COLLECTION OF DIFFERENT PRESENTATIONS:

ALGEBRA-GRADE 10COMPILED BY: BEATRICE S ZWANE

LOCATION: UNIVERSITY OF JOHANNESBURG

DATE:06 MARCH 2014

DEFINITIONS

• ALGEBRAIC EXPRESSION – A GROUP OF NUMBERS, SYMBOLS, AND VARIABLES THAT EXPRESS AN OPERATION OR A SERIES OF OPERATIONS.

EXAMPLES: ( A)M + 8 (A)R – 3• 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.

EXAMPLES: M + 8 M = 22 + 8 = 10

DEFINITIONS CONTI……

• SIMPLIFY – COMBINE LIKE TERMS AND COMPLETE ALL OPERATIONS

E.G. M = 2• M + 8 + M 2 M + 8• (2 X 2) + 8 4 + 8 = 12

Solving

Simplifying

Definitions

Checking

Using aFormula

Exit

OBJECTIVELEARNERS WILL BE ABLE TO:

1) write equations using slope-intercept form.

2) identify slope and y-intercept from an equation.

•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

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.

M= - 4 ___ 4

(-3,2) and (1,-2)

• Now go back to your original coordinates and fill in this equation

• Choose one of the coordinates, it doesn’t matter which one.

2=(- 4)(- 3)+b

•After filling in everything you should have

y = 2m = (- 4)x = (- 3)

www.mathequations.com

SOLVING TYPE II USING ALGEBRA TILES

262 xLet,

= -x

= x

= -1

= 1

262 xALGEBRAICALLY

66

2242 x

2x

Steps:1) Write the Equation2) Add +6 to each side

3) Divide each side by +2

4) Check your answer

2(2) – 6 = -2 CORRECT!!

262 xSteps1) Write the Equation

2) Add +6 to both sides3) Cancel using Zero Property

4) By the sharing principal

Therefore x =2

SIMPLIFY1266432 yxyx

1064 yx

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 = 10

• X + 8 18

• X + 49 59• X + X 20• X – X 0• X – 7 3• 42 – X 32

WRITE AN ALGEBRAIC EXPRESSION FOR THESE SITUATIONS

•SCOTT’S BROTHER IS 2 YEARS YOUNGER THAN SCOTT

•THE SUM OF TWO NUMBERS IS 12

•THE DIFFERENCE BETWEEN TWO NUMBERS IS 5

s - 2

v + c = 12

m – n = 5

IMPORTANT!!!THIS IS ONE OF THE BIG

CONCEPTS IN ALGEBRA 1. YOU NEED TO

THOROUGHLY UNDERSTAND THIS!

SLOPE – INTERCEPT FORMY = MX + B

M REPRESENTS THE SLOPEB REPRESENTS THE Y-INTERCEPT

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.

M= - 4 ___ 4

•You should end up with

www.rlsmart.net

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) =Y – INTERCEPT (B) =

WE HAVE BOTH!! PLUG THEM INTO SLOPE-INTERCEPT FORM

Y = MX + B

26

y = 2x + 6

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

TO FIND THE SLOPE AND Y-INTERCEPT 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

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 = 0B = 5

Algebraic Fractions

Adding/Subtracting

Amsco Math A, Chapter 19

Combining with Like Denominators

Example:

Combine the numerators over the denominator

The Answer!

x2

Simplify

58

52 xx

5

10x

Combining fractions with Different Denominators

Example:

Multiply by 1 to get the same denominator

Distribute

123

122

x

Combine the numerators over the denominator

1212

1212

xx

)12(12)12(3

121224

x

xx )12(12

3631212

24

x

xx

REFFERENCES

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

HTTP://WWW.SLIDESHARE.NET/GUESTD5D6CC/ALGEBRA-205375?QID=C8764C4B-3994-465E-AAA7-88D9E454C2F3&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-AAA7-88D9E454C2F3&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-B871-84BEB50CF4AF&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