Download 2 Math and Study Course

Preparation
for
Commercial /
ATP Pilots
Your instructor for this
Ground School…
Brand Wessels
Cell: 073-591 3907
Email: [email protected]
Agenda:
• Personal Introductions – name,
background, qualifications
• What is our expectations from this
course
• Course Rules – be on time, be prepared
and participate constructively
• Be Professional
• Course Schedule
• Have FUN!
Mathematics
What do we need to know?
We need to have basic understanding of:
• Basic Algebra - cross-multiplication, crossaddition and -subtraction, averaging, powers
and roots, bracketing, percentages, inverse
calculation and vectors.
• Basic Trigonometry – Triangles, Ratio’s,
Pythagoras.
• Basic Interpolation.
• How to operate the Navigation Computer and
Scientific Calculator.
The Myth – “this is difficult…”
• If you passed Mathematics up to Grade
10 standard grade, you have covered
everything you will need.
• There is NOTHING in the CAA theory
syllabus, that is as difficult as passing
a current Grade 12 Higher Grade
Mathematics' exam – go try one….
SA Grade
12 formulas
in 2008……
That Being Said….
•
•
•
•
You have to know the basics WELL.
You have to know your calculators WELL.
You have to stay CURRENT.
You have to show enough RESPECT for the
basics required.
• The CPL/ATPL exam is quite a lot of work –
about the same volume as the first 3 month’s of
Engineering studies at University. If you are not
on top of the required mathematics, you will
waste time.
The ABC of this course….
•APPLY your
•BACKSIDE to the
•CHAIR….
Trig Example: You are taking off from a
runway, with a hill 300’ high, 6000’ from
the threshold. What angle of climb must
you maintain to clear the hill?
tan c = b/a
Push this button just
you choose a 2nd
And y=300’ before
and x=6000’
function button
Tan x = 0.05
Inverse
Force
of 3(or cot, or
Divide byButton
tan same as
inverse
tanˉ¹)
Force of 2
Thus c = 2,86º
10 to the
force …
Square
Root
Brackets
Degree, minutes,
seconds – also
hours, minutes,
seconds
% Button
Functions
A fraction is an ordered pair of whole
numbers, the 1st one is usually written on top of
the other, such as ½ or ¾ .
a
b
numerator
denominator
The denominator tells us how many pieces the
whole is divided into, thus this number cannot be 0.
The numerator tells us how many such pieces are
being considered.
• Variable – A variable is a letter or
symbol that represents a number
(unknown quantity).
• 8 + n = 12
• A variable can use any letter of
the alphabet.
•n+5
•x–7
• w - 25
An Equation is like a balance
scale. Everything must be
equal on both sides.
=
10
5+5
When an amount is unknown
on one side of the equation it is
an open equation.
=
7
n+2
When you find a number for n
you change the open equation
to a true equation. You solve
the equation.
=
7
5n + 2
Simple Algebra
• Remember Rules:
• The sum of two positive numbers is always
positive.
• The sum of two negative numbers is always
negative.
• Multiplication/Division of two positive
numbers is always positive.
• Multiplication/Division of two negative
numbers is always positive.
• Multiplication/Division of a positive and a
negative number is always negative.
Addition and Subtraction
26+(-38)-(-55)+(-61)-(23) =
-41
On the calculator – type it all without the
brackets….
Powers and Roots
2 x 2, same as 2², same as 2 to
the power of 2, same as 4.
The root of 4, same as √4,
same as 2.
On the calculator:
2x², enter = 4
√4, enter = 2
Inverse operation
the opposite operation used to
undo the first.
•4+3=7
7–4=3
• 6 x 6 = 36
36 / 6 = 6
• Use “xˉ¹” on you calculator.
Parentheses and Brackets)
Use brackets when you want to do certain
calculation before the rest:
b² = 60² - (35000÷6080)²
b² = 3566,8. Now press √ and
b = 59,72
C = 2 x ((9÷3) + (4+3)²)
C = 2 x (3 + 49)
C = 104
Order of Algebraic Operation:
“PEMDAS”
Solve in the following sequence:
• P for solving Parentheses(or brackets)
• E for solving Exponents next
• MD for Multiplication and Division next
• AS for Adding and Subtracting next.
