tiu math2 session: algebra by young einstein learning center
DESCRIPTION
TIU Math2 Session: Algebraby Young Einstein Learning Centerwww.yeinstein.comCollege Entrance Test ReviewTopics:Absolute ValueAlgebraic ExpressionsAddition / Subtraction / Multiplication / Division of AE'sFOIL methodTRANSCRIPT
Math, Session 2
TIU College Entrance Test Review
WHAT IS THE DISTANCE BETWEEN
ANY NUMBER X AND Y?
What is the distance between 15 and 0?
15
What is the distance between 21 and 46?
25
What is the distance between -8 and 0?
8 What is the distance
between -30 and 50?80
What is the distance between -12 and -5?
7
| 9 | =
| -4 | =
Absolute value is the same number, in positive form.
What is the distance between 15 and 0?
Is it | 15 – 0| or | 0 – 15| ?
15 0
15
15
0 15
15
15
9
4
What is the distance between -8 and 0?
Answer: | -8 -0 | or | 0 - -8 |
8 0
8
8
0 8
0 8
8
8
Distance = | X – Y | = | Y – X |
7 5 9 6
Rule for addition of signed numbers of the same sign: Add the numbers and prefix the common sign.
8 9 25 17
Rule for addition of signed numbers of different signs: Subtract the numbers and prefix the Sign of the number with the larger value.
12 15
1 8
4 8 13 8
Rule for subtraction of signed numbers: Change the operation to addition, and change The sign of the second number. Then perform as in addition of signed numbers.
4 5
7 6
8 4
Rule for two numbers with the same sign: The product/quotient of the two will be positive.
42
32
121
1111
63
97
The rule for two numbers of different signs:
The product/quotient of the two will be negative.
4 956
836 7
14 8 3
2 7
1.) Solve by disregarding signs.2.) Do cancellation when possible.3.) Count the negative signs.
If even result is positiveIf odd result is negative
2 4
24
3! 3 2 1In general,
Therefore,5! =?
! ( 1) ( 2) ( 3)... 1n n n n n
5! 5 4 3 2 1
120
Math, Session 2, Algebra
Evaluate the following expression for x = 4:2 2 1x x
24 2 4 1
16 8 1
23
We can only add or subtract like terms.
x x
5 2y y
3 2 4 9w x w x
2x
3y
11w x
Is the answer 11x –w also correct?YES!
We can only add/subtract like terms.
23 5 6 2 9 4ab a ab b a b
The simplified form of the AE above is:
23 2 14 4ab b a b
We use the laws of exponents.
Some examples:
5y y y y y y
x x2x
2 3x x5x x x x x x
32x 2 2 2 6x x x x
7
3
x
x
4x x x x x x xx
x x x
0 1x
2x 2
1
x
Master multiplication of simple terms
3 techniques to multiply (x+a)(x+b)
◦ Distributive Property of Multiplication over Addition
◦ F-O-I-L Method
◦ Column Format
3 23 5x x 515x
Technique 1: DPMA
2 3x x 2 2 3x x x
2 2 3 6x x x
2 5 6 x x
2 3x x
FirstOuterInnerLast
2
3
2
6
x
x
x
2 5 6
Answer
x x
2
2
2
3
3 6
2 ___
5 6
x
x
x
x x
x x
You can use DPMA and the Column Format to multiply not only binomials, but also trinomials and AE’s with many terms.