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Sydney Tutor in Calculus, Engineering, GAMSAT, Maths, Physics, HSC Mathematics all levels

One to one tuition in the comfort and convenience of students home at $ 60 / hour.

During first lesson assess students level of knowledge and understanding by asking questions,

Show how to correctly answer questions from high school teacher or other sources eg textbooks

Explain fundamental concepts in detail and using examples show how fundamental concepts are used to answer specific questions from school or tuition

Set homework based only on topics and examples discussed during tuition

Find out date of next exam and topics and prepare appropriately by focusing tuition on future examinable topics

Working with children check approval from NSW government## Subjects

## Service Areas

Epping Castle Hill Carlingford Eastwood Cherrybrook Winston Hills Glenwood Ryde Parramatta
## Experience

Parents and students

Hi

One to one tuition is conveniently held at students home at a mutually agreed time and day (weekends and weekdays are available)so parents avoid spending the time and hassle of driving and delivering student to and from tuition held at coaching centre.

For year 7 - 10 students fee $60 / hour

For year 11- 12 students fee $60/ hour

The first lesson only is half the above rates

Students should prepare a list of questions and concepts causing difficulty to be discussed at

tuition...this will enable me to determine the students academic level and plan an appropriate program of learning.

Tuition is more effective if done on a one to one basis rather then tutoring several students of differing abilities and different ages and school years at same time in a group.

One and half hours tuition for a group of three students at a time implies that each student receives approximately 30 minutes of one to one tuition .This is in general insufficient to cover background and understand the scope and depth of various topics.

My tuition is personal as possible as there is only one person in the group and the style of tuition is tailored to suit the learning style of the student ,to explain how to obtain correct answer to school and exam problems and other relevent questions.

As there are no other students present , the student need not feel embarassed asking questions. By the way if a students asks many questions there is no increase in fees...if a students asks very few questions there is no decrease in fees.

My emphasis is to explain the fundamental

concepts in mathematics and physics in simple terms and ideas and whenever reasonably possible use existing fundamental laws to deduce more laws equations and rules.When students understand they begin to learn and enjoy the subject. It is difficult if not impossible to enjoy a subject which is only partially understood.It is more interesting and challenging to derive an equation rather then receive it without background explanation and derivations.

I have also prepared some Mathematics / Physics experiments and there is excellent agreement between measured and predicted value

Experiments in Mathematics help students bridge the gap between theory and practise and better able to understand the more abstract theories eg Simpsons rule...integration and Simpsons and Trapezoidal rule to find area...Newtons law of cooling...maximum and minimum turning points

For physics the following experiments are available:

potential and kinetic energy...parabolic motion...period of normal pendulum and conical pendulum.measurement of earths gravity...conservation of momentum for elastic and inelastic experiments

. ..Galileos experiment. etc..how to calculate

radius and mass of earth using three simple measurements and Newtons Law of Universal Gravitation, Lenzs Law . A good quality accurate experiment is a very effective learning tool and a means to better understand fundamental concepts.

Please note that Year 11 students will follow the new revised Physics syllabus starting this year 2018

It is far more diificult and of higher standard then the previous syllabus.

Homework is given at the end of each tuition session and is based on what has been taught in tuition.

All steps needed to find solution should be written in clear logical order.

Students should study examples and explanations given in tuition before attempting homework which should be attempted as soon as possible after tuiition This should preferablybe completed no later then 4 days after tuition ( while concepts taught in tuition are still fresh in the mind)

Students should not spend too much time correcting a solution if the answer is wrong as this can be frustrating and demoralizing. It is better to let me find

the source of error which in many cases is a very simple mistake.

All homework should be written into an A4 sized notebooks . These must be kept as a record of topics covered and the

scope and depth of coverage.A summary book will be developed by the student which will incude formulas examples and an index of topics.

A seprate smaller note book containing index and summary of topics as written by student immeditely after successfully answering homework questions.These contain formula and examples and a list of common mistakes to avoid.

My experience is based on 20 years tuition in following subjects:

Mathematics Years 7-10 all levels

Mathematics

2U General Advanced Years 11-12

2U Advanced Years 11-12

Mathematics ( Ext 1 and Ext 2 ) Years 11-12

Engineering Studies Years 11-12

Physics 2 U Years 11-12

International Baccalaureate Years 11-12 Mathematics (All levels)

International Baccalaureate Years 11- 12 Physics

Gamsat Physics

UMAT Physics

Ten years teaching High School Mathematics (all levels)

Science Years 7-10

Physics (years 11-12) in High School.

Marking of HSC Physics examinations.

