OU Essential Mathematics: Unit 1, book A

222 flashcards · Mathematics · by charlie42

natural numbers, also known as the ...
positive integers
ellipsis
...
natural numbers, together with their negatives and zero
integers
integers etymology
untouched (whole)
rational numbers
numbers that can be written as integer/integer
real numbers
numbers on the real line
positive square root of 2 multiplied by itself
2
how to obtain pi
divide circumference of any circle by its diameter
decimal number
number with a dot (1.2)
decimal form with finite number of digits
terminating
decimal form where one or several numbers repeat indefinitely
recurring
two notation for recurring decimals
rational numbers are decimals that .. or ..
terminate or recur
4 types of numbers by subset
Round 80 014 to three significant figures
800 000 (to 3 s.f.)
Round −0.25 to 1 d.p. (decimal places)
−0.3 (to 1 d.p.).
Alternative to specifying rounding, e.g. (to 1 d.p)
≈
how to avoid rounding error
use full calculator precision when using result from the previous calculation
SI units
metric system units (Systeme International d’Unites)
nano - abbreviation / meaning / power
n / a billionth /
micro - abbreviation / meaning / power
μ / a millionth /
milli - abbreviation / meaning / power
m / a thousandth /
centi - abbreviation / meaning / power
c / a hundredth /
kilo - abbreviation / meaning / power
k / a thousand / 1000
mega - abbreviation / meaning / power
M / a million /
A quotient of two numbers is
the result of dividing one by the other
15 is a ... of 5
multiple
5 is a ... of 15
factor
one of the positive factor pairs of 12
(3, 4)
another word for square number
perfect square
square number definition, example
an integer that can be written in the form a2 (e.g. 9)
composite number
an integer >1 that is not a prime number
The prime factorisation of an integer greater than 1 is
any expression that shows it written as a product of prime factors
index notation
in increasing order
another word for greatest common divisor
highest common factor
LCM
lowest (least) common multiple
HCF
highest common factor
GCD
greatest common divider
an equation is made up of two
expressions
The quantities that are added are called the terms of the expression
A term like −4, that doesn’t contain any variables, is known as a constant term
If a term has the form a fixed value × a combination of variables, then the fixed value is called the coefficient of the term
5ab has coefficient 5 and is a term in ab
x + x and 2x are equivalent
Removing the brackets from an expression, or multiplying out the brackets, expanding the brackets
The result of multiplying out the brackets is called the expansion of the original expression
3b here is called a multiplier
For any expressions A and B, the negative of A−B is
B−A
difference of two squares
An expression that contains letters is an algebraic expression. An expression, such as 10 - 2 x 4, that contains only numbers and mathematical symbols is a numerical expression
How many square roots a positive number has?
Two, positive and negative
What do we mean when we say the square root of a number?
The positive square root
Negative numbers have how many real square roots?
None For example, there’s no real number that when squared gives −36.
How many square roots 0 has?
One, 0
What's a cube root?
The cube root of a number is a number that when cubed results in the given number.
How many cube roots a real number has?
One
What are whole numbers?
A number without fractions; an integer
For every even natural number n (2, 4, 6...), how many n-th roots every positive number has?
Two, positive and negative
What's an even number?
A whole number that is able to be divided by two into two equal whole numbers E.g. 0, 2, 4, 6, 8
For every even natural number n, how many n-th roots every negative number has?
None
For every even natural number n, how many n-th roots 0 has?
One, 0
For every odd natural number n, how many n-th roots every real number has?
One
How many real sixth roots 64 has?
Two
How many real sixth roots -64 has?
None
How many real fifth roots 243 has?
One
How many real fifth roots -243 has?
One
Symbol to write positive and negative roots together?
± For example, the two square roots of 36 are ±6
What does the symbol √ denote?
Positive square root of a positive real number
What's √ 36 equal to? Explain
6 √ denotes only the positive square root, -6 is a negative square root
Why is this incorrect? How should you write it instead?
√ denotes only the positive square root, -2 is a negative square root
Who introduced the symbol √?
René Descartes
What kind of numbers are square root of natural numbers that are not a perfect square?
Irrational
What an expression like this is called?
A surd
What exactly is a surd? How universal is this definition?
Numerical expression that contains one or more irrational roots of numbers
Where does the word surd come from?
Latin surdus = deaf or silent
Simplify:
Simplify:
Simplify:
Simplify and explain:
Use prime factorization to find a factor of 48 that is a perfect square.
What is this methods of simplifying surds called?
Rationalizing the denominator
How do you remove irrational root from a denominator? 2 cases.
If no sum in denominator: multiply the whole expression by the root: If sum in denominator: multiple the whole expression by a conjugate of the denominator:
What's a conjugate?
The expression that you get when you change the sign of one of the two terms (usually second)
For any expression A and B,
What's this rule called?
Difference of two squares
The fundamental theorem of arithmetic
Every integer greater than 1 can be written as a product of prime factors in just one way (except that you can change the order of the factors).
What does prime factorization look like?
What's a common multiple of two integers? Example
A number that is a multiple of all of them
How many multiples a number has?
An infinite amount
How many common multiples two numbers have?
An infinite amount
How to find LCM and HCF of negative numbers?
They're exactly the same as their positives.
Algorithm to find HCF of two integers
Write their prime factorization, lining up primes: Multiply lowest power of each prime IF PRIME IS MISSING THE POWER IS 0
Algorithm to find LCM of two integers
Write their prime factorization, lining up primes: Multiply highest power of each prime
What's an expression?
Arrangement of letters, numbers, and symbols, which is such that if all the letters are substituted by numbers, you can work out the value of the arrangement.
Example of an arrangement of letters, numbers, and symbols that is not an expression, why?
Because we can't work out the value of the arrangement
What's a subexpression?
A part of an expression that can be enclosed in brackets without affecting the meaning of the larger expression
What's the result of multiplication is called?
A product
What's a multiple?
A number that may be divided by another a certain number of times without a remainder
Why is this not an expression? What is this instead?
Expressions don't contain equals signs. This is an equation. An equation is made up of two expressions, with an equals sign between them.
What year was the first equals sign used?
1577
In this expression, what 5ab, (-2a2), etc. are called?
Terms of the expression