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When considering zero product property if one expression or variable is known to be zero, what about the other variable/expression.
D.S. TIP! |
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Definition
If one is 0, the other may or may not be 0. it could be other values.
e.g. x=0
x(y-3)=0.
Here since x=0, y-3=0 or y-3/=0 so we cant with certainty equate y-3. |
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| What can be said about 2 INTEGERS when the product is 1. |
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Definition
| D.S. TIP If we know 2 integers product = 1 then each integer is either -1 or +1 |
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Term
| What are negative integers |
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Definition
| Numbers without fraction or decimal to left of 0 on the number line are negative integers, farther away from 0 smaller they are. |
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| What are positive integers |
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Definition
| Whole numbers to the right of 0 on the number line are positive integers. Farther from 0, larger they are. |
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Definition
| All positive integers and 0 are whole numbers |
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Term
| Is 0 positive or negative. |
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Definition
| Zero is neither positive nor negative |
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Term
| What is the square root of 0 |
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Definition
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Term
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Definition
| 0. 0 is the only number where k=-k |
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| What is a multiple of every number |
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Definition
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Term
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Definition
| 1. Any number raised to 0 is 1 |
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Term
| Which number is a factor of all numbers |
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Definition
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Term
| What is the first prime number |
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Definition
| 2. 0 is even and 1 is odd and not prime |
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Term
| What type of integer does the expression 2N represent |
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Definition
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Term
| What type of integer does the expression 2n+1 or 2n-1 represent for all integers n |
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Definition
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Term
| What combination of odd or even integers in addition or subtraction gives an odd integer? |
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Definition
| Odd+Even or Odd-Even. All other combinations are even |
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Term
| What combination of odd or even integers when multiplied results in an odd integer |
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Definition
| Odd*odd. All other integers combination give a even integer |
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Term
| Given XY + Y^2 is odd. What can we say about x and y. |
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Definition
| X must be even and Y must be odd. Y(X+Y) = odd. so Y and (x+Y) must be odd. For x+y to be odd, x has to be odd, since y is odd. |
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Term
| What could be said about x,y and z if xyz=even |
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Definition
IF just one variable is even, xyz = even.
Can have any combination of odds (yz, xz, zy). Just one even makes it even. Similarly if all odd, it would be odd. |
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Term
If x is an integer. Is x odd or even if
Even/Even = X |
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Definition
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Term
If x is an integer. Is x odd or even if
Even/Odd = X |
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Definition
| X must be Even. This is corollary of Even*Odd=Even => Even = Even/Odd |
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Term
| What is the remainder when even numbers are divided be 2 |
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Definition
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Term
| What is the remainder when odd numbers are divided by 2 |
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Definition
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Term
| What is a factor. Define using x & Y |
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Definition
| Considering whole numbers, If X/Y = Integer. then Y is a factor of X. |
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Term
| What are the largest and smallest factors of any whole number? |
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Definition
| The smallest is 1 and largest is the number itself. range of values for the factor is 1<=y<=x, given x/y = whole number. Note this is the same as saying X is the factor of "something" if "something"/x = integer |
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Term
| How to check if "something" is a multiple of x |
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Definition
| "something"/X should be = integer/whole number |
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Term
| what number has only the number itself and 1 as factors |
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Definition
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Term
| If y is a positive integer. How many more prime factors does Y^5 and y^11 have compared to Y. |
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Definition
| None. A positive integer raised to another positive integer has the same number of unique prime factors as the base number |
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Term
| What can be said about GCF and LCM in a set of positive integers |
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Definition
The LCM will be greater or equal to the largest number in the set.
GCF will be greater than or equal to the smallest number in the set |
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Term
| What can be said about consecutive integers and the divisibility by 3 |
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Definition
| 3 consecutive integers, at least one will be divisible by 3. This can be extrapolated to 2,5 et.c |
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Term
| What is the factorial divisbility rule |
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Definition
| The product of any set of n consecutive integers is divisible by n! |
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Term
| Numbers that are perfect squares and perfect cubes under 1000 |
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Definition
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Term
| How can we determine if a fraction m/n is going to be terminating decimal or not |
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Definition
| If denominator has only factors of 2 or only factors of 5 or only both 2&5. However, be careful of what the numerator is. |
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Term
| What is the power of prime factors of perfect cubes |
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Definition
| All exponents must be multiples of 3 |
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Term
| What are the common prime factors of x and x+1 ? |
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Definition
| None. 2 consecutive integers don't share any prime factors. |
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Term
| What is the GCF of 2 consecutive integers? |
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Definition
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Term
| What is the units digit of x given 7,15 and 24 are factors of x ? |
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Definition
| 0. Any number that has prime factors of at least one 2 and at least one 5 must end with at least one zero. |
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Term
| How do we get rid of a single term radical in the denominator |
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Definition
| Rationalize. x/(a)^(1/2) * (a/a)^(1/2) |
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Term
| For where x>1 & n>0 & both are integers.What is the relationship between xn and x if n is even |
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Definition
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Term
| For x>1 and n>1 and both integers. What is the relationship between xn and x if n is odd? |
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Definition
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Term
| For x<-1 and n>0, both integers. What is the relationship between xn and x if n is even? |
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Definition
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Term
| For x<-1 and n>1, both integers. What is the relationship between xn and x if n is odd? |
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Definition
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Term
| For 0<x<1 and n>0 n is integer. What is the relationship between xn and x if n is even? |
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Definition
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Term
| For -1<x<0 and n>0 n is integer. What is the relationship between xn and x if n is even? |
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Definition
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Term
For 0<x<1 and n>1 n is integer. What is the relationship between xn and x if n is odd? |
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Definition
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Term
| For -1<x<0 and n>1 n is integer. What is the relationship between xn and x if n is odd? |
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Definition
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Term
| For x>1 and n where 0<n<1. What is the relationship between x and xn |
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Definition
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Term
| For x where 0<x<1 and n where 0<n<1. what is the relationship between xn and x |
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Definition
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Term
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Definition
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Term
| What is the formula for consecutive even or odd integers? |
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Definition
| x, (x+2), (x+4), (x+6) and so on. |
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Term
| 0 and 1 rules when talking about multiples |
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Definition
0 is multiple of all numbers and is the only number equal to all its multiples
all numbers are a multiple of 1 |
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Term
| Pattern of units digit 2^n |
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Definition
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Term
| Pattern of units digit 3^n |
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Definition
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Term
| Pattern of units digit 4^n |
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Definition
| starting n=1 4-6 (4 is odd power,6 is even) |
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Term
| Pattern of units digit 6^n |
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Definition
| starting n=1 all end in 6 |
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Term
| Pattern of units digit 5^n |
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Definition
| Starting n=1 all powers end in 5 |
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Term
| Pattern of units digit 7^n |
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Definition
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Term
| Patterns of unit digit 8^n |
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Definition
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Term
| Patterns of unit digit 9^n |
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Definition
| Starting n=1 9-1 (odd powers end 1, even powers end in 9) |
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Term
| Number of factors of perfect squares are |
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Definition
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Term
| Number of factors of positive integer other than a perfect square are |
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Definition
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Term
| If a is a factor of b is b larger than a? |
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Definition
| Could be. a factor of a number is lesser than OR equal to that number. therefore a is equal or less than b |
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