Example:
• y = ((4³ + √((3+27) – (25÷5))) ÷ 3) + 273
• P is y = ((4³ + √(30 – 5)) ÷ 3) +273
And y = ((4³ + √25) ÷ 3) +273
• E is y = ((64 + 5) ÷ 3) +273
• MD is y = (69 ÷ 3) + 273
• AS is y = 23 + 273 = 296
Prove it by typing the whole equation into
your calculator at once….
Solving Addition and
Subtraction Equations
Procedure
• Isolate the variable by performing the inverse
operation on that variable.
• The inverse of subtraction is adding. The
inverse of adding is subtracting.
• Perform the same operation on the side of the
equal sign that does not have a variable.
Example
y + 13 = 25
- 13 - 13
y
= 12
We want to get the y by
itself. Perform the inverse
operation. The inverse of
adding is subtracting.
Do the same operation on
the other side of the equal
sign.
Check the answer in the
original equation.
y + 13 = 25
12 + 13 = 25
25 = 25
Example 2
k – 12 = 4
+ 12 + 12
k = 16
To get k by itself, we
perform the inverse
operation. The
opposite of “minus
12” is “plus 12.”
Check
k – 12 = 4
16 – 12 = 4
4 = 4
Solving Multiplication and
Division Equations
Procedure
• Isolate the variable by performing the inverse
operation on the number that is attached to the
variable.
• The inverse of multiplication is division. The
inverse of division is multiplication.
• Use the “Golden Rule.” Perform the same
operation on the other side of the equal sign.
Example
The inverse of
division is
multiplication.
Repeat the operation
on the other side.
m ÷ 3 = 10
x3 x3
m
= 30
Check. Use the original
equation.
m ÷ 3 = 10
30 ÷ 3 = 10
10 = 10
Example 2
The inverse of
multiplying is
dividing.
7b = 105
÷
7
÷
7
15
7 105
b
=
15
7
35
35
0
Check
7b = 105
7(15) = 105
105 = 105
Cross Multiplication
Moving the variable around in a function, until the
unknown variable is isolated.
Example:
In
a² = b² + c², if we have to
c
solve for we have to isolate it on one side of the
equal sign.
Important: What you do on one side of the equation
has to be done on the other side.
a² = b² + c² - b² leaves c² isolated,
but then we have to subtract b² on the left side of the
Thus:
equation as well:
a² - b² = c²
And solving for B in the following
function:
xb
bx
Something
divided by
itself = 1
SIN B
=
• Remember “of”
means multiply in
mathematics.
•“Per” means division
in mathematics.
Solve the Problems
3a = 21
To solve a, divide both sides by 3:
a=7
b + 17 = 59
To solve a, subtract 17 from both sides:
b = 42
c – 22 = 100
To solve c, add 22 to both sides
d = 50
5
To solve for d, multiply both sides by 5
d = 250
Exponents
Vocabulary
exponent – the number of times a number is multiplied by itself.
base – the number that is being multiplied.
3
base
8
This is read “8 to the 3rd power” or “8 cubed.”
It means 8 x 8 x 8.
exponent
Evaluating Exponents
5
2 = 2 x 2 x 2 x 2 x 2 = 32
3
6 = 6 x 6 x 6 = 216
4
1.3 = 1.3 x 1.3 x 1.3 x 1.3 = 2.8561
Exponents with a base of 10
• Any multiple of ten can be expressed as
an exponent with a base of ten.
• The base is 10. The number of zeroes
gives us the exponent.
2
• Example: 100 = 10
4
• 10,000 = 10
1,000,000 = 10
6
Writing in Expanded Form
Using Powers of 10
• First, write the problem in expanded form.
• Then, change each term to a multiplication
of the value and its place.
• Change the place values to exponents
with powers of 10.
Example
7, 946
7, 000 + 900 + 40 + 6
(7 x 1,000) + (9 x 100) + (4 x 10) + (6 x 1)
3
2
1
7 x 10 + 9 x 10 + 4 x 10 + 6
Percentages
Simply a fraction of 100 (meaning “cent)
Examples:
•1/3 = 33.33% (1÷3x100)
•¾ = 75% (3÷4x100)
•1½ = 150% (3÷2x100)
•15% of 3267 = 490
•230 expressed as a % of 430 =
On the calculator –
230÷430x100 = 53,5%
use “shift, %” to do
it faster.
Percents Have Equivalents in
Decimals and Fractions
Percent
Fraction
Decimal Fraction Simplified
1
20
20% = .20 = 100 = 5
Finding a Percent of a
Number
Using a Proportion
• Set up a proportion that uses the percent
over 100.
