Chap 14 - simultaneous equations, linear inequalities & regions, factorising quadratic equations, algebraic fractions Flashcards

1
Q

https://www.youtube.com/watch?v=ov3r4hXBU98

A
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2
Q

2 ways to solve simultaneous equations

A

-graphically
-algebraically

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3
Q

why is solving simultaneous equations graphically not good?

A

-gives an approximation if there are decimals

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4
Q

how to solve simultaneous equations graphically

A

-graph the equations
-find coordinate of intersection
-if decimal approximate

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5
Q

2 ways to solve simultaneous equations algebraically

A

-elimination
-substitution
(give ans in fraction, not decimal unless stated)

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6
Q

how to solve simultaneous equations algebraically (substitution)

A

-make one of the letters the subject
-substitute the equations in place of the letter
-solve
-double check ans

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7
Q

how to solve simultaneous equations algebraically (elimination)

A

-( + ) or ( - ) the equations to make one 1 letter left
-solve for the other letter
-double check ans

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8
Q

≤, ≥, <, >

A
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9
Q

note: when divide / multiply by a negative no. flip signs
eg. < to >, ≤ to ≥

A
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10
Q

representing the inequality signs on a number line

A
  • ≤ & ≥ shaded circle
  • < & > unshaded circle
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11
Q

how to find regions in a graph for inequalities

A

-graph the lines
-take a coordinate not on the line & substitute with equation to find the wanted/ unwanted region

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12
Q

note: ≤ & ≥ have (_________) lines - straight lines
< & > have (————) lines - dotted lines

A
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13
Q

finding greatest & least points in a region

A

-find the region
-find coordinates of the corners
-substitute in the equation

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14
Q

note: be careful which region the Q wants & the line type

A
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15
Q

FOIL for expansion

A

-first
-outer
-inner
-last

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16
Q

methods to factorise

A

-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

17
Q

note: about √

A

-ans can be + / - so 2 ans
-if √ ( - ) number = no ans

18
Q

Quadratic formula

A
         2a -put bracket in calc when (b)^2
19
Q

how to complete squares to factories

A
  • 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
20
Q

what is needed to solve an equation

A

-equation has to equal to something

21
Q

quadratic equation format

A

y = ax^2 +bx + c

22
Q

expand ( x + 2 )^2

A
  • x^2 + 2ax + a^2
23
Q

how to take out common factor to factorise

A

-find common factor for a, b & c
-once a = 1, factorise normally

24
Q

how to factorise normally

A

-find factors of c which add up to b

25
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
26
note: anything divided by itself = 1 eg. x /x = 1
27
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
28
how to solve algebraic fractions for + / -
-factorise equation if needed -make denominators same -ADD numerators under same denominator -cancel same top & bottom/ simplify
29
how to solve algebraic fractions for division
-solve like normal fraction: flip second fraction & multiply -factorise equation & cancel same top & bottom/ simplify
30
note: DO NOT MULTIPLY FOR ADDITION OF ALGEBRIC FRACTIONS
31
surd form = leave in the radical
32
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
33
note: be careful of signs & always expand to make sure its correctly factorised
34
note: if √ ( - ) no., ans is impossible
35
note: ALWAYS LOOK FOR COMMON FACTORS BEFOR FACTORISING