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IS 220 – JOHN J. PERSHING LORETTA M. WITEK Principal 837’s ABC’S of MATH SY 2005 - 2006 TEACHERS: MRS. MA. GRACIA S. VISICO MR. ALFRED JOHN DENISE A. LEWIS Technology Staff Developer NYCDOE Region 7 ROTATION Eddy Wu Zhen Hua Chen Kai Fai Zheng Julio Wong ANGLES AND TRIANGLES Moisey Yusufov Hubert Lasota Luis Quizphi EQUATIONS Priscilla Ochoa Kamilla Kulas Maria Amaya EXPONENTS Tahrir Said Johanna Aquino Karina Iglesias Ribhia Nassar ALGEBRAIC EXPRESSION Chia Hua Lee An Zhang Mei Lu ABC`s of Math Angles and Triangles Hubert Lasota-Leader Moisey Yusufov-Presenter Luis Quizhpi-Research Terms and Formulas Angle - is a set of point that is a union of two rays having the same endpoint Adjacent angles – two angles in same plane that have a common vertex and ea common side but do not have any interior points in common Complementary angles – two angles that can be add to 90° Supplementary angles – two angles that can be add up 180° Vertical angles – two angles whose sides are opposite Pythagorean Theorem says that length of hypotenuse squared is equal to the sum of the squares of the length of the legs c²=a²+b² Question #1 • Angle ABC and DBE are which of the following: • a) vertical angles • b) complementary angles • c) supplementary angles • d) vertical and supplementary angles • • c a b d e Answer #1 a) Vertical angles Because the sides of angles are opposite to each other Question #2 • The complement of an angle is 8 times as large as the angle. Find the number of degrees in each angle. x 8 x 90 9 x 90 9 9 0 x 10 8 x 10 8 Answer #2 x 10 0 8 x 80 0 The measures of the two angles are 10° and 80° • A ladder 39 feet long leans against a building and reaches the ledge of a window. If the foot of the ladder is 15 feet from the foot of the building, how high is the window ledge above the ground? 39ft ? 1)Draw the diagram 2)Form an equation 3)Square the known sides 15ft c²=a²+b² 4)Find unknown side by using additive inverse 39²=a²+15² 5)Find the root 1521=a²+225 -225 -225 1296=a² 36ft=a Ans Reference • - www.sparknotes.com. • -Mathematics A. Dressler, and Keenan. • Amsco School Publication, INC. ABC’s of Math Class 837 Equations!!!!! Group Members : Priscilla Kamila Leader Researcher Maria Presenter Terms and Formulas • An equation is a sentence that states that two algebraic expressions are equal. • To solve an equation means to find its solution set. • The reflexive property of equality states that for every number a: a=a. • The symmetric property of equality states that for all numbers a and b : if a=b, then b=a. • The transitive property of equal states that for all numbers a, b and c : if a=b and b=c then a=c • The addition property of equality states for all numbers a, b and c if a=b, then a +c = b+ c • The multiplication property of equality states that for all numbers a, b and c: if a= b, then a c = b c Question # 1 • Write an algebraic expression to represent the sum of 6 and three times a number square. • • • • A) 6 (3x) B) 6 (3x) 2 C) 6+3x 2 D) 6 3 x Answer #1 • D) 6 3x 2is the answer • D) is the correct choice because the sum means to add and times means to multiply Also, a square number express an exponent of two. Question #2 Constructed Response • Find the solution set of 3 x 6 18 4 • Solution Answer #2 3 x 6 18 5 6 6 3 x 12 5 5 3 5 ( x ) 12( ) 3 5 3 x 20 Answer: The solution set is {-20} Question #3 •Solve and check 7x+15=7 Answer #3 • • • • • • Solve and check: 7x+15=71 How to proceed 1)Write the equation 2)Add -15 to each member 3)Divide each member by 7 4)Check the solution 7 x 15 71 - 15 -15 7x 56 X=8 7 x 15 71 7(8) 15 71 56 15 71 71 71 References Mathematic A Dressler and Amsco School www.glancoe.com www.aplusmath.com ABC’s of Math EXPONENTS by Tahrir, Karina, Johanna & RIbhia TERMS AND FORMULA EXPONENTS- A numeral that indicates how any times a number or expression to multiplied by itself Formula(am)(an)=am+n am mn a an 1 m a m a a0=1 for any real number except 0 Question#1 What Value Of X Satisfies The Equation Below? 