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A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor

ARITHMETIC & GEOMETRIC SERIES

Question 1

A set consists of four integers {24 , a , b , 108} such that 24 < a < b < 108. The first three integers are consecutive terms of an arithmetic progression and the last three integers are consecutive terms of a geometric progression. Find the integers a and b. Ans a=48 b=72 Question 2 The fifth, tenth and twentieth terms of a convergent geometric progression, G, are the first three consecutive terms of an arithmetic progression, A. (i) Determine the common ratio of G. [0.908] Given that the first term of G is 2, (ii) evaluate the sum to infinity for G. [21.8] (iii) find the sum of the first 10 odd-numbered terms in A. [- 33.2] Question 3 The second, fifth and tenth terms of an arithmetic progression are consecutive terms of a geometric progression. The eighth term of the arithmetic progression is 6. Find the sum of the first 12 terms of the arithmetic progression. [432/7] Question 4 A geometric progression and an arithmetic progression has the common first term, a. The sum of the first three terms of the geometric progression is 19/27 of the sum to infinity. Find the common ratio, r. [2/3] The second and third terms of the geometric progression are increasing consecutive terms of the arithmetic progression respectively. Find the sum of the 1st 55 terms of the arithmetic progression in terms of a. [ −275a ] Question 5 An arithmetic series A has first term a and a geometric series G has first term b. The common difference of A is four times the first term of G and the common ratio of G is twice the first term of A. Each term of A is added to the corresponding term of G to form the terms of a third series S. Given that the first two terms of S are 1/2 and 0 respectively, find the value of a.[-1] Please contact Angie @96790479 or Mr Ong @98639633 if you need help in Mathematics

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O-Level Singapore/O-Level Combine Chemistry and Physics Tuition/Physics Tutor

Kinetic Particle Theory – Concise Notes

1.1 State of Matter

Solids:
• Have a fixed shape, fixed volume; cannot be compressed.
• Particles vibrate and rotate about fixed positions.

Liquids:
• Have no fixed shape but have fixed volumes; cannot be compressed.
• Particles move.

Gases:
• Have no fixed shape, no fixed volume; can be compressed easily.
• Particles move about rapidly.

1.2 Kinetic Particle Theory and the Changes of State
• The kinetic particle theory states that (a) all matter is made up of tiny particles, and (b) all particles are in constant, random motion.
• Particles have kinetic energy.
• When matter is heated or cooled, heat energy is taken in or given out. This causes the kinetic energy of the particles to change, leading to a change of state.

1.3 Diffusion
• Diffusion provides evidence that the particles in gases and liquids are constantly moving.
• Examples of diffusion include: the spreading of the smell of perfume, the spreading of bromine in a gas jar of air, and the spreading of potassium manganate(VII) in water.
• The lower the molecular mass of the particles, the faster the rate of diffusion.
• The higher the temperature, the faster the rate of diffusion.

If you need help in the O level Chemistry, please contact Angie @96790479 or Mr Ong 98639633

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O-Level Singapore/O-Level Combine Chemistry and Physics Tuition/Physics Tutor

Chapter 2 Kinematics

Exam Tip 1
An example to show non-zero distance but zero displacement: An object is under a circular motion. It completes one revolution and goes back to the starting point. The distance travelled is the circumference of the circular path but the displacement is zero.

Exam Tip 2
An example of constant speed but changing velocity: When an object is under circular motion, the direction of motion changes with time. Its speed can be the same but the displacement keeps changing when the object is moving along the circle.

Exam Tip 3
A misconception for acceleration is that many students think that acceleration must be zero if an object is at rest. This is not always true.

A case of zero velocity but non-zero acceleration: When an object is thrown upwards, it is momentarily at rest at the highest point. The velocity is zero. However it is a free falling body as gravity is the only force acting on it.

For free falling body, the acceleration is always 10 m/s^2 (if there is no air resistance) no matter whether it is moving downwards, upwards or at rest momentarily

If you need help in the above topics, please contact Angie @96790479 or Mr Ong @98639633

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O-Level Singapore/O-Level/Pure Physics Tuition/Physics Tutor

Chapter 2 Kinematics Part 1

Exam Tip 1
An example to show non-zero distance but zero displacement: An object is under a circular motion. It completes one revolution and goes back to the starting point. The distance travelled is the circumference of the circular path but the displacement is zero.

