COLLECTION OF DIFFERENT
PRESENTATIONS:
ALGEBRA-GRADE 10
COMPILED BY: BEATRICE S ZWANE
LOCATION: UNIVERSITY OF JOHANNESBURG...
DEFINITIONS
• ALGEBRAIC EXPRESSION – A GROUP OF
NUMBERS, SYMBOLS, AND VARIABLES THAT
EXPRESS AN OPERATION OR A SERIES OF
O...
DEFINITIONS CONTI……
• SIMPLIFY – COMBINE LIKE TERMS AND
COMPLETE ALL OPERATIONS
E.G.

•M+8+M
• (2 X 2) + 8

M=2

2M+8
4 + ...
Simplifying

Solving
Definitions
Checking

Using a
Formula
Exit
OBJECTIVE
LEARNERS WILL BE ABLE TO:

1)
2)

write equations using slope-intercept form.
identify slope and y-intercept fro...
•Write an equation of the line passing through the points (-3,2)
and (1,-2)

•Before answering this question you need to k...
WRITING EQUATIONS
 WHEN ASKED TO WRITE AN EQUATION, YOU
NEED TO KNOW TWO THINGS – SLOPE (M) AND
Y-INTERCEPT
 THERE ARE T...
• Now go back to your original
coordinates and fill in this equation
(-3,2) and (1,-2)
• Choose one of the coordinates, it...
SOLVING TYPE II USING ALGEBRA TILES

2x 6

2

Let,
= -x
=x

= -1
=1
ALGEBRAICALLY

2x 6

6

2

6

2x 4
2

x 2

2

Steps:
1) Write the Equation

2) Add +6 to each side
3) Divide each side by ...
2x 6

2
Steps
1) Write the Equation
2) Add +6 to both
sides
3) Cancel using Zero
Property
4) By the sharing
principal

The...
SIMPLIFY

2x 3 4 y 6 6x 2 y 1

4 x 6 y 10
WORDS THAT LEAD TO ADDITION
• SUM
• MORE THAN
• INCREASED
• PLUS
• ALTOGETHER
WORDS THAT LEAD TO SUBTRACTION
• DECREASED
• LESS
• DIFFERENCE
• MINUS
• HOW MANY MORE
EVALUATE EACH ALGEBRAIC EXPRESSION WHEN: X
•X+8

18

• X + 49

59

•X+X

20

•X–X

0

•X–7

3

• 42 – X

32

= 10
WRITE AN ALGEBRAIC EXPRESSION FOR THESE
SITUATIONS

• SCOTT’S BROTHER IS 2 YEARS
YOUNGER THAN SCOTT

s-2

• THE SUM OF TWO...
IMPORTANT!!!
THIS IS ONE OF THE BIG
CONCEPTS IN
ALGEBRA 1. YOU NEED TO
THOROUGHLY UNDERSTAND THIS!

SLOPE – INTERCEPT FORM...
TYPES OF LINES
• 1. ALL LINES ARE STRAIGHT.
• 2. THEY CAN BE HORIZONTAL, VERTICAL, OR DIAGONAL.
•Fill in the formula

M= (-2)-2
_____
1-(-3)

•Then subtract.
•You should end up with
M= - 4
___
www.rlsmart.net

4
WRITING EQUATIONS
WRITE AN EQUATION IN SLOPE-INTERCEPT FORM OF THE
LINE THAT HAS A SLOPE OF 2 AND A Y-INTERCEPT OF 6.
TO W...
2=(- 4)(- 3)+b
•Multiply: (-4) (-3)= 12
•2=12+b
•Subtract 12 from both
sides
•2-12= -10 12-12=0
(cancel out)
•And you answ...
TO FIND THE SLOPE AND YINTERCEPT OF AN EQUATION, WRITE
THE EQUATION IN SLOPE-INTERCEPT
FORM: Y = MX + B.
FIND THE SLOPE AN...
1. FIND THE SLOPE AND Y-INTERCEPT OF
Y = -2X + 4

M = 2; B = 4

2. FIND THE SLOPE AND Y-INTERCEPT.
Y=5

Y = MX + B
Y = 0X ...
Algebraic Fractions
Adding/Subtracting
Amsco Math A, Chapter 19
Combining with Like Denominators

Example:
Combine the
numerators over the
denominator

Simplify

The Answer!

