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

Question 1

2 ways to solve simultaneous equations

Answer 1

-graphically
-algebrically

Question 2

why is solving simultaneous equations graphically not good?

Answer 2

-gives an approximation if there are decimals

Question 2

how to solve simultaneous equations graphically

Answer 2

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

Question 3

2 ways to solve simultaneous equations algebraically

Answer 3

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

Question 4

how to solve simultaneous equations algebraically (substitution)

Answer 4

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

Question 5

how to solve simultaneous equations algebraically (elimination)

Answer 5

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

Question 6

≤, ≥, <, >

Question 7

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

Question 7

representing the inequality signs on a number line

Answer 7

• ≤ & ≥ shaded circle
• < & > unshaded circle

Question 8

how to find regions in a graph for inequalities

Answer 8

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

Question 8

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

Question 8

finding greatest & least points in a region

Answer 8

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

Question 9

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

Question 10

FOIL for expansion

Answer 10

-first
-outer
-inner
-last

Question 11

methods to factorise

Answer 11

-ALWAYS TRY TO TAKE OUT COMMON FACOTRS FIRST
-Quadratic formula: works for all
-completing squares: works when a = 1
-taking out common factor: work when there’s common factors
-trick: a > 1

Question 12

note: about √

Answer 12

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

Question 13

Quadratic formula

Answer 13

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

Question 14

how to complete squares to factorise

Answer 14

• 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

Question 15

what is needed to solve an equation

Answer 15

-equation has to equal to something

Question 16

quadratic equation format

Answer 16

y = ax^2 +bx + c

Question 17

expand ( x + 2 )^2

Answer 17

• x^2 + 2ax + a^2

Question 18

how to take out common factor to factorise

Answer 18

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

Question 19

how to factorise normally

Answer 19

-find factors of c which add up to b

Question 20

how to use trick to factorise

Answer 20

• 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

Question 21

note: anything divided by itself = 1
eg. x /x = 1

Question 22

how to solve algebraic fractions for multiply

Answer 22

-factorise equation/ simplify
-cancel common no & letters in top & bottom / cross multiply
-multiply top with top/ bottom with bottom
-simplify

Question 23

how to solve algebraic fractions for + / -

Answer 23

-factorise equation if needed
-make denominators same
-ADD numerators under same denominator
-cancel same top & bottom/ simplify

Question 24

how to solve algebraic fractions for division

Answer 24

-solve like normal fraction: flip second fraction & multiply
-factorise equation & cancel same top & bottom/ simplify

Question 25

note: DO NOT MULTIPLY FOR ADDITION OF ALGEBRIC FRACTIONS

Question 26

surd form = leave in the radical

Question 27

how to make something = 0 when there is no. in front of letter

Answer 27

ab + c ——> -c/a
ab - c ——> c/a
eg. 3a + 2
3 x -2/3 + 2 = 0

Question 28

note: be careful of signs & always expand to make sure its correctly factorised

Question 29

note: if √ ( - ) no., ans is impossible

Question 30

note: ALWAYS LOOK FOR COMMON FACTORS BEFOR FACTORISING