• Cross multiply to write an equation.
• Solve the equation.
To set up your proportion, think, “IS over OF equals
PERCENT over 100.”
Example – What is 20%
of 30?
x
=
30
100x =
100x =
100
x =
20
100
30(20)
600
100
6
part
whole
Using a Decimal
• Change the percent to a decimal.
• Multiply that decimal by the number you
are finding the percent of.
Example – What is 18%
of 70?
18% = 0.18
0.18 x 70 =
12.6
Vocabulary
• A percent is a ratio that compares a
number to 100. It means “per 100.”
• 49 out of 100 is 49%.
Writing Percents as Decimals
• Imagine a decimal point in the place of
the percent sign, and move the decimal
two spaces to the left (the same as
dividing by 100).
26%
40%
7%
.26
.40
.07
.4
Writing Percents as Fractions
• Place the percent in a fraction with a
denominator of 100.
• Simplify the fraction.
26%
26
100
13
50
75%
75
100
3
4
Writing Decimals as Percents
• Move the decimal point two spaces to
the right, and add a % symbol (this is
the same as multiplying by 100).
.34
.19
.125
.6
34% 1
19%
12.5%
60%
100%
Included %
When asked to work out the % of reserve fuel when it’s already included
in the total given, care must be taken with the mathematics:
Example:
We have 11 500 Lt of fuel which include 15% reserve – how much fuel
do we have available without using the reserve fuel?
If we started with 10 000 Lt and then had to add 15% reserve it means:
10 000 x 15% = 1500 + 10 000 = 11 500 Lt total fuel.
To reverse the calculation (how much fuel do we have without the 15%),
we have to divide the total with 1.15 (or 115%).
Or 11 500 ÷ 1.15 = 10 000 Lt
Averages
Simply add all the quantities
and divide it by the number of
quantities
Example:
7, 11, 14, 8, 3, 26
means
(7 + 11 + 14 + 8 + 3 + 26) ÷ 6 = 11.5
Hint
• If you don’t see a negative or
positive sign in front of a
number it is positive.
+9
Rounding of Decimal Numbers
• When the digit to the right of the last
retained digit is 5 or greater, round up by 1
• When the digit to the right of the last
retained digit is less than 5, keep the last
retained digit unchanged
Example:
23.46 becomes 23.5
Note: Only do
rounding at the final
calculation…..
And 2.1938 becomes 2.2
Ratios
• A comparison of two numbers
• Can be expressed as:
– a fraction
– A colon (:)
– The word “to”
Example:
A gear ratio of 5:8 can be
express as:
⅝ or 5:8 or 5 to 8
Ratios in Aviation
•
•
•
•
•
•
•
•
•
Compression Ratio
Mach Number
Aspect Ratio
Air-Fuel Ratio
Glide Ratio
Gear Ratio
Interpolation
Trigonometry
Map Scales
No Unit of
Measure….
i.e.: cm, lt
or nm, etc.
Ratios
• A ratio is a comparison between two numbers
by division.
• It can be written in three different ways:
5 to 2
5:2
5
2
Equal Ratios
• When two ratios name the same number,
they are equal. It’s like writing an equivalent
fraction.
20 : 30
Equal Ratios:
10 : 15 2 : 3 80 : 120
Example:
If the cruising speed of an airline is
200knots and its maximum speed is
250knots, what is the ratio of
cruising speed to the maximum
speed?
• Solution:
• First express the speeds as a fraction:
– Or Ratio =
200
250
• Then reduce fraction to smallest terms:
– Or Ratio =
200
250
=
4
5
or 4 to 5, or 4:5
Angles
Vocabulary
• An angle has two sides and a
vertex.
• The sides of the angles are rays.
The rays share a common
endpoint (the vertex)
• Angles are measured in units
called degrees.
Types of Angles
When lines intersect to
form right angles, then
they are classified as
perpendicular lines.
Measuring Angles
• Place the center point
of the protractor on
the vertex of the
angle and turn the
protractor so that one
side lines up with 0 on
the inner scale.
Measuring Angles (strategy 2)
• Place the center point
of the protractor on
the vertex of the
angle. Note where
both rays cross the
protractor. Subtract
the two numbers
(from the same scale)
Property of triangles
• The sum of all the angles
equals 180º degrees.
60º
90º
30º
What is the missing
angle?
40º
?
70º 70º
70º
70º
+ ?
