Archive of ‘Grade 11’ category

Week 3- Absolute Values of a Real Number

The absolute value of a real number is defined as the principle square root of the square of a number.

for instance the absolute value of \mid 4 \mid is 4

when a number is between the brackets, it must be brought out of the bracket like this:

\mid 4 \mid

 

=4^2

 

=\sqrt {16}

 

=4

 

Whenever a number is between brackets, the answer must be a positive number. However, after the number is out of the brackets it can become negative in an equation.

We also learned about roots and radicals. Numbers with square roots can never be negative, like \sqrt {-25} because it cannot be calculated and results in an error when put into a calculator. On the other hand, a cubed number can be negative. Roots with an index that’s even cannot be negative, but roots that have an uneven index can be negative.

when simplifying roots that are not perfect, a different approach must be taken.

for example:

\sqrt {24}

 

=\sqrt {4*6} find two multiples of a number, one being a perfect square

 

=\sqrt {4} * \sqrt {6} separate the roots

 

=2 \sqrt {6} square the perfect square and leave the radical as a square root

 

this applies to other index’s as well, just find perfect cubes instead of perfect squares, etc.

 

Week 2-Geometric sequences

This week we learned about geometric sequences and series. A Geometric sequence differs from an arithmetic sequence because instead of adding a common difference, a common ratio is multiplied by the term to get the next term.

the equation used to find a term in a sequence is

 

t_n=ar^{n-1}

in this equation t_1 is represented by a

for example: 5,10,20,40… find t_{10}

 

t_{10}=5(2)^{10-1}

 

t_{10}=5(2)^9

 

t_{10}=5(512)

 

t_{10}=2560

 

A finite geometric series can be found using the equation

Week 1 – My Arithmetic Sequence

 

4, 9, 14, 19, 24

d=5, t_1=4

 

t_n=t_1+(n-1)d

 

t_n=4+(n-1)5

 

t_n=4+5n-5

 

t_n=5n-1

using this information, we can find any value of t using the equation t_n=5n-1. We can plug in any term into n to find t_n

 

this equation will work for any term within the sequence, as long as the starting term and common difference are constant. If either of these change it is no longer an arithmetic sequence.

To find S_{50}, the sum of all 50 terms, we must use the equation S_n={n}{2}(a+1)

In this equation, n= number of terms(50) and a= the first term(4)

 

S_{50}={50}{2}(4+1)

 

S_{50}=25(5)

 

S_{50}=125

 

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