Exam Tip 2
An example of constant speed but changing velocity: When an object is under circular motion, the direction of motion changes with time. Its speed can be the same but the displacement keeps changing when the object is moving along the circle.

Exam Tip 3
A misconception for acceleration is that many students think that acceleration must be zero if an object is at rest. This is not always true.

A case of zero velocity but non-zero acceleration: When an object is thrown upwards, it is momentarily at rest at the highest point. The velocity is zero. However it is a free falling body as gravity is the only force acting on it.

For free falling body, the acceleration is always 10 m/s^2 (if there is no air resistance) no matter whether it is moving downwards, upwards or at rest momentarily

If you need help in the above topics, please contact Angie @96790479 or Mr Ong @98639633

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O Level Chemistry Tuition Singapore/Chemistry O Level Tuition/Tutor

Kinetic Particle Theory – Concise Notes

1.1 State of Matter

Solids:
• Have a fixed shape, fixed volume; cannot be compressed.
• Particles vibrate and rotate about fixed positions.

Liquids:
• Have no fixed shape but have fixed volumes; cannot be compressed.
• Particles move.

Gases:
• Have no fixed shape, no fixed volume; can be compressed easily.
• Particles move about rapidly.

1.2 Kinetic Particle Theory and the Changes of State
• The kinetic particle theory states that
(a) all matter is made up of tiny particles, and
(b) all particles are in constant, random motion.
• Particles have kinetic energy.
• When matter is heated or cooled, heat energy is taken in or given out. This causes the kinetic energy of the particles to change, leading to a change of state.

1.3 Diffusion
• Diffusion provides evidence that the particles in gases and liquids are constantly moving.
• Examples of diffusion include: the spreading of the smell of perfume, the spreading of bromine in a gas jar of air, and the spreading of potassium manganate(VII) in water.
• The lower the molecular mass of the particles, the faster the rate of diffusion.
• The higher the temperature, the faster the rate of diffusion.

If you need help in the O level Chemistry, please contact Angie @96790479 or Mr Ong 98639633

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O-Level Additional Mathematics Tuition Singapore

Exam Questions

Question 1

Find the range of values of x for which 1+ x^2 > – (7x – x^2)/3 .
Hence or otherwise, find the minimum value of y if
y = 1 + x^2 + (7x – x^2)/3

Question 2

A polynomial, f(x), of degree 4 has a quadratic factor of x^2 — x+ 2 and a linear factor of (x + 3). Given that f(x) leaves a remainder of 8 and —24 when divided by (x — 1) and (x+ 1) respectively, find

(i) the remaining factor of f(x),

(ii) the number of real roots of the equation f(x) = 0, justifying
your answer,

(iii) the remainder when f(x) is divided by x.

For exam based question with full worked solution, please contact Mr Ong
@98639633 0r Angie @96790479

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O Level E Maths Tuition Singapore/Tuition O Level E Maths/Tutor

Fractions

1. Proper fractions: The numerator is smaller than the denominator. A proper fraction is part of a whole, so it is smaller than 1.

e.g. 3/5 and 5/7.

2. Improper fractions: The numerator is greater than or equal to the denominator. The fraction is greater than or equal to 1.

e.g. 5/3 7/7 and 13/5.

3. Mixed numbers: Numbers that contain a whole number part and a proper fraction part.

e.g. 1 1/3 and 6 2/5.

4. Equivalent fractions: Fractions having the same value but are in different form. When the numerator and denominator of a fraction are multiplied or divided by the same non¬zero number, we get an equivalent fraction.

e.g. 1/3 = 2/6 = 5/15

5. A fraction is in its lowest terms or simplest form when its numerator and denominator has no more common factor other than 1.

e.g. 1/5 is reduced to lowest terms but 2/10 not.

