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HSC Physics and Mathematics

 Sydney - Baulkham Hills

Physics and mathematics is much easier if taught correctly

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

We travel to these locations
Epping Castle Hill Carlingford Eastwood Cherrybrook Winston Hills Glenwood Dural Kellyville


One to one tuition in the comfort and convenience of students home at $ 60 / hour.
During first lesson assess i ask questions and and assessing quality of answers and time taken to answer.

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 as outlined in exam notification sheet.

Working with children check approval from NSW government



Parents and students

One to one tuition is conveniently held at students own 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...often after hard day at work.

For year 7 - 12 students fee based on $60/ hour at students home or public library
The first lesson only is half the above rates.

Advance payments not required.
No contracts to sign and therefore parents not locked into paying for unsatisfactory tuition for months in advance

Students should prepare a list of questions and concepts causing difficulty to be discussed during
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.Student does not have to wait for question to be answered.

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 group size consists of one student only.

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. 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
which is far more difficult and of higher standard then the previous syllabus. It is far more appropriate in terms of scope depth and choice of subject matter.for students wishing to study Engineering/ Science at University. .

Homework is given at the end of each tuition session and is based on what has been taught in tuition and at school.
All steps needed to find solution should be written legibly in clear logical order.
Students should study written examples and explanations given in tuition before attempting homework which should be attempted as soon as possible after tuiition This should preferably be completed no later then 4 days after tuition ( while concepts taught in tuition are still fresh in the mind of student)
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

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.



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

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

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

3) given length of each side of a scalene 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

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 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

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

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)


(Square root of 2) + ( square 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
( Do not actually use this recipe...the result will
almost certainly be an inedible disaster)

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)

c) What do you notice?
d) Why?

Increase the mass of each ingredient by the same amount.
Answer (a) (b) (c) (d)

Drecrease the amount of each ingredient by the same amount...but there must always be 5 ingredients.
Answer (a) (b) (c) (d)

Multiply or divide each ingredient by the same
positive integer or mixed numeral.
Answer (a) (b) (c) (d)

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 (2 + 1÷ 3)

25) consider the integers 1, 2, 3....100
What is the sum of the even numbers minus the
sum of the odd numbers?

26) the chocolate problem
Conider a rectangular box containing one layer of circular discs of chocolate of identical diameter and
thickness.The diameter does not necessarily equal to the thickness.

The discs touch each other or the sides of the box.
The discs are packed so that they connot move with respect to each other or sides of box.

Which contains more chocolate

a box containing a large number of small diameter discs


a box containing a small number of large diameter discs



Give reasons for your answer.

27) which is larger

99 to power 101

101 to power 99

Do not use logs or calculator
Give reasons

Consider a triangle whose sides are of length

4c + 5



What are the allowable values of c

29) consider a mass m rotating at radius r about
a mass M

a) what is the speed of m relative to M

b) what is the speed of M relative to m

c) according to a clock on m the time taken to
boil an egg is t minutes

What is the time taken for this event as measured
by a clock on M ?

d) according to a clock on M the time taken to
eat an egg on M is j minutes

According to a clock on m what is time taken to eat
this egg?

If the true shape of m and M is spherical what is the shape of M as seen by an observer on m?

30) explain the following dillema

Cathode rays are beams of electrons
Cathode rays are blue red green etc in colour
Therefore electrons are blue red green etc in colour

Do cathode rays travell only in straight lines?
Give reasons for your answers.

Why does it appear that light in a cathode ray tube is deflected by an electric / magnetic field?
What is happening?

Why does it appear that light causes a paddle wheel inside a cathode ray to rotate?

If a cathode ray has absolutely no gas presemt
and a high voltage is applied what would you expect
to see?Why?

What is the definition and characteristics of cathode rays?

31) Prove that in general that it is incorrect to say

Square root of ( a xa - bxb) = a-b

Square root of ( axa + bxb) = a+b

Under what conditions are above statement true?

32) Prove that Lenzs law must be true by considering a frictionless horizontal surface,permanent magnet, light globe,a metal coil fixed in place but joined at both ends allowing current to flow..

33) Consider two different investments A and B

In A the principle is invested on the 1/2/18... the interest rate is 5% pa compounded annually.

In B the principle is invested on the same day 1/2/18...the interest rate is 10% pa compounded annually.

The Principle in A Is 3 times the principle in B.

a) A fter how many years is the worth of each investment the same in value?

b) After how many years is the interest earned on each investment the same value?

34)consider thefollowing

7 ÷ (2× square root of 5 - 4×square root of 3 + 3 × square root of 6)

Rationalise the denominator.
Check your answer using calculator.

35) is it possible to construct a circle through all
vertices of

a) any triangle
b) any quadrilateral

Give reasons

35) consider two hemispheres of different diameters
The sum of the diameters is square root of 17
The difference in diameters is square root of 11

Find exact difference of surface area of each hemisphere in terms of pi

36) consider a rectangle ABCD...the length of sides is a and b
the length of each side is increased by one metre to form rectangle EFGH

Find the differerence in area and perimeter of the rectangles


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.


$60 per hour for years 7-12 (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).


Joined TutorFinder on 13-Mar-2017 (updated profile on 24-Apr-2018)
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Tutor in Baulkham Hills


Calculus (Secondary)
Maths (Secondary)


Physics (Secondary)


Engineering (Secondary)


GAMSAT (Tertiary)

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HSC Mathematics all levels
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