Chap 14 - simultaneous equations, linear inequalities & regions, factorising quadratic equations, algebraic fractions Flashcards
https://www.youtube.com/watch?v=ov3r4hXBU98
2 ways to solve simultaneous equations
-graphically
-algebraically
why is solving simultaneous equations graphically not good?
-gives an approximation if there are decimals
how to solve simultaneous equations graphically
-graph the equations
-find coordinate of intersection
-if decimal approximate
2 ways to solve simultaneous equations algebraically
-elimination
-substitution
(give ans in fraction, not decimal unless stated)
how to solve simultaneous equations algebraically (substitution)
-make one of the letters the subject
-substitute the equations in place of the letter
-solve
-double check ans
how to solve simultaneous equations algebraically (elimination)
-( + ) or ( - ) the equations to make one 1 letter left
-solve for the other letter
-double check ans
≤, ≥, <, >
note: when divide / multiply by a negative no. flip signs
eg. < to >, ≤ to ≥
representing the inequality signs on a number line
- ≤ & ≥ shaded circle
- < & > unshaded circle
how to find regions in a graph for inequalities
-graph the lines
-take a coordinate not on the line & substitute with equation to find the wanted/ unwanted region
note: ≤ & ≥ have (_________) lines - straight lines
< & > have (————) lines - dotted lines
finding greatest & least points in a region
-find the region
-find coordinates of the corners
-substitute in the equation
note: be careful which region the Q wants & the line type
FOIL for expansion
-first
-outer
-inner
-last
methods to factorise
-ALWAYS TRY TO TAKE OUT COMMON FACOTRS FIRST
-Quadratic formula: works only when there is x intercept at y)
-completing squares: works when a = 1
-trick: a > 1
note: about √
-ans can be + / - so 2 ans
-if √ ( - ) number = no ans
Quadratic formula
2a -put bracket in calc when (b)^2
how to complete squares to factories
- b / 2
- ( x +/- b/2 )^2 = make it into a perfect square
- ( + )/ ( - ) no. to make perfect square to match with equation
-check if it matched by expanding
what is needed to solve an equation
-equation has to equal to something
quadratic equation format
y = ax^2 +bx + c
expand ( x + 2 )^2
- x^2 + 2ax + a^2
how to take out common factor to factorise
-find common factor for a, b & c
-once a = 1, factorise normally
how to factorise normally
-find factors of c which add up to b
how to use trick to factories
-multiple c by a
-remove a from equation
-fractorise equation normally
-divide no.s by a only, not x
-simplify fractions
-multiple x by denominator of fraction for each bracket
-expand to check
note: anything divided by itself = 1
eg. x /x = 1
how to solve algebraic fractions for multiply
-factorise equation/ simplify
-cancel common no & letters in top & bottom / cross multiply
-multiply top with top/ bottom with bottom
-simplify
how to solve algebraic fractions for + / -
-factorise equation if needed
-make denominators same
-ADD numerators under same denominator
-cancel same top & bottom/ simplify
how to solve algebraic fractions for division
-solve like normal fraction: flip second fraction & multiply
-factorise equation & cancel same top & bottom/ simplify
note: DO NOT MULTIPLY FOR ADDITION OF ALGEBRIC FRACTIONS
surd form = leave in the radical
how to make something = 0 when there is no. in front of letter
ab + c ——> -c/a
ab - c ——> c/a
eg. 3a + 2
3 x -2/3 + 2 = 0
note: be careful of signs & always expand to make sure its correctly factorised
note: if √ ( - ) no., ans is impossible
note: ALWAYS LOOK FOR COMMON FACTORS BEFOR FACTORISING