_____________________________________________

22/9/17

1) How to find the value of e from first principles

Must first understand the concept of e

given that f(x)= B ( power x)

Does there exist a value of B such that

df/dx = B (power x)

(Unchanged by differentiation) and if so find its value

Using the fundamental definition of differentiation

(f(x+h) - f(x))/h= ( B (power (x+h)) - B (power x))/h

B (power x)= B(power x)(B (power h) -1)/h

1 =( B(power h ) -1) / h

Rearranging

h + 1 = B (power h)

Log (h+1) = h Log B (must use base 10 ..why)

B = 10 power(Log(h+1)/h )

Let h equal a very small number eg 0.000001

B = 10 (power( (Log 1.000001)/0.000001)

B = 10 power 0.4329

B= 2.718 (approximately value of e)

I would appreciate any feedback on this derivation...whether you agree or disagree

Regards

David

2) prove that there is only one value of e ( using calculus)

3) given length of each side of a triangle find its area

( without using Herrons formula or trigonometry)

4) Generate Pythagorean triads

These are whole numbers a,b, c such that

axa +bxb= cxc

Eg

5×5 + 12×12 = 13× 13

5) prove that

a (to the power of zero) equals 1

You may use the rule

a (power m) x a(power n) = a(power m+ n)

6) a rectangular prism has 3 faces of area 7 , 8 and 9 square metres

What is its volume and length of each side

What is the length of each diagnol for each

face of the prism

7) a star has a radius of 42673 4896875 metre

If its radius increases by 3.5metre what is its change

in circmference and surface area.

8) how to balance complex chemical equations using simple techniques ( no guesswork)

9) show that a (to the power of zero) = 1

10) at the end of 6 months the price of a house

Increases by 10%

In another 6 months the price decreases by 10%

How much has the price increased over one year?

11) using a pencil,compass, straight edge only show how to divide a straight line

into any numer of equal lengths ..eg 3 ,5,6 , 11 equal lengths

12) using a compass ,straight edge , pencil only show how to construct angles of

60, 45, 90, 30, 15,75 ,150, degrees

13) using a compass ruler pencil construct an exact length of ( square root of 34 ) cm

14)using a compass ,ruler ,sharp pencil construct an area

of ( square root of 35) square centimetres.

15) given a rectangle sand compass pencil straight edge only show how to divide it into 7 smaller equal area rectangles

16) given a triangle ABC ,compass ,sharp pencil, straight edge show how to divide any triangle ABC into

a triangle having

One fifth of area of ABC

One eleventh area of ABC

17) develop the formula for the area of the trapezium given that the lengths of the parallel sides are a and b

and h is the perpendicular distance between the parallel sides.

18) show that the sum of the two lengths of any triangle is larger then third side

19) consider a triangle

AB= 4m-10

BC=8m-20

AC=10m-25

Find the value of

(sinA) ÷ ( sinB)

Find value of all internal angles

20) Assuming the sum of positive numbers is positive

and the product of positive numbers is positive

prove that

a) the product of a positive and negative number is

negative

b) the product of two negative numbers is positive

21) Without using calculator find which is larger

( square root of 7) + (square root of 5)

or

(Square root of 2) + ( ssquare root of 10)

22) a triangle has side lengths

m×m + 1

m×m +7

3m + 1

Find the minimum value of m and minimum

area of triangle.

23) The Chefs Problem

Recipe is as follows

43 grams sugar

53 grams oil

51 grams flour

32 grams eggs

36 grams water

Find the following

a) mass of sugar to to total mass of ingredients

b) mass of water to total mass of ingredients

In response to customer demand the chef decreases the total mass of this " cullinary masterpiece"

by reducing the mass of each ingredient by 20 grams

Find the answer to (a) and (b)

What do you notice?

Why?

Increase the mass of each ingredient by the same amount.

Answer (a) and (b)

What do you notice.?

Why?

Drecrease the amount of each ingredient by the same amount...but there must always be 5 ingredients.

Answer (a) and (b)

What do you notice?

Why?

Multiply or divide each ingredient by the same

positive integer or mixed numeral.

Answer (a) and (b)

What do you observe?

Why?

23) Factorise

4 x(a to power 4)+ 81×(c to power 4)

24) consider a straight line AB of length m

Using compass, straight edge , sharp pencil

show how to locate a point C on AB such that

(AB) ÷ (AC) = any mixed numeral ...eg (2 + 1÷ 3)## Qualifications

Bachelor of Mechanical Engineering (University of New South Wales)

Master of Engineering Science (University of New South Wales)

Diploma of Education (Australian Catholic University)

Qualified experienced teacher.

Working with children check approval from NSW Government.## Services

## Rates

$60 per hour for years 7-10 (one to one tuition at students home)

$60 per hour for years ll- 12 ( one to one tuition at students home)

Introductory lesson at half the normal rate

Am available all days of week except Thursday

No contracts to sign

Advance payments not necessary## Student Discount

Mention that you found this advertisement on Tutor Finder and you will receive your first lesson for half the normal hourly rate ($30 instead of $60).

