Standard 11
Writing Exponential form to Logarithmic
form
First we must learn how to read logarithmic form:
The expression log b y is read as log of base b of y
Examples:
log 5 125
log of base 5 of 125
log 6 36
log of base 6 of 36
1
log 3
5
log of base 3 o
Trigonometry
Pythagoras Theorem
a2 + b2 = c2
where c is the hypotenuse while a
and b are the lengths of the other two
sides.
c
a
b
Trigo Ratios of Acute angles
P
hypotenuse
opposite
O
adjacent
Q
Hypotenuse = side opposite right angle/longest side
Adjacent
Topic 3 :Linear
Functions
Vocabulary:
Linear Function: a function of the form y =
mx + b such as y = 2x + 1. The graph of a
linear function is a line.
Function Notation: by naming a function
f, you can use function notation: f(x) =
mx +b
Example 1: Evalu
Topic 5:Polynomials
Polynomials
A polynomial is an expression that has one
or more variables and constants (numbers),
using the operations of addition, subtraction,
multiplication, and positive whole number
exponents.
Polynomials are one of the most impo
Topic 2 : Relations
and Functions
Prepared by Jess Tan
1
A relation is a set of ordered pairs.
The domain is the set of all x values in the relation
domain = cfw_-1,0,2,4,9
These are the x values written in a set from smallest to largest
This is a
relatio
Trigonometry
Pythagoras Theorem
a2 + b2 = c2
where c is the hypotenuse while a
and b are the lengths of the other two
sides.
c
a
b
Trigo Ratios of Acute angles
P
hypotenuse
opposite
O
adjacent
Q
Hypotenuse = side opposite right angle/longest side
Adjacent
Topic 9 : Basic Concepts of
Probability
Probability
Experiments
A probability experiment is an action through which
specific results (counts, measurements or responses)
are obtained.
Example:
Rolling a die and observing the
number that is rolled is a
prob
Topic 8 :Statistics
Prepared by Jess Tan.
1
Measures of Central Tendency:
Ungrouped Data
Measures of central tendency yield information about
particular places or locations in a group of
numbers.
Common Measures of Location
Mode
Median
Mean
Percentiles
Q
Topic 1 : Revision
and Advanced
Theories
Prepared by Jess Tan.
1
A Quick Recap
Multiply out the brackets in (x + 5)(x 3)
Grid
x
+5
x
x2
+5x
-3
-3x
-15
= x2 + 5x - 3x 15
= x2 + 2x 15
2
A Quick Recap
Using either method calculate (b + 3)(b - 6)
b
+3
b
b2
Topic 4 :Quadratic
Functions
Quadratic Functions
y
The graph of a quadratic function
is a parabola.
Vertex
A parabola can open up or down.
If the parabola opens up, the
lowest point is called the vertex.
x
If the parabola opens down, the
vertex is the hig
Thomas Euriga
There are four principal assumptions which justify the use of linear regression models:
Linearity and additivity of the relationship between dependent and independent variables
1. The expected value of dependent variable is a straight-line f
Thomas Euriga
Chapter 13 p. 609 #4
250
200
150
100
50
0
50
a.
b.
c.
d.
e.
f.
g.
100
150
200
250
B1 = .8357 b0 = 17.2366
Ha: P = 0, Ho: P does not = 0, Ho: P>a Yes there is evidence of linear relationship
Variance of error = 82.507
T value = 2.306
Variance
Weekly and hourly earnings data from the Current Population Survey
Original Data Value
Series Id:
LEU0254524600
Not Seasonally Adjusted
Series title:
(unadj)- Median usual weekly earnings (second quartile), Employed
full time, Wage and salary workers, Man
Thomas Euriga
Chapter 12
p. 547 #14
P < or = to .80
P > .80
a. 54 / 65 = .831
(.831 - .80) / .80 * (1-.80) / 65 = .62
P Value = 0.2676
b. .2676 > .05 = Fail to reject
p. 551 #6
p1 > or = to p2
p1 < p2
a. 75 73 + 1.28 = 2
Square (64 / 41) + (81 / 31) = 2.0
Thomas Euriga
Chapter 8: p. 363 #4
a. 800 + 830 = 1630 / 2 = 8:15 is the average time of arrival
b. 830 800 = 30 / 3.4641 = 8.66 standard deviation
c. 1 / 830 800 = 1/30
1/30 * (810 800) = 1/30 * 10 = 1/3 or .3333 probability that the employee will be the
Thomas Euriga
Chapter 6: p. 276 #8
a. 270 husbands divided by 1000 policies = .27 probability
b. 80 wives divided by 1000 policies = .08 probability
c. 60 wives divided by 1000 policies = 60/1000
168 husbands divided by 1000 policies = 168/1000
In conclus
Thomas Euriga
Chapter 1: p. 17 #4
A. Identify the population.
A.1. Nonsmoker students from a large Midwestern University
B. What characteristics of the population are being measured?
B.1. Nonsmoking women and men
C. Identify the sample.
C.1. 330 Women & 2
Thomas Euriga
Chapter 4: p. 168 #8
a. Parameters
b. I would choose the portfolio with the small deviation because it would be more stable and
predictable
c. Portfolio A 7.07 Portfolio B 33.32 are the standard deviations
d. Portfolio A is closer to predict