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Summary Week 1 math
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Summary of 25 pages for the course Mathematics at VU (Week 1 math)
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Week 1: Chapter 1-3Week 1- Integer powers:
An example:
- (p/q)^4 (breuk) = p/q X p/q X p/q X p/q
- A^-N = 1 / A^N
- A^r X A^S= A^r+s
- (A^r)^s=A^rs
- A^r:A^s = A^r-s
- (A X B)^r = A^r X b^R
-
Dus: X to the power 3 times x to the power 5 = x to the power 8 but (x to the power 3) to the
power 5 = X to the power 15.
An example:
,Week 1- Quadratic identities
There are 3 important quadratic identities: Learn them, know them, recognize them.
An example from the weekly assignment:
Answer A: x=5, y=-3-> so yes, X+y =2. That does not mean it is true due to converse implication. X can
also be -3 and y can be 5 (many more) to get x+y=2.
Answer B: x2=16-> x=4 -> yes this is true but does not have to be the case with converse implication->
-4^2 is also 16.
Answer C: y is greater than -2 -> yes because is y is -3 then y+2 = negative, so the whole equation
could be negative, with converse implication: -> you do not know, because X could be 3en then 0
times something positive is 0.
Answer D: x=2, true because 2x2x2 = 8, and true converse because -2x-2x-2 = -8.
An example out of the book:
Simplify-> dus: streep ze allemaal weg aan elkaar, er is totaal 0p2q en 0pq2, p3 en q3 blijven over.
, Week 1- Factoring
Factoring is searching for the common factor.
49=7x7, 672= 2x2x2x2x2x3x7. Algebraic expressions can often be factored in a similar way:
To factor an expression means to express it as a product of simpler factors. For example:
6x^2y=2x3xXxXxy but note that this is not factoring. This is factoring:
- 5X^2+15x=5x(x+3)
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A simple example from the book:
An example from the weekly assignments:
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