2x=128 A)4 B)6 C)7 D)9 Answer#1 THE ANSWER IS C. The answer is 7 because we multiplied by 2. 2x2x2x2x2x2x2=128 Question #2 Simplify: express using exponents. (a3b2)(a3b5)= Answer #2 (a3b2)(a3b5)= =(a3a3)(b2b5) =a3+3 b2+5 =a6b7 Question #3 The speed of light is about 3 x 108 meters per second. How far would a beam of light travel in 5 second? Express the answer in scientific notation. Answer #3 5(3)(108) (15)(108) 1.5 x 109 1.Multiply by 5 2.Apply the distributive property. 3.Move the decimal one place to the left. References 1.www.glencoe.com 2. Mathematics Advantage by Kaplan 3.Quick Review Math Handbook Glencoe Mathematics. Operation On Algebraic Expression Member: An Zhang Chia Hua Lee Mei Lu Formula: (a-b)2=a2-2ab+b2 1. An algebraic expression that is a number, a variable, or a product or quotient of numbers and variables is called a term. Example 5,x,8z,- 4 y2,0.7a2b2,and 7 - 5. w 2. Two or more terms that contain the same variable or variables, with corresponding variables having the same exponents, are called Like terms or similar terms. Example 6k and k, 5x2 and -7x2 , 9ab and 52 ab, 9 x2y3 and 2 11 - 3 x2y3 3. Two terms are unlike terms when they contain different variables, or the same variable or variables with different exponents. Example. 3x and 4y, 5x2 and 5x3, 9ab and 2 a, and 8 x3y2 and 4 x2y3. 5 3 7 4. A term that has no variable in the denominator is called a monomial. A polynomial is the sum of monomials. 5. A polynomial with three terms which are not like terms is x2+2x-3,3x5-8x4+x3, and a2b+13x+c. Find 5x(2x2-6x+12) A. B. C. D. 10x2-30x+60 10x3-30x+60 10x3-30x2+60x 10x3-30x2-60x 5x(2x2-6x+12) =10x3-30x2+60x Ans. C Explain: First 5x times 2x2 is equals to 10x3. 5x times 6x is equals to 30x2. 5x times 12 is equals to 60x and the answer is 10x330x2+60x (C). Find: (2x2-3x+1)+(3x2_x-5) (2x2_3x+1)+(3x2 - x-5) 2x2-3x+1 3x2-x-5 =5x2-4x-4 • Find the measure of the area of the shaded region in simplest form. 4d+2 d d 3d A=LxH =[(4d+2)x3d] =12d2+6d A=sxs =dxd =d2 12d2+6d-d2 =11d2+6d Step: 1.Find rectangles area. 2.Find squares area. 3.Subtract. www.glencoe.com www.google.com Mathematics A The End 837’s ABC’s of Math Translation , Rotation , Reflection By : Eddy Wu , Julio Wong , Kai Fai Zheng , Zhen Hua Zhen Terms / Definitions • Translation : A translation in which a geometric figure is slide to another position without rotation or reflection . • Rotation : Is a transformation that turns a line or a shape around a line point . This point is called the center of rotation . Rotation are usually measurement in the counter clockwise directions. • Reflection : Is one kind of transformation. When you hear the word “Reflection” you may think of a mirror . The mirror image , Or reverse image of a point or shape is called a reflection. Which translation will translate angle ABC with vertices A(-2,3), B(0,-2), C(-3,-4) to Angle A’ B’ C’ with vertices A’(-5,4), B’(3,1) and C’(-6,-3) ? A - 3 units right 1 unit up B - 3 units left 1 unit up C - 3 units right 1 unit down D - 3 units left 1 units down Triangle DEF has vertices D(2,2) , E(5,3), and F(7,1) draw the image of angle DEF under a rotation of 45 degree clockwise about the origin Reference • www.glencoe.com • Mathematics A