2x
5

8x
5
...
Combining fractions with
Different Denominators
Example:
Multiply by 1 to get
the same
denominator

12
12

2
3
x 12 12

x ...
REFFERENCES
•

BY MRS CLEVETTE J. ACCESSED ON 17 DECEMBER, 2007.

HTTP://WWW.SLIDESHARE.NET/GUESTD5D6CC/ALGEBRA-205375?QID...
Algebra  slide share presantation
Algebra  slide share presantation
Algebra  slide share presantation
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Algebra slide share presantation

  1. 1. COLLECTION OF DIFFERENT PRESENTATIONS: ALGEBRA-GRADE 10 COMPILED BY: BEATRICE S ZWANE LOCATION: UNIVERSITY OF JOHANNESBURG DATE:06 MARCH 2014
  2. 2. DEFINITIONS • ALGEBRAIC EXPRESSION – A GROUP OF NUMBERS, SYMBOLS, AND VARIABLES THAT EXPRESS AN OPERATION OR A SERIES OF OPERATIONS. EXAMPLES: (A)R – 3 ( A)M + 8 • A VARIABLE CAN USE ANY LETTER OF THE ALPHABET. : EXAMPLES N+5 X–7 • EVALUATE AN ALGEBRAIC EXPRESSION – TO FIND THE VALUE OF AN ALGEBRAIC EXPRESSION BY SUBSTITUTING NUMBERS FOR VARIABLES.
  3. 3. DEFINITIONS CONTI…… • SIMPLIFY – COMBINE LIKE TERMS AND COMPLETE ALL OPERATIONS E.G. •M+8+M • (2 X 2) + 8 M=2 2M+8 4 + 8 = 12
  4. 4. Simplifying Solving Definitions Checking Using a Formula Exit
  5. 5. OBJECTIVE LEARNERS WILL BE ABLE TO: 1) 2) write equations using slope-intercept form. identify slope and y-intercept from an equation.
  6. 6. •Write an equation of the line passing through the points (-3,2) and (1,-2) •Before answering this question you need to know two formulas: and www.mathequations.com
  7. 7. WRITING EQUATIONS  WHEN ASKED TO WRITE AN EQUATION, YOU NEED TO KNOW TWO THINGS – SLOPE (M) AND Y-INTERCEPT  THERE ARE THREE TYPES OF PROBLEMS YOU WILL FACE.
  8. 8. • Now go back to your original coordinates and fill in this equation (-3,2) and (1,-2) • Choose one of the coordinates, it doesn’t matter which one. www.mathequations.com y=2 m = (- 4) x = (- 3) •After filling in everything you should have 2=(- 4)(- 3)+b M= - 4 ___ 4
  9. 9. SOLVING TYPE II USING ALGEBRA TILES 2x 6 2 Let, = -x =x = -1 =1
  10. 10. ALGEBRAICALLY 2x 6 6 2 6 2x 4 2 x 2 2 Steps: 1) Write the Equation 2) Add +6 to each side 3) Divide each side by +2 4) Check your answer 2(2) – 6 = -2 CORRECT!!
  11. 11. 2x 6 2 Steps 1) Write the Equation 2) Add +6 to both sides 3) Cancel using Zero Property 4) By the sharing principal Therefore x =2
  12. 12. SIMPLIFY 2x 3 4 y 6 6x 2 y 1 4 x 6 y 10
  13. 13. WORDS THAT LEAD TO ADDITION • SUM • MORE THAN • INCREASED • PLUS • ALTOGETHER
  14. 14. WORDS THAT LEAD TO SUBTRACTION • DECREASED • LESS • DIFFERENCE • MINUS • HOW MANY MORE
  15. 15. EVALUATE EACH ALGEBRAIC EXPRESSION WHEN: X •X+8 18 • X + 49 59 •X+X 20 •X–X 0 •X–7 3 • 42 – X 32 = 10
