles – angels that are equal. The angles are on the same side of the transversal one exterior and one interior. a, e are corresponding angles. Angles c, g are corresponding angles. b, f are corresponding angles. d, h are corresponding angles.
Example Of Corresponding Angles:
Transversal – A line that intersects two or more other lines to form eight or more angles.
Example Of Transversal:
Interior Angles – Angles formed inside a polygon. To find the sum of interior angles use: Sum of interior angles = 180(n-2); n = number of sides
Exterior Angles – Angles formed outside of a polygon.
Alternate Interior Angles – Angles that are created on the opposite sides of the transversal inside the parallel lines. d, e, and c, f are alternate interior angles.
Example Of Alternate Interior Angles:
Alternate Exterior Angles – Angles on the outside of the parallel lines. a, h, and b, g are alternate exterior angles.
Example Of Alternate Exterior Angles:
Pythagorean Theorem
If a and b are the measures of the legs of a right triangle and c is the measure of the hypotenuse, then a2 + b2 = c2.
Example Of Pythagorean Theorem:
Transformation *NOTE* Notation is normally not used in Math State Exam.
The image of a point, P, being transformed. P’ is P prime.
Reflection – mirror image. The line acts like a mirror. Notation is raxis.
If the image reflect across the x-axis use (x,y) → (x, -y)
If the image reflect across the y-axis use (x,y) → (-x, y)
Rotation – turning the figure either 90o or 180o or 270o. Angles of rotation assume a figure is rotated counterclockwise. All formulas below are ONLY used when the figure is rotated counterclockwise. If the figure is rotated clockwise FIRST use 360o minus the rotated degree THEN follow the formula. Notation is Rdegree.
If the figure is rotated 90o counterclockwise use: (x, y) → (-y, x)
If the figure is rotated 180o counterclockwise use: (x, y) → (-x, -y)
If the figure is rotated 270o counterclockwise use: (x, y) → (y, -x)
If the figure is rotated 90o clockwise use: 360 – 90 = 270, then use the 270 degree counterclockwise formula: (x, y) → (y, -x).
If the figure is rotated 180o clockwise use: 360 – 180 = 180, then use the 180 degree counterclockwise formula: (x, y) → (-x, -y).
If the figure is rotated 270o clockwise use: 360 – 270 = 90, then use the 270 degree counterclockwise use: (x, y) → (y, -x).
Translation
Moving a figure a specific distance in a specific direction. After translating the figure will still have the same orientation. Notation is Ta,b
a is direction for left (negative) or right (positive); b is direction for up (positive) or down (negative).
Formula: Ta,b (x, y) → (x + a, y + b)
Example: The coordinates of the vertices of figure ABC are A (-3, 5), B (4, 6), C(0, 2). What would the coordinates of the vertices of figure ABC be under the translation T3,2 ?
We know a is 3, b is 2, and we know all the coordinates for figure ABC. So now we would plug everything into the formula, which is Ta,b (x, y) → (x + a, y + b).
A’ = (-3, 5) → (-3 + 3, 5 + 2) → (0, 7) that is the new coordinates for vertex A.
B’ = (4, 6) → (4 + 3, 6 + 2) → (7, 8) that is the new coordinates for vertex B.
C’ = (0, 2) → (0 + 3, 2 + 2) → (3, 4) that is the new coordinates for vertex C.
Dilation – When the figure gets larger or smaller. Dilation creates figures that are similar but nor necessarily congruent. Use a scale factor to dilate the figure. Notation is Dk.
Formula is: (x, y) → (xk, yk) k = the scale factor.
Example: Figure ABC has vertices whose coordinates are A (0, 4), B(-1, 1), and C(-3,2). Dilate figure ABC and find the new coordinates using the scale factor 2 (D2).
We know that the scale factor is 2, and we also know all the coordinates for figure ABC.