180º
Classifying Triangles
Classifying by Angle
•Acute triangles have three acute angles.
•Obtuse triangles have one obtuse angle.
•Right triangles have one right angle.
Classifying by Sides
•Equilateral triangles have three congruent
sides.
•Isosceles triangles have two congruent
sides.
•Scalene triangles have zero congruent
sides.
Finding Missing Angles
•The three angles of a triangle always add
to 180°.
•Use a variable to stand for the missing
angle and set an equation equal to 180.
x + 49 + 47 = 180
x + 96 = 180
– 96 = -96
x = 84
Trigonometry
The Right Angled
Triangle
Trigonometric
functions are
commonly defined
as ratios of two
sides of a right
triangle containing
the angle
Study Tip
Acronym's to
use:
• Sin-oh
• Cos-ah
• Tan-oa
Example: There is a hill 250’ high, 3000’ from the threshold
of the runway.
What must the angle of climb be to clear the hill by 100’?
Answer:
Tan ∞ = 350
Can you see it’s a Right Angled Triangle?
•Sin-oh
•Cos-ah
•Tan-oa
3000
Tan ∞ = 0.116
Thus we use
∞
Tan…
tan
Which ratio to
use?
350’
Hill AoC = 6.65º
Opposite
∞
Threshold
= 0.116
Adjacent
3000’
90º
The SINE Rule.
A
Non-Right Angle
Triangle
c
b
B
a
C
=
=
SIN A
c
b
a
SIN B
SIN C
The COSINE Rule.
a² = b² + c² - 2bc x COS A
b² = a² + c² - 2ac x COS B
A
c² = a² + b² - 2ab x COS C
c
b
B
a
C
COSINE RULE
is used in
NON-RIGHT ANGLED
TRIANGLES when given the length
of two sides and one angle and the
unknown is the length of the side
opposite the known angle or when
given the length of all three sides
and the unknown is any angle.
Example:
Solve the length of Side a.
a²
=
b² + c² - 2bc COS A
a²
=
3² + 7² - (2  3  7  COS 40)
a²
=
9 + 49 - 32,17
a²
=
25,83
a
=
√25,83
a
=
5,08 UNITS
SINE RULE
is used in
NON-RIGHT ANGLED
TRIANGLES when given the length
of two sides and one angle and the
unknown is the length of the side
adjacent to the known angle.
Example:
At 1205, aircraft A and B are 75 nm's apart
and are on a collision course. Aircraft A
330 Kts. Aircraft B 360 Kts. The relative
bearing from A to B is 075. What angle
needs to be closed by aircraft B to
intercept aircraft A?
SIN B
=
SIN B
=
SIN B
=
B =
?
0.885
62.3º
Graphs of the Trig Functions
• Sine
– The most fundamental sine wave has the
graph shown.
– It fluctuates from 0 to a high of 1, down to –1,
and back to 0, in a space of 2.
Graphs of the Trig Functions
• Cosine
– The graph of cosine resembles the graph
of sine but is shifted to the left.
– It fluctuates from 1
to 0, down to –1,
back to 0 and up to 1.
THE CIRCLE
Various questions may be asked relating to the
radius, diameter, surface or circumference of a circle.
FORMULA
c
d (diameter)
=
2r
c (circumference) =
2r
r
s (surface)
=
r²
s
EXAMPLE 1:
If the radius of a circle is 7 units, determine its
circumference?
c
=
2r
=
2  3,14  7
=
43,98 UNITS
Example:
To Calculate the Radius of a Turn
TAS 240 Kts
RATE 1 TURN
RATE 1 TURN = 2 mins. (360º)
What is the radius of the turn in feet?
2
Circ=240 x 6080' x
60
Circ=48640’
Circ = 2 r
r
= Circ/ 2
r
=48640/ 2
r
=7741'
Example:
What is the value of Convergency between Point
A(26º40’S 24º15’E) and Point B (26º40’S 55º15’E)?
Convergency = Dlong x sin Mid Lat
Solution:
The difference in longitude is: 55º15’ - 24º15’ = 31º
And: Convergency = Dlong x sin Mid Lat
Convergency = 31º x sin 26º40’
Convergency = 31º x 0,449
Convergency = 13,91º
Pythagoras
• Used with Right Angle Triangles
• Used for DME Slant Range Calculation
B
a² = b² + c²
a
c
90º
C
A
b
Example:
An aircraft at 35 000' is 60 DME from a ground station. What is the
ground range?
