the
reference MATHS GRAMMAR PUNCTUATION PLANNING AN ESSAY the INTERNET CONVERSIONS
PHYSICS
pERIODIC table REVISION WELLBEING UK, EUROPE
WORLD MAPS
Being able to understand even basic maths is always going to be useful in life. We all use maths every day – in shopping, cooking, games… Just about everything we do. If you’re good at maths, you’re good at solving problems!
MATHS
Vertically Opposite Angles The opposite angles are equal when two lines cross l = l and
s = s
When a line crosses two parallel lines the angles in a ‘Z’ shape are equal l = l (called alternate angles)
The angles in an ‘F’ shape are equal when a line crosses two parallel lines l = l (called corresponding angles)
180o Angles a b
c
When a line crosses two parallel lines the o angles in a ‘C’ or ‘U’ shape total 180 o a + b = 180 (called interior angles)
e
d
When angles form a straight line they total 180 o c + d + e = 180
g 130
h
f
When lines make a triangle the angles o inside total 180 o f + g + h = 180
Algebra
o
110
o
When angles are around a point the angles total 360 Use subtraction to find the missing angle o o o 360 - 110 - 130 =
In algebra, letters are used to stand for numbers. It is important to understand the ‘shorthand’ used in algebra: a -a 3a a
ab 2ab a2 a3 3a2 (3a)2 3ab2
means means means means means means means means means means means
o
1 x a or 1a -1 x a or -1a 3 x a or (a + a + a) 1 a ÷ 3 or of a axb 2 x a x b or (ab + ab) axa axaxa 3 x a2 or 3 x a x a or (a2 + a2 + a2) 3a x 3a or 3 x a x 3 x a or 9a2 3 x ab2 or 3 x a x b x b or (ab2 + ab2 + ab2)
o
Areas Shape
Formula
Triangle:
base x height ÷ 2
1
A = b x h ÷ 2 or 2 x b x h
Rectangle:
length x width
A=lxw
Circle:
π x radius squared
A = πr2
Parallelogram:
base x perpendicular height
Trapezium:
1 2
A=bxh A=a+bxh
(sum of parallel sides) x height
π = 3.14159...
2
a w
h
h
Triangle
b
b
l
b
h
Rectangle
Parallelogram
Trapezium
Volumes Shape
Formula
Cuboid:
length x width x height
Prisms:
area of cross-section x length
h
V=lxwxh
l
l w
Cuboid
Prism
Circumference of a Circle rad
er umf ence
ius
rc
ci
C = π x diameter or C = 2 π r
dia
me
ter
Sequences Even numbers Odd numbers Square numbers Cube numbers Triangular numbers Prime numbers Square Numbers
1
4
9
2, 1, 1, 1, 1, 2,
4, 3, 4, 8, 3, 3,
6, 8, 10, 12, 14, 16, 18, 20... 5, 7, 9, 11, 13, 15, 17, 19, 21... 9, 16, 25, 36, 49, 64, 81, 100... 27, 64, 125, 216, 343, 512, 729... 6, 10, 15, 21, 28, 36, 45, 55... 5, 7, 11, 13, 17, 19, 23, 29, 31... Triangular Numbers
1
3
6
Grammar Noun
Let’s eat Mum! Let’s eat, Mum! what you write. If Write what you mean and mean quences may your punctuation is wrong, the conse be disastrous!
A noun is a word we use to name a person, a place, a thing or an idea Common noun = chair, pen, book Proper noun = France, Tuesday, Sarah (A proper noun will always have a capital letter)
Verb A verb is a ‘doing’ or ‘action’ word. The tense of the verb shows when the action happened e.g. When he broke the window, he felt unhappy. (Past tense)
Adjective An adjective describes a noun or a pronoun e.g. The tall lady reached for the green bottle.
Adverb This is a word used to modify (give further information about) a verb, another adverb or adjective (often ends in ‘ly’) e.g. The very large choir sang loudly.
Pronoun This is used in place of a noun e.g. He gave her a bar of soap. It was scented.
Determiner A word that goes before a noun to help specify which or how much or how many of the noun e.g. I go there every day. Some people have no sense.
Preposition A preposition identifies the relationship between one noun or pronoun and another e.g. The book was under the newspaper, on the table. The bird flew over the house.
Conjunction Conjunctions (also known as connectives) connect phrases to form longer sentences e.g. I tried so hard, but I could not do it. Tom broke the glass, the plate and the saucer.
Interjection This is an exclamation and is used to express feeling e.g. Ouch! I’ve stubbed my toe.
When we speak, we use changes in our voices to emphasise what we are saying. Punctuation does the same thing, only in writing.
PUNCTUATION
Capital Letter Used for the start of a sentence or for a proper noun e.g. Paris, Emily, This is my house.
Full Stop. Used to show that a sentence has finished e.g. My name is Jack.
Exclamation Mark! Used at the end of a sentence instead of a full stop to show shock, surprise, horror or pleasure e.g. Watch out!
Question Mark? Used instead of a full stop when the sentence asks a question e.g. Do you live here?
