Year 2 Chapter 1: Algebraic Methods Flashcards
Write steps for proof by contradiction question:
1) Assume original statement is false by writing new statement that is opposite to original.
2) Use logical steps to reach a contradiction (show all working).
3) Statement saying what contradicts original assumption.
4) Finish proof by concluding that original statement is true (therefore….).
Give features of rational numbers (that are different to the features of irrational numbers):
. Rational numbers can be expressed as a/b, where a and b are integers and a/b can’t be simplified any further therefore don’t have any common factors.
How do you express even and odd numbers in proof questions?
. Even: 2n or 2k
. Odd: 2n +1 or 2k+1.
What to remember when doing long division
. Dad Mum Sister Brother.
. Start with dividing first part of numerator by first part of denominator then multiply answer (which goes on top of bus stop) by whole of denominator.
. Before you subtract and bring down new term, draw horizontal line to represent new bus stop.
. Always divide top left term of each bus stop by first term of denominator (that is on outside to the left of bus stop).
How do you determine whether ‘x+n’ is a factor of another term (you know what the value of ‘n’ is)?
Sub ‘-n’ into each ‘x’ part of the other term and your answer should come out as 0.
In partial fraction questions, what do you need to remember about repeated factors?
You write one of the denominators under A,B or C as ‘(n)’ and another denominator under A, B or C as ‘(n)² and then write the rest of the factors as denominators under the remaining letters.
How do you know if an algebraic fraction is improper?
Because the numerator’s maximum power is larger than or equal to the denominator’s maximum power.
How do you express an improper algebraic fraction into partial fractions?
. Use long division or comparing coefficients to get it into a mixed fraction.
. If there’s a remainder, then express as A + B + C + (D/x), where D is the remainder and x is the denominator of the top heavy algebraic fraction.
In a partial fractions question, if you can’t find A and B even when trying to make other product equal to 0, what method do you use?
Comparing coefficients: Check what power A and B are coefficients of and find all the other same powers on both sides of the equations as this particular power and solve the equation, excluding all the other different powers and coefficients of those powers.
If -3 is a root of a particular term, what does that tell you about that term?
That ‘X+3’ is a factor of that particular term