Solution:
a² = b² + c² or
b² = a² - c²
b² = 60² - (36000÷6080)²
B
b² = 3564.9
b = √ 3566,8
35000
a
c
90º
A
?
b
60
b = 59,72 nm (Ground Dist.)
C
Vectors - Lines with Direction and speed
Triangle of Velocities
Ground
Position
Drift
Angle
Depart
Destination
THDG/TAS
Air Vector/Air Plot
Air Position
Interpolation:
1. to insert between or among
others
2. to change by putting in new
material
3. to estimate a missing value
by taking an average of
known values at neighboring
points
Interpolate one series at a time:
PALT
14 000
AUW 12 000 LBS
1237
AUW 10 750 LBS
AUW 10 000 LBS
15 500 16 000
1260
1169
1098
1115
1268
1268 – 1237 = 31/2000
X 1500 = 23,25 (+1237)
1260=– 1260
1115 = 124/2000 X
750 = 54,37 (+1115)
= 1169
1120
1120 – 1098 = 22/2000
X 1500 = 16,5 (+1098)
= 1114.5
Exercises:
1. Subtract the
following
numbers:
5920
2. Express as a
%:
13/44
3. If full tanks of fuel = 90 000
kg of fuel, and 15% reserves
are carried, what is the fuel
without reserves?
= 29.54%
-2744
-4889
3921
90 000 ÷ 1.15
26/85
= 30.58%
-492
= 10 124
5. Sin A = .0876.
What is value of A?
A = 5.02º
= 78269.86 kg
1/33
4. Logging the following hours
per week, what is the average
trip length (hour and minutes)?
= 3.03%
3.73
4.5
1.9
2.5
5.7
3h39min57sec
Primary Radar Ranging
A radar system has the following specifications : PRF of 400 PPS and a pulse width of
2µ seconds. Find the maximum and minimum range.
Minimum Range :
Range (M)
=
Speed
X
Time
2
Range (M)
= 3 x
8
10
Meters / second
X
2
600 Meters
Range (M)
=
Range (M)
= 300 Meters
2
Or
0.3 KM
6
2 X 10
Seconds
If the Local Speed of Sound is 1100 feet per second, what is the TAS
of an aircraft flying at Mach 0.73?
We can not work in feet per second as TAS is in knots. To
convert feet per second proceed as follows : 1100 x 60 = 66000
feet / minute: 66000 x 60 = 3960000 feet / hour: 3960000 / 6080
= 651 Kts
TAS
MachNumber 
LSS
0.73 
TAS
651.32
0.73  651.32  475.5 Knots
Two aircraft flying at the same Flight Level, Aircraft A has a Mach
Number of 0.815 and a TAS of 500 Knots, Aircraft B has a Mach
Number of 0.76. At what Flight Level are the aircraft flying and
what is the TAS of aircraft B?
MachNumber 
TAS
LSS
LSS  613.5 Knots
LSS  38.945 coat  273
613.5  38.945 coat  273
613.5

38.945
coat  273
15.75 
coat  273
15.75 2  coat  273
248.06  coat  273
248.06  273  coat
coat   24.9
Problem Solving
Problem Solving is easy if you
follow these steps
Understand
the
problem
•
•
•
•
Step 1 – Understand the
problem
Read the problem carefully.
Find the important information.
Write down the numbers.
Identify what the problem wants
you to solve.
• Ask if your answer is going to
be a larger or smaller number
compared to what you already
know.
Step 2 - Decide how you’re
going to solve the problem
Choose a method
Use a graph
Write an equation
Find a pattern
Use reasoning
Make a table
Use formulas
Make a list
Work backwards
Draw a picture
Act it out
Step 3 - Solve the
problem
Example:
TAS
MachNumber 
LSS
Step 4 - Look Back & Check
Reread the problem
Substitute your new number
Did your new number work?
Strategy
• When a problem contains difficult numbers (like
fractions or mixed numbers), then imagine the
problem with simpler numbers.
• Solve a problem using the simpler numbers.
• Check to see if the strategy worked. Does the
answer make sense?
• Go back and use the same strategy, only this
time you can use the more difficult numbers.
If you get stuck…
• Remember, there are only four operations
to choose from: multiply, divide, add, or
subtract.
• Try a few operations and see which
answer makes the most sense.