## Updated

Profile last updated on 17-Feb-2018 (registered 13-Mar-2017)

## Contact

0412995933 David

One to one tuition in the comfort and convenience of students home at $ 60 / hour.

During first lesson assess students level of knowledge and understanding by asking questions,

Show how to correctly answer questions from high school teacher or other sources eg textbooks

Explain fundamental concepts in detail and using examples show how fundamental concepts are used to answer specific questions from school or tuition

Set homework based only on topics and examples discussed during tuition

Find out date of next exam and topics and prepare appropriately by focusing tuition on future examinable topics

Working with children check approval from NSW government

- Calculus - Secondary
- Engineering - Secondary
- GAMSAT - Tertiary
- Maths - Secondary
- Physics - Secondary
- HSC Mathematics all levels

Hi

One to one tuition is conveniently held at students home at a mutually agreed time and day (weekends and weekdays are available)so parents avoid spending the time and hassle of driving and delivering student to and from tuition held at coaching centre.

For year 7 - 10 students fee $60 / hour

For year 11- 12 students fee $60/ hour

The first lesson only is half the above rates

Students should prepare a list of questions and concepts causing difficulty to be discussed at

tuition...this will enable me to determine the students academic level and plan an appropriate program of learning.

Tuition is more effective if done on a one to one basis rather then tutoring several students of differing abilities and different ages and school years at same time in a group.

One and half hours tuition for a group of three students at a time implies that each student receives approximately 30 minutes of one to one tuition .This is in general insufficient to cover background and understand the scope and depth of various topics.

My tuition is personal as possible as there is only one person in the group and the style of tuition is tailored to suit the learning style of the student ,to explain how to obtain correct answer to school and exam problems and other relevent questions.

As there are no other students present , the student need not feel embarassed asking questions. By the way if a students asks many questions there is no increase in fees...if a students asks very few questions there is no decrease in fees.

My emphasis is to explain the fundamental

concepts in mathematics and physics in simple terms and ideas and whenever reasonably possible use existing fundamental laws to deduce more laws equations and rules.When students understand they begin to learn and enjoy the subject. It is difficult if not impossible to enjoy a subject which is only partially understood.It is more interesting and challenging to derive an equation rather then receive it without background explanation and derivations.

I have also prepared some Mathematics / Physics experiments and there is excellent agreement between measured and predicted value

Experiments in Mathematics help students bridge the gap between theory and practise and better able to understand the more abstract theories eg Simpsons rule...integration and Simpsons and Trapezoidal rule to find area...Newtons law of cooling...maximum and minimum turning points

For physics the following experiments are available:

potential and kinetic energy...parabolic motion...period of normal pendulum and conical pendulum.measurement of earths gravity...conservation of momentum for elastic and inelastic experiments

. ..Galileos experiment. etc..how to calculate

radius and mass of earth using three simple measurements and Newtons Law of Universal Gravitation, Lenzs Law . A good quality accurate experiment is a very effective learning tool and a means to better understand fundamental concepts.

Please note that Year 11 students will follow the new revised Physics syllabus starting this year 2018

It is far more diificult and of higher standard then the previous syllabus.

Homework is given at the end of each tuition session and is based on what has been taught in tuition.

All steps needed to find solution should be written in clear logical order.

Students should study examples and explanations given in tuition before attempting homework which should be attempted as soon as possible after tuiition This should preferablybe completed no later then 4 days after tuition ( while concepts taught in tuition are still fresh in the mind)

Students should not spend too much time correcting a solution if the answer is wrong as this can be frustrating and demoralizing. It is better to let me find

the source of error which in many cases is a very simple mistake.

All homework should be written into an A4 sized notebooks . These must be kept as a record of topics covered and the

scope and depth of coverage.A summary book will be developed by the student which will incude formulas examples and an index of topics.

A seprate smaller note book containing index and summary of topics as written by student immeditely after successfully answering homework questions.These contain formula and examples and a list of common mistakes to avoid.

My experience is based on 20 years tuition in following subjects:

Mathematics Years 7-10 all levels

Mathematics

2U General Advanced Years 11-12

2U Advanced Years 11-12

Mathematics ( Ext 1 and Ext 2 ) Years 11-12

Engineering Studies Years 11-12

Physics 2 U Years 11-12

International Baccalaureate Years 11-12 Mathematics (All levels)

International Baccalaureate Years 11- 12 Physics

Gamsat Physics

UMAT Physics

Ten years teaching High School Mathematics (all levels)

Science Years 7-10

Physics (years 11-12) in High School.

Marking of HSC Physics examinations.

