First Derivative Test
Math Studies IB
What is it used for?
- Finding the intervals where functions are increasing or
decreasing and where your function has critical/Stationary points
(max, min, or point of inflectionpt where the graph is level)
and whethe
Completing the Square Notes
2 + + = 0 can be solved easily by
factoring. For example, the equation 2 + 6 16 = 0 can be factored easily to
( + 8)( 2) = 0 to give solutions of = 8 = 2
Some quadratic equations in the form of
When a quadratic equation cannot
Polynomials
Local Max and Min:
Types of Polynomials and their properties:
Cubic
Example! This cubic flips over the x-axis, and moves left 1,
down 3.
Quartic
Properties of all Polynomials:
If in factored form, finding roots (x-intercepts) are
quick!
P(x)=(
Venn Diagram Notes
Name:_
What does a Venn diagram look like?
This!
It could also have Elements in it!
Properties!
A Subset:
Intersection:
Union:
Disjoint (Mutually Exclusive) Sets:
Examples:
Venn Diagram Regions:
Example:
This time with numbers!
But what
Math Studies IB
Its so logical!
Name: _
Some words/symbols you should know:
Word
Symbol/Definition
Proposition
Negation
(Negative or opposite)
Inclusive disjunction
p (When one or both propositions are
true)
Exclusive disjunction
Conjunction
Implication
Math Studies
Power Rule Notes
Name _
Derivatives Slope of a Tangent
The expression found when determining the expression for the slope of a tangent ( m t a n ) for a function is called
the derivative of the function. The derivative is used to find the ins
Geometry and Trig Review
54 min
60 marks
D0 it. 1. In the diagram, triangle ABC is isosceles. AB = AC, CB = 15 cm and angle ACB is 23°.
Diagram not to scale
15 cm
Find
(a) the size of angle CAB;
(b) the length of AB.
Answers:
(Total 4
Angela needs $4000 to pay f: ir a car. She was given two options by the car seller.
Option A: Outright Loan
A loan of $4000 at a rate of 12% per annum compounded monthly.
(a) Find
(i) the cost of this loan for one year;
(2)
(ii) the equivalent annual si