For Exam based questions with full worked solution. Please contact Mr Ong @98639633 or Angie @96790479

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A-Level Chemistry Tuition Singapore/H2 Chemistry Tuition/JC Chemistry Tutor

2015 A Level Chemistry Schedule

J1 H2 FRI 7.30pm – 9.30pm

J1 H1 FRI 7.30pm – 9.30pm

J1 H2 SAT 1.30pm – 3.30pm

J1 H2 SUN 12pm – 2pm

J2 H2 TUE 5.30pm – 7.30pm

J2 H2 FRI 7.30pm – 9.30pm

J2 H2 SAT 3.30pm – 5.30pm

J2 H1 SAT 3.30pm – 5.30pm

J2 H2 SUN 2pm – 4pm

Please contact Angie @ 96790479 or Mr Ong @ 98639633 if you need help in Chemistry

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A Level GP/General Paper Tuition Singapore

2015 A level General Paper

J1/J2 H1 THU 7.30pm – 9.30pm

J1/J2 H1 SUN 4pm – 6pm

Please contact Angie @ 96790479 or Mr Ong @ 98639633 if you need help in General paper

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A-Level Biology Tuition Singapore/H2 Biology Tuition/JC Biology Tutor

2015 A level Biology Schedule

J1 H2 SAT 3.30pm – 5.30pm

J2 H2 SAT 5.30pm – 7.30pm

Please contact Angie @ 96790479 or Mr Ong @ 98639633 if you need help in Biology

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A-Level Physics Tuition Singapore/H2 Physics Tuition/JC Physics Tutor

2015 A level Physics Schedule

J1 H2 THU 7.30pm – 9.30pm

J1 H2 SAT 9am – 11am

J1 H1 SAT 9am – 11am

J1 H2 SUN 2pm – 4pm

J2 H2 TUE 7.30pm – 9.30pm

J2 H1 WED 5.30pm – 7.30pm

J2 H2 SAT 7.30pm – 9.30pm

J2 H2 SUN 12pm – 2pm

Please contact Angie @ 96790479 or Mr Ong @ 98639633 if you need help in Physics

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A-Level Economics Tuition Singapore/H2/H1 Economics Tuition

J1 H2 SAT 7.30pm – 9.30pm

J1 H1 SAT 7.30pm – 9.30pm

J2 H2 SAT 9am – 11am

J2 H2 SAT 5.30pm – 7.30pm

J2 H1 SAT 5.30pm – 7.30pm

J2 H2 SUN 9am – 11am

J2 H1 SUN 9am – 11am

Please contact Angie @ 96790479 or Mr Ong @ 98639633 if you need help in Economics

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A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor

2015 A level Mathematics Schedule

J1 H2 Thu 5.30pm – 7.30pm

J1 H1 FRI 5.30pm – 7.30pm

J1 H2 SAT 11am – 1pm

J1 H2 SUN 4pm – 6pm

J2 H2 MON 7.30pm – 9.30pm

J2 H1 MON 5.30pm – 7.30pm

J2 H2 SAT 5.30pm – 7.30pm

J2 H2 SUN 10am – 12pm

Please contact Angie @96790479 or Mr Ong @98639633 if you need help in Mathematics

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O-Level Singapore/O-Level/Pure Physics Tuition/Physics Tutor

2015 Schedule – Physics

S3 1.5 hrs SAT 10.30am – 12pm

S3 1.5 hrs SAT 2pm – 3.30pm

S3 1.5 hrs SUN 1pm – 2.30pm

S4 1.5 hrs FRI 4.30pm – 6pm

S4 1.5 hrs SAT 2pm – 3.30pm

S4 1.5 hrs SUN 10.30am – 12pm

Please contact Angie @ 96790479 or Mr Ong @ 98639633

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O Level Chemistry Tuition Singapore/Chemistry O Level Tuition/Tutor

2015 Schedule – Chemistry

S3 1.5 hrs SAT 9pm – 10.30pm

S3 1.5 hrs SAT 12.30pm – 2pm

S3 1.5 hrs SUN 12.30pm – 2pm

S4 2 hrs FRI 5pm – 7pm

S4 1.5 hrs SAT 12.30pm – 2pm

S4 1.5 hrs SUN 9am – 10.30pm

Please contact Angie @ 96790479 or Mr Ong @ 98639633

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