Download ABC`s Of Math

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
mn

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