_____________________________________________

22/9/17

1) How to find the value of e from first principles

Must first understand the concept of e

given that f(x)= B ( power x)

Does there exist a value of B such that

df/dx = B (power x)

(Unchanged by differentiation) and if so find its value

Using the fundamental definition of differentiation

(f(x+h) - f(x))/h= ( B (power (x+h)) - B (power x))/h

B (power x)= B(power x)(B (power h) -1)/h

1 =( B(power h ) -1) / h

Rearranging

h + 1 = B (power h)

Log (h+1) = h Log B (must use base 10 ..why)

B = 10 power(Log(h+1)/h )

Let h equal a very small number eg 0.000001

B = 10 (power( (Log 1.000001)/0.000001)

B = 10 power 0.4329

B= 2.718 (approximately value of e)

I would appreciate any feedback on this derivation...whether you agree or disagree

Regards

David

2) prove that there is only one value of e ( using calculus)

3) given length of each side of a triangle find its area

( without using Herrons formula or trigonometry)

4) Generate Pythagorean triads

These are whole numbers a,b, c such that

axa +bxb= cxc

Eg

5×5 + 12×12 = 13× 13

5) prove that

a (to the power of zero) equals 1

You may use the rule

a (power m) x a(power n) = a(power m+ n)

6) a rectangular prism has 3 faces of area 7 , 8 and 9 square metres

What is its volume and length of each side

What is the length of each diagnol for each

face of the prism

7) a star has a radius of 42673 4896875 metre

If its radius increases by 3.5metre what is its change

in circmference and surface area.

8) how to balance complex chemical equations using simple techniques ( no guesswork)

9) show that a (to the power of zero) = 1

10) at the end of 6 months the price of a house

Increases by 10%

In another 6 months the price decreases by 10%

How much has the price increased over one year?

11) using a pencil,compass, straight edge only show how to divide a straight line

into any numer of equal lengths ..eg 3 ,5,6 , 11 equal lengths

12) using a compass ,straight edge , pencil only show how to construct angles of

60, 45, 90, 30, 15,75 ,150, degrees

13) using a compass ruler pencil construct an exact length of ( square root of 34 ) cm

14)using a compass ,ruler ,sharp pencil construct an area

of ( square root of 35) square centimetres.

15) given a rectangle sand compass pencil straight edge only show how to divide it into 7 smaller equal area rectangles

16) given a triangle ABC ,compass ,sharp pencil, straight edge show how to divide any triangle ABC into

a triangle having

One fifth of area of ABC

One eleventh area of ABC

17) develop the formula for the area of the trapezium given that the lengths of the parallel sides are a and b

and h is the perpendicular distance between the parallel sides.

18) show that the sum of the two lengths of any triangle is larger then third side

19) consider a triangle

AB= 4m-10

BC=8m-20

AC=10m-25

Find the value of

(sinA) ÷ ( sinB)

Find value of all internal angles

20) Assuming the sum of positive numbers is positive

and the product of positive numbers is positive

prove that

a) the product of a positive and negative number is

negative

b) the product of two negative numbers is positive

21) Without using calculator find which is larger

( square root of 7) + (square root of 5)

or

(Square root of 2) + ( ssquare root of 10)

22) a triangle has side lengths

m×m + 1

m×m +7

3m + 1

Find the minimum value of m and minimum

area of triangle.

23) The Chefs Problem

Recipe is as follows

43 grams sugar

53 grams oil

51 grams flour

32 grams eggs

36 grams water

Find the following

a) mass of sugar to to total mass of ingredients

b) mass of water to total mass of ingredients

In response to customer demand the chef decreases the total mass of this " cullinary masterpiece"

by reducing the mass of each ingredient by 20 grams

Find the answer to (a) and (b)

What do you notice?

Why?

Increase the mass of each ingredient by the same amount.

Answer (a) and (b)

What do you notice.?

Why?

Drecrease the amount of each ingredient by the same amount...but there must always be 5 ingredients.

Answer (a) and (b)

What do you notice?

Why?

Multiply or divide each ingredient by the same

positive integer or mixed numeral.

Answer (a) and (b)

What do you observe?

Why?

23) Factorise

4 x(a to power 4)+ 81×(c to power 4)

24) consider a straight line AB of length m

Using compass, straight edge , sharp pencil

show how to locate a point C on AB such that

(AB) ÷ (AC) = any mixed numeral ...eg (2 + 1÷ 3)

Master of Engineering Science (University of New South Wales)

Diploma of Education (Australian Catholic University)

Qualified experienced teacher.

Working with children check approval from NSW Government.

- Private Tuition
- Home Visits
- Online Help

$60 per hour for years ll- 12 ( one to one tuition at students home)

Introductory lesson at half the normal rate

Am available all days of week except Thursday

No contracts to sign

Advance payments not necessary

hscmathsandphysics@hotmail.com