PreWork Flashcards
What is a term?
One or more numbers and/or letters divided or multiplied together
What is an expression?
One or more terms subtracted or added together
What is a co-efficient?
The number part of a term
What are like terms?
Terms which have exactly the same letter
What is simplifying an expression?
Writing an expression in the simplest form (i.e. combining like terms)
Why are 3yx and 8xy like terms?
Because they have the exact same letters
What are positive powers?
Multiplying a term by itself (x) amount of times. (x) = positive power
How do you multiply powers?
If the bases are the same you add the powers together
How do you divide powers?
If the bases are the same you subtract them
How you work out the powers of powers?
You multiply the powers together
How do you multiply terms?
Multiply the coefficents and then multiply the letters by adding their powers
What is BODMAS?
Oder of operations. Brackets, Order of Powers or Roots, Division, Multiplication, Addition, Subtraction
When a value is multiplied by a power, what takes precendece? I.e. 10a^4
The power takes precedence i.e. 10 times (a^4)
What can expanding brackets also be called?
Multiplying out brackets
How do you expand brackets with one term outside the brackets?
Multiply the terms outside the brackets by each term within the brackets
What is factorising an expression?
It is the opposite of expanding the brakets
How do you factorise an expression?
You take the largest common factor of each term in the expression and bring the LCF outside the brackets. Then you find what term the LCF needs to be multiplied by to get to the term in the original expression.
How do you check if the expression has been factorised?
By expanding the brackets and getting the same expression as the original expression
How do you know if the expression has not been fully factorised?
If the expression inside the bracket still has common factors
How to find the negative power?
Work out as though the power was positive, then the reciprocal of the positive power is the answer
What is a reciprocal?
Flipping the fraction
What is a fractional power?
When a number is raised to the power of a fraction
What is the formula for a fractional power with a 1 in the numerator?
a^(1/n) = n root of a
What does a fractional power represent?
A root
What is the formula for finding the root of a fractional power?
numerator = power denominator = root
Which order is the fractional power calculated?
Either power or root
Which is easier to calculate the power or the root?
Taking the root first is easier than taking the power first
When a parenthesis is raised to a power what happens to each term inside?
Each term is raised to that power
What to always check for on general?
Powers, further simplification, negative signs
How do you calculate a fraction which is raised to a negative power?
- Split the index into three parts
- Raise the base to the three parts separately as powers
What 3 parts can you split the negative fractional power into?
- 1
- 1/the denominator
- The numerator
How would you split -5/2
-1(1/2)5
What is 36^-1?
1/36
