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44 Cards in this Set
- Front
- Back
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Natural numbers
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positive whole numbers
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Integers
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whole numbers including negatives and Zero
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Rationals
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numbers which can be written as fractions
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Irrationals
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numbers which can't be written as fractions in lowest terms
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Reals
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the rationals and the irrationals put together. The reals will include every possible number you could meet in the course
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Arithmetic sequence
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previous number plus a constant
un = a + (n-1)d Sn = n/2 (2a + (n-1)d) |
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Geometric sequence
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previous number multiplied by a constant
un = ar^n-1 Sn = (a(r^2 -1))/(r-1) |
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(Sequences and Series) a
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the first number of the sequence
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(Sequences and Series) n
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the number of terms in the sequence
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(Sequences and Series) l
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the last term of the sequence
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(Sequences and Series) d
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the common difference
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(Sequences and Series) r
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the common ratio
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(Sequences and Series) un
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the value of the nth term
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(Sequences and Series) Sn
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the sum of the first n terms
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(Sequences and Series) S (endless)
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the sum to infinity
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sum to infinity
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S= a/r-1
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Simple interest
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The interest earned is not added to the total amount which thus stays constant.
-->AS |
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Compound interest
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The interest earned is added to the amount invested. Thus the investment grows by a larger amount each year.
--> GS |
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Exponents > 1
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have te konventional meaning of multiplying a number by itself several times
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Exponents = 1
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a^1 is always a for all values of a
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Exponents = 0
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a^0 is always 1 for all values of a
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Negative Exponents
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never make the number itself negativ. A negative power means "take the resiprocal"
a^-n = 1/a^n |
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Fractional powers
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involve roots
eg the power 1/2 means suqare root in general a^m/n = nth root of a^m |
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Laws of exponents (4)
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1. a^x ° a^y = a^x+y
2. a^x / a^y = a^x-y 3. (a^x)^y = a^xy 4. (ab)^x = a^xb^x |
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2^2
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4
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2^3
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8
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2^5
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32
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2^6
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64
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2^7
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128
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3^2
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9
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3^3
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27
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3^4
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81
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3^5
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243
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4^2
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16
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4^3
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64
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4^4
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256
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5^2
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25
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5^3
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125
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5^4
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625
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6^2
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36
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6^3
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216
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rules for manipulating surds (4)
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1. root a ° root b = root ab
2. root a / root b = root a/b 3. root a + root b does not equal root a+b 4. root a - root b does not equal root a-b |
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laws of logarithms (3)
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1. loga + logb = log (ab)
2. loga - logb = log (a/b) 3. log a^n = nloga |
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The binomial expansion
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general formula gives a quick way of multiplying out brackets of the form (a + b)^n
eg (a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 |