A’ = (0, 4) → (0*2, 4*2) → (0, 8)
B’ = (-1, 1) → (-1*2, 1*2) → (-2, 2)
C’ = (-3, 2) → (-3*2, 2*2) → (-6, 4)
Measurement
Geometry Formulas
Area (click the picture to get a better view) :
Area:
Square: A= s2
Circle: A= pi × r2
Rectangle: A= a × b
Triangle: Area = 1/2(b × h)
Parallelogram: A= b × h
Trapezoid: A= 1/2h(b1 + b2)
Volume (click the picture to get a better view) :
Volume
Cube: V= a3
Rectangular Prism: V= a × b × c
Pyramid: V= (1/3) × b × h
Cylinder: V= pi × r2 × h
Perimeter (click the picture to get a better view) :
Perimeter:
Square: P= 4a
Circle P= 2 × r × pi
Rectangle: P= 2 (a + b)
Parallelogram: P= 2a + 2b
Triangle: P= a + b + c
Trapezoid: P= a + b + c + d =2m + c + d
Equations / Inequalities
Practice for equations http://www.sosmath.com/algebra/solve/solve0/solve0.html
Practice for inequalities http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut18_ineq.htm
Exponents
Any number raised to the first power is that number itself.
Any number raised to the zero power is ALWAYS 1, EXCEPT zero to the zero power it is undefined.
Any number to the negative power the expression becomes a fraction with a numerator of 1 and a denominator if the positive power.
Adding and subtracting with exponents – like bases with unlike exponents CANNOT be added or subtracted unless they can be evaluated first.
Multiplying with exponents – to multiply powers of like bases, add the exponents.
Dividing with exponents – to divide powers of like bases, subtract the exponents of the divisor from the exponents of the dividend.
Raising a power to a power (power to the power rule) – to raise a term with an exponents to some power, multiply the exponents.
Raising a fraction to a power – to raise a fraction to a power, raise the numerator and the denominator to that power.
Raising a product to a power – to raise a product to a power, raise each factor to that power.
Percent
Percent increase/ decrease use the new price minus the old price and divided by the old price, and then multiply it by a 100 to get the percent increase/ decrease.
Percent increase/ decrease 100 (New – Old / Old )
Polynomial
Term – is an algebraic expression written with numbers, variables, or both and using multiplication, division, or both.
Constant – a term that has no variables
Coefficient- is the numerical part of the term. If no coefficient is written, then it is understood to be 1.
Like terms- terms that contain the SAME VARIABLE with corresponding variables having the SAME EXPONENTS. Terms are separated by plus (+) and minus (-) signs.
Monomial – an algebraic expression of exactly on term.
Add or Subtract Monomials With Like Terms – Use the distributive property and the rules of signed numbers to add or subtract the coefficients of each term. Write the sum with the variable part from the terms.
Polynomial – an algebraic expression of on or more unlike terms is a polynomial.
Binomials – polynomials with two unlike terms.
Trinomials – polynomials with three unlike terms.
Standard Form – a polynomial with one variable. When it has no like terms and is written from the largest exponents to the smallest.
Add polynomials – use the commutative property to rearrange the terms so like terms are beside each other. Combine like terms.
Unit Price
Unite Price is a rate: the rate of cost, or price, per 1 unit of measure, such as $1 per pound. To find the unit price, divide the total cost by the number of units.
Example: 4 pounds of grapes cost $7. How much does it cost to buy 1 pound?
So we use the total cost $ 7 divided by the number of units, which is 4, and we get an answer of $ 1.75 per pound of grape. 7/4 = 1.75.
Map Scale
If 1 unit on the map is equal to 15 mile real life, and you want to find out how many miles is 8 units on the map is in real life you would set up a proportion.
1 / 15 = 8 / x; where x is # of miles in real life. Then you cross multiply. You will get 120 = x
Convert Money
Use the conversions that the test give you and set it to a proportion.
Download this study sheet at (Only ofr Pc NOT for Mac):
http://www.megaupload.com/?d=N6UUFKL3
Subscribe to:
Posts (Atom)