  16. 16. WRITE AN ALGEBRAIC EXPRESSION FOR THESE SITUATIONS • SCOTT’S BROTHER IS 2 YEARS YOUNGER THAN SCOTT s-2 • THE SUM OF TWO NUMBERS IS 12 v + c = 12 • THE DIFFERENCE BETWEEN TWO NUMBERS IS 5 m–n=5
  17. 17. IMPORTANT!!! THIS IS ONE OF THE BIG CONCEPTS IN ALGEBRA 1. YOU NEED TO THOROUGHLY UNDERSTAND THIS! SLOPE – INTERCEPT FORM Y = MX + B M REPRESENTS THE SLOPE
  18. 18. TYPES OF LINES • 1. ALL LINES ARE STRAIGHT. • 2. THEY CAN BE HORIZONTAL, VERTICAL, OR DIAGONAL.
  19. 19. •Fill in the formula M= (-2)-2 _____ 1-(-3) •Then subtract. •You should end up with M= - 4 ___ www.rlsmart.net 4
  20. 20. WRITING EQUATIONS WRITE AN EQUATION IN SLOPE-INTERCEPT FORM OF THE LINE THAT HAS A SLOPE OF 2 AND A Y-INTERCEPT OF 6. TO WRITE AN EQUATION, YOU NEED TWO THINGS: SLOPE (M) = 2 6 Y – INTERCEPT (B) = WE HAVE BOTH!! PLUG THEM INTO SLOPE-INTERCEPT FORM Y = MX + B y = 2x + 6
  21. 21. 2=(- 4)(- 3)+b •Multiply: (-4) (-3)= 12 •2=12+b •Subtract 12 from both sides •2-12= -10 12-12=0 (cancel out) •And you answer is -10=b www.rlsmart.net
  22. 22. TO FIND THE SLOPE AND YINTERCEPT OF AN EQUATION, WRITE THE EQUATION IN SLOPE-INTERCEPT FORM: Y = MX + B. FIND THE SLOPE AND Y-INTERCEPT. 1) Y = 3X – 7 Y = MX + B M = 3, B = -7
  23. 23. 1. FIND THE SLOPE AND Y-INTERCEPT OF Y = -2X + 4 M = 2; B = 4 2. FIND THE SLOPE AND Y-INTERCEPT. Y=5 Y = MX + B Y = 0X + 5 M=0 B=5
  24. 24. Algebraic Fractions Adding/Subtracting Amsco Math A, Chapter 19
  25. 25. Combining with Like Denominators Example: Combine the numerators over the denominator Simplify The Answer! 2x 5 8x 5 10x 5 2x
  26. 26. Combining fractions with Different Denominators Example: Multiply by 1 to get the same denominator 12 12 2 3 x 12 12 x 12 x 12 Distribute 24 12 x 12 3( x 12 ) 12 ( x 12 ) Combine the numerators over the denominator 24 12 x 12 3x 36 12 ( x 12 )
  27. 27. REFFERENCES • BY MRS CLEVETTE J. ACCESSED ON 17 DECEMBER, 2007. HTTP://WWW.SLIDESHARE.NET/GUESTD5D6CC/ALGEBRA-205375?QID=C8764C4B-3994-465E-AAA788D9E454C2F3&V=DEFAULT&B=&FROM_SEARCH=5 • KURUVILLA JEFFREY 6-B IIS.ACCESSED ON 08 OCTOBER, 2007. HTTP://WWW.SLIDESHARE.NET/JEFFREYKURUVILLA/MATHS-26989115?QID=C8764C4B-3994-465E-AAA788D9E454C2F3&V=DEFAULT&B=&FROM_SEARCH=3 • J0SERRA.ACCESSED ON 31 OCTOBER, 2007. HTTP://WWW.SLIDESHARE.NET/JOSERRA/ALGEBRA?QID=5E5A47F4-987C-44A4-B871-84BEB50CF4AF&V=DEFAULT&B=&FROM_SEARCH=46 • KRISTEN T. ACCESSED ON 16 JANUARY 2008. HTTP://WWW.SLIDESHARE.NET/KRILLION/OPERATIONS-WITH-ALGEBRAIC-FRACTIONS-PART-2?QID=5E5A47F4-987C-44A4-B87184BEB50CF4AF&V=DEFAULT&B=&FROM_SEARCH=129 • ROSSOW PATRICIA. ACCESSED ON 07 JUNE, 2013 HTTP://WWW.SLIDESHARE.NET/201100160/ALGEBRA-22599192?QID=5E5A47F4-987C-44A4-B871-84BEB50CF4AF&V=DEFAULT&B=&FROM_SEARCH=13

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