1.2 Algebra Flashcards
What is substitution in relation to algebra?
When you replace letters with values in a equation
What is the process of transposition?
When you make a different letter the subject of the formula
When doing transposition what is the must important thing to remember?
You must do it to both sides of the equation
When simplifying algebraic equations what is important to remember?
You can only simplify if they have the same letter
When using algebra what is the number in front of a symbol called?
A coefficient
In relation to algebra what is cancelling down or lowest term?
When you can simplify the equation by expressing both sides (i.e a^2xb / a b^2 turns int a/b)
What is meant by expanding brackets?
When you remove the brackets and each term within them is multiplied by the quantity outside the bracket
What happens when you expand the brackets but a negative is outside he bracket?
You multiply them by the negative
What is factorisation?
It is changing an equation by putting them into brackets
What is the opposite of expanding a question?
Factorisation
what is the opposite of factorisation?
Expanding
How do you factorise an algebraic equation?
Find the highest common factor. Place it outside the brackets then divide each term inside by the highest common factor
When two brackets are written next to each other what must you do?
Multiply both of them
When expanding two sets of brackets what methods can you use?
FOIL or crab claw
What does the method FOIL stand for?
First (F )x(F )
Outside (O )x( O)
Inside ( I)x(I )
Last ( L)x( L)
When expanding a pair of brackets when can’t you use the method FOIL?
When one of the brackets contains more than two digits
Why is the crab claw method better than FOIL when expanding brackets?
Because you can always use the crab claw method but FOIL can only be used when there is no more than two digits
When multiplying or dividing algebraic fractions what should you do?
Express it into a single fraction i.e a/b x c/d is axc/bxd
What is algebraic maths?
Maths with letters
When simplifying algebraic fractions what can you do if the numerator and denominator have a common digit?
Cancel them out
When cancelling out in an equation to get rid of something what must you do?
The opposite
What are the two methods used in algebra to show two quantities are equivalent to each other?
Equation and identity
In algebra what is meant by the equation method?
When there is only one value that will satisfy the question
In algebra what is meant by the identity method?
Is when a question is true no matter what value is chosen to represent the letter
In algebra what should the left hand side and right hand side be?
Equal
When told to solve a linear equation what is it asking you to do?
To find what the letter equals
When a number has a power or index or exponent what is the original number referred as? I.e 5^3
The base
If a base number has a negative power what must you do? i.e 2^-3
Invert it into 1 over the base and power but its now positive. I.e 1/2^3 = 1/8
What happens when you have a negative power against a fraction? i.e (3/2)^-3
You must flip it which turns it positive then solve
What are the two key points with a negative power?
Its never a negative and you must have it in a fraction
What do you get if your base number has a power number of 0?
It equals 1
What happens when you get a number to the power of a fraction? I.e 4^½
You square root the number and The denominator indicates the root of the number. I.e 2^√4
What happens when you have a base number that is being powered by a fraction with a numerator above one? i.e 8^⅔
Same as any fractional power but you give your number the numerator power to the digit before rooting. I.e 3^√8^2
What happens when you have a base number being powered by a negative fraction?
Simply put your base number under 1 and being powered by your now positive fraction
If a digit has a power of 1 what is the outcome?
It equals the base digit. I.e 8^1 = 8
When multiplying two numbers with powers. If the bases are the same what can you do?
Add them together. I.e 2^5 x 2^3 = 2^8
When dividing two numbers with powers. If the bases are the same what can you do?
Subtract the powers by each other 5^7 ÷ 5^3 = 5^4
What happens when a digit has a power and then raised to another power?
The two powers are multiplied
What two digits does binary use?
1 and 0
What type of numbering system does a computer use when processing information?
Binary
What digits does the octal number system use?
0-7
What is the base value when using binary in an equation?
2
What is the base value when using the octal numbering system?
8
What numbering system does a computer use when sending information?
Octal
What digits does hexadecimal use?
0-9 and A-F
Why are letters used in the hexadecimal numbering system?
The tenth digits aren’t sufficient so letters are used to represent the numbers
In the hexadecimal numbering system what do the letter A-F represent?
10-15
What is the base value in the hexadecimal numbering system?
16
What is a simultaneous equation?
When two or more equations can work together by having at least one variable that is the same
How do you solve a simultaneous equation?
Multiply so that both coefficients are the same then add or subtract to find one value then simplify
What is the standard format for quadratic equations?
Ax^2+bx+c=0
How can you solve quadratic equations?
By factorisation (placing in brackets)
When is a formula used instead of factorisation when solving a quadratic equation?
When factorisation is too difficult
What is logarithm another word for?
Index or power
If you had 3^2=9 and was told to write it into logarithm what would the answer be?
2=Log3^9
What is the general rules for logarithms?
Log^y A+B then y^B=A
What is the logarithmic scale that is used to measure sound?
Decibel scale
If you had log x (1) what is the answer no matter what x is equal?
0
If you had a logarithm with the same number after the log and in the brackets. What is the answer? I.e log x (x)
1
If there is no given number after the log what is it being powered to?
10
What would the answer to this question be? Log2 (16)
4 because 2x2x2x2= 16
What would happen if you had this equation? 5log5(14)
You’d cancel out the 5s leaving you with log(14) which equals 14
What would the answer be if you had 0.1, 0.01,0.001 after the log?
I.e log(0.1),log(0.01),log(0.001)
Log(0.1)=-1
Log(0.01)=-2
Log(0.001)=-3
What will the answer be if you have a fraction in the brackets after your log? I.e log3(1/9)
Negative i.e log3(1/9)=-2
If the log number is bigger than the bracket number what will the answer be? I.e log9(3)
A fraction i.e log9(3)=1/2
What happens if you have a log with a fraction in the bracket and a larger log number? I.e log9(1/3)
The answer will be a negative fraction i.e log9(1/3)=-½
