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Free tutorials on estimation


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Discussing how to prepare for combined science


Will be going live tomorrow 8:30am for zimsec june exam tips


Zimsec Olevel past exam papers are available
June revisions


Tips on English writting

Writing speeches:

Introducing a guest speaker

Your school has invited someone to speak during the school assembly, and you have been asked to give a speech introducing the guest speaker. Write the speech, with the following points in mind.

● Who the person is
● What his/her achievements are
● What topic he/she will be talking about
● Why he/she has the credentials for the talk
You are to address the speech to a school of students, so be sure not to be overly formal. You may begin as follows:

Ladies and gentlemen. I'm very pleased to introduce a very special guest.....

Features of a speech

1) Should we use formal or informal language in an introduction speech?
It depends on the audience. You have to know your audience

If you are speaking to a group of school students, you should not be overly formal. A touch of informality with the use of contractions:
● I'm very pleased.
● Let's give Mr Ang a round of applause
This helps to tone down the seriousness of the occasion and helps both the speaker and the audience to relax.

2)Variety of sentence structures:

● Avoid overly long and complex sentence structures.
● Short and simple sentences help to convey a speech message more effectively.
Readers can always go back to a written text to re-read a sentence if he/she doesn't get the idea on the first reading. But if your audience misses what you say the first time, the cannot"rewind" your message; and if they cannot understand what you say most of the time, their attention may wander, and you may be left standing, talking to no one in particular. This does not mean. however that you should avoid long sentences altogether.
● Using long sentences to pave the way for a short sentence can give your speech a strong impact.

3) How to write a good introduction
● The occasional anecdote gives a slice of interesting news about your guest speaker is a good start to an introduction. Your guest speaker will appreciate the complimentary gesture, and your audience will look forward to the speech.


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Separating Solid/Liquid Mixtures:
A solution is formed when a solute is dissolved in a solvent.
Solute: This is a substance that dissolves in a solvent forming a solution
Solvent: This is a substance in which a solute dissolves forming a solution
Solution: A uniform mixture which is formed when a solute is dissolved
in a solvent.
Dilute Solution: A solution with a small amount of solute/dm3
Concentrated Solution: A solution with a large amount of solute/dm
. 3
Concentration: The amount of solute (in grams or moles) that can
dissolve in 1dm
Saturated Solution: A very concentrated solution with the maximum
amount of solute that dissolve in it already dissolved in it.
of a solvent.
If you leave a hot saturated solution to cool, crystals of the solute will
form. This is because as the temperature decreases the solvent can hold
less solute so excess will form in the form of crystals.
The rate of dissolving can be increased by:
• Increasing temperature
• More stirring
• Crushed solute (larger surface area)
Solubility: The maximum amount of solute that can dissolve in 100g of
water at a particular temperature.


good evening students please use whatsap for communication


Morning, have a blessed day.



Definition of numbers

Sets of numbers can be described in different ways:
natural numbers 1, 2, 3, 4, 5, …
positive integers +1, +2, +3, +4, +5, …

negative integers –1, –2, –3, –4, –5, …
square numbers 1, 4, 9, 16, 25, 36, …
triangle numbers 1, 3, 6, 10, 15, 21, …
The multiples of a number are the products of the
multiplication tables.
e.g. Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, …
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, …
The lowest common multiple (LCM) is the lowest
multiple which is common to all of the given
e.g. Common multiples of 3 and 4 are 12, 24, 36, …
The lowest common multiple is 12.
The factors of a number are the natural numbers
which divide exactly into that number (i.e. without a
e.g. Factors of 8 are 1, 2, 4 and 8.
Factors of 12 are 1, 2, 3, 4, 6 and 12.
The highest common factor (HCF) is the highest
factor which is common to all of the given numbers.
e.g. Common factors of 8 and 12 are 1, 2 and 4.
The highest common factor is 4.
Prime numbers
A prime number is a natural number with exactly
two factors (i.e. 1 and itself).
The following numbers have exactly two factors so
are prime numbers.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, …
Prime factors
A prime factor is a factor which is also prime.
All natural numbers can be written as a product of
prime factors.
e.g. 21 can be written as 3 ¥ 7 where 3 and 7 are
prime factors.
60 can be written as 2 ¥ 2 ¥ 3 ¥ 5 where 2, 3 and
5 are prime factors.
The prime factors of a number can be found by
successively rewriting the number as a product of
prime numbers in increasing order (i.e. 2, 3, 5, 7, 11,
13, 17, … etc.).
e.g. 84 = 2 ¥ 42 Writing 84 as 2 ¥ 42.
= 2 ¥ 2 ¥ 21 Writing 42 as 2 ¥ 21.
= 2 ¥ 2 ¥ 3 ¥ 7 Writing 21 as 3 ¥ 7.


We offer Online Zimsec revision for Primary and Secondary students . We assist students via whatsapp, video calling and emails. Contact Mr Makani on +263773288359 or +27710555294.


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