tiu math2 session: algebra by young einstein learning center

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.