Words that mean “Add”
•
•
•
•
•
•
•
In all
Increased by
How many / how much
Sum
Total
Added to
Altogether
Words that mean “Subtract”
•
•
•
•
•
•
•
How many / how much MORE
Decreased by
Difference
Less than
Fewer than
Left / left over
Reduced by
Words that mean “Multiply”
•
•
•
•
•
Of
Product
Times
Multiplied by
In all / total / altogether (when referring to
repeated addition)
Words that mean “Divide”
•
•
•
•
•
Quotient
Out of
Per
Ratio
Percent
Navigation
Computer
Study Methods
How to Mind Map
1. Use just key words, or wherever possible images.
2. Start from the center of the page and work out.
3. Make the center a clear and strong visual image that depicts the
general theme of the map.
4. Create sub-centers for sub-themes.
5. Put key words on lines. This reinforces structure of notes.
6. Print rather than write in script. It makes them more readable and
memorable. Lower case is more visually distinctive (and better
remembered) than upper case.
7. Use color to depict themes, associations and to make things
stand out.
8. Anything that stands out on the page will stand out in your mind.
9. Think three-dimensionally.
10. Use arrows, icons or other visual aids to show links between
different elements.
11. Don't get stuck in one area. If you dry up in one area go to
another branch.
12. Put ideas down as they occur, wherever they fit. Don't judge or
hold back.
13. Break boundaries. If you run out of space, don't start a new
sheet; paste more paper onto the map. (Break the 8x11
mentality.)
14. Be creative. Creativity aids memory.
15. Get involved. Have fun.
Your mind
think in
Pictures!!!
Memorize the following
shopping list in 10
seconds….
Eggs
Bacon
Knife
Bananas
Dough Nuts
Pencils
Spaghetti
Yoghurt
Syrup
Red Paint
Body List Method
1 = Toes
2 = Knees
3 = Thighs
4 = Back side
5 = Love Handles
6 = Shoulders
7 = Throat
8 = Face
9 = Point
1. Eggs
2. Bacon
3. Knife
4. Bananas
5. Dough Nuts
6. Pencils
7. Spaghetti
8. Yoghurt
9. Syrup
10.Red Paint
10 = Ceiling
Now create your own house list….
Always use
something that
you know already
as your list….
11 Tips to Improve Studying Results
1 Study in Short, Frequent
Sessions – no more than one hour
at a time, with 10min break.
2 Take Guilt-Free Days of Rest.
3 Honor Your Emotional State. Do
not study if you are tired, angry,
distracted, or in a hurry.
4 Review the Same Day.
5 Observe the Natural Learning
Sequence. if you try first to grasp
the big picture and then fill in the
details, you often have a more
likely chance of success.
6 Use Exaggeration. Why do
runners sometimes strap lead
weights to their legs?
7 Prepare Your Study Environment. For
example, do you need special lighting, silence,
music, privacy, available snacks, etc.?
8 Respect “Brain Fade.” As you place more
information on top, the lower levels become
older and less available to your immediate
recall. The trick here is simply to review.
9 Create a Study Routine. An effective way to do
this is to literally mark it down in your datebook
calendar as if you have an appointment, like
going to the doctor. For example: “Tuesday 34:30 P.M. — Study.
10 Set Reasonable Goals. Set your vision on
the long-term dream, but your day-to-day
activity should be focused exclusively on the
short-term, enabling steps.
11 Avoid the Frustration Enemy. Don’t waste
energy blocking, getting upset, and thinking that
you’re not good enough — simply keep moving
forward at a slower (but un-blocked) pace.
The 7 Habits of Highly
Effective People
Habit 1: Be Proactive
Habit 2: Begin with the End in Mind
Habit 3: Put First Things First
Habit 4: Think Win-Win
Habit 5: Seek First to Understand, then
to be Understood
Habit 6: Synergize
Habit 7: Sharpen the Saw
Use a Diary – any plan
is not a plan untill it’s
written down. That
includes a study plan..
The Time Management Quadrant
1
URGENT
NOT URGENT
•Preparation
IMPORTANT
•Crises
•Pressing Problems
•Deadline driven
projects, meetings,
preparations
2
•Prevention
•Values clarification
•Planning
•Relationship building
•Empowerment
NOT IMPORTANT
•Interruptions, phone
calls
3
•Trivia, busywork
•Some mail, some
reports
•Some telephone calls
•Some meetings
•“Escape” activities
•Many popular
activities
•Excessive TV
•Time wasters
4
Make it
FUN!!