This document contains a collection of presentations on algebra for grade 10 compiled by Beatrice S Zwane at the University of Johannesburg on March 6, 2014. It includes definitions of key algebra terms like algebraic expressions, variables, and evaluating expressions. It provides examples and discusses simplifying expressions by combining like terms. It also covers writing equations in slope-intercept form, finding the slope and y-intercept of lines, and operations with algebraic fractions. References are listed at the end from various sources accessed between 2007-2013.

1. COLLECTION OF DIFFERENT
PRESENTATIONS:
ALGEBRA-GRADE 10
COMPILED BY: BEATRICE S ZWANE
LOCATION: UNIVERSITY OF JOHANNESBURG
DATE:06 MARCH 2014

3. 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.

4. 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

5. Simplifying
Solving
Definitions
Checking
Using a
Formula
Exit

6. OBJECTIVE
LEARNERS WILL BE ABLE TO:
1)
2)
write equations using slope-intercept form.
identify slope and y-intercept from an equation.

7. •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

8. 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.

9. • 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

10. SOLVING TYPE II USING ALGEBRA TILES
2x 6
2
Let,
= -x
=x
= -1
=1

11. 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!!

12. 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

13. SIMPLIFY
2x 3 4 y 6 6x 2 y 1
4 x 6 y 10

15. WORDS THAT LEAD TO ADDITION
• SUM
• MORE THAN
• INCREASED
• PLUS
• ALTOGETHER

16. WORDS THAT LEAD TO SUBTRACTION
• DECREASED
• LESS
• DIFFERENCE
• MINUS
• HOW MANY MORE

17. 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

18. 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

19. 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

20. TYPES OF LINES
• 1. ALL LINES ARE STRAIGHT.
• 2. THEY CAN BE HORIZONTAL, VERTICAL, OR DIAGONAL.

21. •Fill in the formula
M= (-2)-2
_____
1-(-3)
•Then subtract.
•You should end up with
M= - 4
___
www.rlsmart.net
4

22. 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

23. 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

24. 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

25. 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

26. Algebraic Fractions
Adding/Subtracting
Amsco Math A, Chapter 19

27. Combining with Like Denominators
Example:
Combine the
numerators over the
denominator
Simplify
The Answer!
2x
5
8x
5
10x
5
2x

28. 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 )

29. 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