Form 4

QUADRATIC EXPRESSION AND
QUADRATIC EQUATIONS

1. Solve quadratic equations by factorization.
Example: Solve
5k² - 8 /3 = 2k
5k² - 8 =  6k
5k² - 6k -8 = 0
(5k=4)(k-2) = 0
k = - 4/5 , 2

2. Solve qudratic equation by formula:
Example: Solve 3x2 – 2x – 2 = 0
x = -b±√b² - 4ac/2a
  = 2±√4-4(3)(-2)/6
   =  2±√28/2
x = 1.215, −0.5486b

MATHEMATICAL REASONING

(a) Statement
A mathematical sentence which is either true or false but not both.

(b) Implication
If a, then b a – antecedent b – consequent „p if and only if q‟ can be written in two
implications:
If p, then q
If q, then p

(c) Argument
Three types of argument:

Type I
Premise 1: All A are B
Premise 2 : C is A
Conclusion: C is B

Type II
Premise 1: If A, then B
Premise 2: A is true
Conclusion: B is true.

Type III
Premise 1: If A, then B
Premise 2: Not B is true.
Conclusion: Not A is true

THE STRAIGHT LINE

(a) Gradient
Gradient of AB =
m = y₂-y₁/x₂- x₁

(b) Equation of a straight line
Gradient Form:
y = mx + c
m = gradient
c = y-intercept

Intercept Form:
x/a + y/b = 1
a = x−intercept
b = y−intercept

Gradient of straight line 
m = - y-intercept/ x-intercept
= - b/a

TRIGONOMETRY
sin q °  = Opposite/hypotenuse
           = AB/AC

cos q ° = adjacent / hypotenuse 
            = BC/AC

tan  q °= opposite/adjacent
           =AB/BC