midterm Flashcards
Polya’s Four Principles of Problem Solving
Understand the problem, Devise a Plan, Carry out the Plan, and Look Back.
Fibonacci Sequence
A sequence where you start with one and one ad add any two consecutive numbers to obtain the next number. For example, the sequence starts with 1,1,2,3,5,8,13,and 21…. The next number would be found by adding 21 + 13 to get 34.
This is an arithmetic progression.
The arithmetic progression is defined by the property that every term is a constant difference greater than or less than its predecessor by the same amount. For example, if you took the sequence 2,5,8,11,…, the constant difference is three.
The intersection of two sets A and B is the set of elements
common to both A and B. A∩B
The union of two sets A and B is
the set of all elements that are in A or B. A∪B
A nominal number is a sequence of digits used
as a name or label like a telephone number.
An ordinal number is a number that describes
where an object is in an ordered sequence, like first place, second place, etc.
A cardinal number is
the number of elements in the set, like 1500 runners in a race.
The sum is the answer when two numbers are added.
The expressions which are added are called the addends.
Commutative property of addition
Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 44+2=2+44, plus, 2, equals, 2, plus, 4.
Associative property of addition:
Changing the grouping of addends does not change the sum. For example, (2 + 3) + 4 = 2 + (3 + 4)(2+3)+4=2+(3+4)left parenthesis, 2, plus, 3, right parenthesis, plus, 4, equals, 2, plus, left parenthesis, 3, plus, 4, right parenthesis.
Identity property of addition:
The sum of 000 and any number is that number. For example, 0 + 4 = 40+4=40, plus, 4, equals, 4.
closure property
If a and b are any two whole numbers, than a + b is a unique whole number
In the equation a x b = c,
a and b are called factors, and c is the product.
Commutative property:
When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example 4 * 2 = 2 * 4
Associative Property:
When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example (2 * 3) * 4 = 2 * (3 * 4)
Multiplicative Identity Property:
The product of any number and one is that number. For example 5 * 1 = 5.
Distributive property:
The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 46 + 43
multiplication over division
multiply first
A binomial is
an expression with two terms.
In the expression , a is the dividend and b is the divisor.
If , c is called the quotient.
A number divided BY zero
is undefined.
Zero-Exponent Rule:
a0 = 1, this says that anything raised to the zero power is 1.
Power Rule (Powers to Powers):
(am)n = amn, this says that to raise a power to a power you need to multiply the exponents.
Product Rule: am ∙ an = am + n,
this says that to multiply two exponents with the same base, you keep the base and add the powers.
Quotient Rule: Quotient Rule, this says that to divide two exponents with the same base,
you keep the base and subtract the powers.
Memorize Roman numerals
DO IT
know place values
one, tens, hundreds, ect
A number is even
when it is divisible by 2.
A prime number is a number that possesses exactly two factors:
one and itself.
A composite number is a number
that possesses more than two factors.
The number 1 is
neither prime nor composite.
The greatest number that divides both a and b is called
the greatest common factor of a and b.
The smallest number that is a multiple of both a and b is called
the least common multiple of a and b.
divisibility 2
The last digit is even (0,2,4,6,8)
divisibility 3
The sum of the digits is divisible by 3
divisibility 4
The last 2 digits are divisible by 4
dvisibility 5
The last digit is 0 or 5
divisibility 6
is even and is divisible by 3 (it passes both the 2 rule and 3 rule above)
divisibility 8
The last three digits are divisible by 8
divisibility 9
The sum of the digits is divisible by 9
divisibility 10
The number ends in 0
