[Week 4]- Multiplying and Dividing Radical Expressions

[Week 4]- Multiplying and Dividing Radical Expressions

What I have learned:

  1. Adding and Subtracting Radical Expressions
  2. Simplifying with more than one set of like terms
  3. Multiplying and dividing radical expressions
  4. simplifying products of expressions with variable radicands
  5. Rationalizing a monomial denominator

 

Ex. Simplify √63+√40-√90-√28

The radicals are different, so simplify each radical.

√63+√40-√90-√28

= 3√7+2√10-3√10-2√7
= 3√7-2√7+2√10-3√10
= √7-√10

Ex. Simplify 2√x-3√y+5√x+2√y; x,y,≥0

2√x and 5√x are like terms because they are radicand x and index 2.
3√y and 2√y are like terms because they have radical y and index 2.

2√x-3√y+5√x+2√y
= 2√x+5√x-3√y+2√y
= 7√x-√y

Ex. Expand and simplify(2√3+5)(2√3-5)

Expand

(2√3+5)(2√3-5)
= (2√3)(2√3)-5*5
= 12- 25
= -13

 

 

[Week 3]- Absolute value of a real number

[Week 3]- Absolute value of a real number

What I have learned:

  1. What is the absolute value of a real number
  2. The absolute value of a real number is defined as the principal square root if the square of a number.
  3. Determine absolute value.
  4. The relationship with absolute and principal square root.
  5. √x ² = |x|

 

Ex. Determine each absolute value.

|4.2|, |-6.1|, |0|, | -3/4 |

4.2, 6.1, 0, 3/4

 

Ex. Evaluate√(3-5) 2

          Use the fact that √(3-5)2  =  |x|

√(3-5)2 = |3-5|

                                             = |-2|

= 2

[Week 2]- Geometric Series

[Week 2]- Geometric Series

What I have learned:

  1. The sum of n terms of a geometric series
  2. Use a rule to determine the sum of n terms of a geometric series, then solve related problems.
  3. Use a rule to determine the nth term in a geometric sequence.
  4. Use a rule to determine any of n, t1, tn, or r in a geometric sequence.
  5. Use a rule to determine n and Sn in geometric series, given the values of r, n, or Sn.

Ex. Find the S15 of the sequence -5, 10, -20…

Ex. Find the n of the sequence 1-2+4-8+…-512

[Week 1]- Arithmetic Sequences

[Week 1]- Arithmetic Sequences

What I have learned:

  1. what is arithmetic sequences and common different.
  2. How to find common different.
  3. How to calculate the sum of n term of an arithmetic series
  4. Use a rule to determine t1 and d in an arithmetic sequence given the values of tn and n.
  5. Use a rule to determine tn and n in an arithmetic sequence given the values of t1 and d.
  6. Use a rule to determine the sum Sn of an arithmetic series.

 

Ex. Use the arithmetic series, determine the indicated value.

1 + 3.5 + 6 + 8.5 + …; determine S42.

Know:                                     Sn = n/2 [2 t1 + d (n-1)]

T1 = 1                                           = 42/2[2+2.5*41]

T2= 3.5                                         = 2194.5

d= 2.5

 

 

Ex. Use the giving data to determine the indicated value.

S20 = -850 and t20 = -90; determine t1

Sn = n/2 (t1 +tn)

-850 = 20/2[t1 +(-90)]

10 t1 = 50

t 1 = 5