Listing Comma, Used in a list wherever you could use the words ‘and’ or ‘or’ instead. Note – you can only connect three or more complete sentences with listing commas e.g. Thomas likes apples, Daniel likes oranges and I like bananas.
Joining Comma, Used to join two complete sentences together. It must be followed by ‘and’, ‘but’, ‘while’ or ‘yet’ e.g. I like watching TV in the evening, but Jessica likes to read.
Apostrophe’ Used to show letters have been missed out or show possession of an object e.g. He’ll (he will) be back. The girl’s bicycle is blue.
(Parentheses) More commonly known as brackets, these are used when you want to insert an explanation into a sentence e.g. Chloe (the girl with the brown hair) is my best friend.
“Quotation Marks” These are used to show that a piece of text has been written or spoken by someone other than the writer e.g. “I will,” said John.
PLANNING AN ESSAY
THE TOPIC • What is your topic? • Are there any themes or guidelines you should follow?
INTRODUCTION • This is the first paragraph of your essay
PR EPAR ATION • What are you trying to achieve?
• It should set the scene for the rest of your essay • It should offer a brief answer for the set question which is developed in the essay
• Create a Mind Map to plan the content of your essay • Number your Mind Map branches what topic/ idea goes where?
• Make sure it captures the interest of the reader
• Remember to include the strongest points that support your ideas • Pick out key words - these should be developed in paragraphs of their own • Main points have sub points - these build depth into a paragraph • Use a dictionary and thesaurus to help vary words and develop ideas
CONCLUSION • The final paragraph should summarise your answer to the question set and not introduce any new information
MAIN BODY • Paragraphs develop the main ideas of your essay • New paragraphs start whenever you introduce a new idea, section or topic • Each paragraph should have at least two or three sentences • Make sure each paragraph links with the next
• Remember to draw a conclusion to your essay and findings • Ask yourself: has the reader gained something from your essay? • Include ideas for further action on the topic, if appropriate • Have you succeeded in writing all you wanted to say?
• Remember, there must be progression within the essay
You can get more help with
English
at www.bbc.co.uk/schools/gcsebitesize/english
Good internet skills will support learning in all the subjects you study. Just remember to stay focused when you’re using it and to carefully consider the information you find.
THE INTERNET
TOP 10 internet search tips with 6. Phrase search (“ “). If you want to find more specific
1. Every word matters. Think about every word you
results try searching for an exact phrase by putting it in speech marks.
type in the search box. Generally, the more words you use, the more likely you are to get exactly the information you are looking for.
7. Words you don’t want. You can tell Google which not to search for by putting a ‘-’ next to words 2. Words to leave out. Some common words are ignored words you don’t want to find. For example, if you’re looking so you don’t need to include them in your query. for information on the animal, 'jaguar –cars' will exclude any results that mention jaguar cars.
For example, ‘the’, ‘a’ and ‘for’. These are called stop words.
3. Capital letters don’t matter. Search is always case insensitive. Searching for 'tower of london' is the same as searching for 'Tower of London'. 4. Definitions. To see the meaning of a word or phrase, simply type the word ‘define’ then a space and then the word(s) you want defined.
5. Spell checker. Google automatically checks your
spelling. If it thinks you will get better results with a different spelling it will ask “Did you mean...?”. Click on the suggested spelling to search for that instead.
8. Calculations. You can use Google like a calculator.
Just enter the sum you want to do in the search box. For example, enter '27,334.56 x 21.3' and Google will give you the answer.
9. Unit conversions. You can use Google to convert
between different units of measurement. These could be height, weight, volume or many more. Just enter the conversion into the search box. For example, enter '5 feet in cm'.
10. I’m Feeling Lucky. The ‘I’m Feeling Lucky™’ button
takes you directly to the website of the first result. You will not see the other search results at all.
Internet Safety
The internet is a great tool for homework, research and chatting with friends. But with all of its advantages, it has disadvantages which can create dangers that you must be aware of:
• There is often a minimum age for those contributing to social networking sites (13 on Facebook, Bebo and MySpace, for example) • Don’t give out personal information and use a nickname in a chat room • Do not accept everything a person says online at face value • You should never meet up with someone you met online
NEED HELP ONLINE? www.THINKUKNOW.co.uk
get the inside info on how to stay safe whilst having fun on the internet.
For more info visit www.childline.org/explore/bullying or call them free on 0800 1111.
Cyberbullying If something worries or scares you in a chat room this can be reported to the chat room provider. Tell your parents, or someone you trust, then document everything by dates, times received and save the emails if you are being bullied or harassed. This can be reported to the police. Never respond to an internet bully. In the same way as you would be careful giving out your mobile number, be equally careful with your email address.
How can you tell if you are using a secure site? • There is a padlock icon in the bottom right hand corner of the page which means that the site is secure to send credit card details • Your web browser may tell you if you are entering a secure site • The letter ‘s’ may appear after the ‘http’ in the site address
CONVERSIONS & PHYSIC
S
do all that for you and more! stretch your mind? Physics can about the world we live in and Want to problem solve, find out
UNITS OF MEASUR EMENT
C ategory
Name
Length Mass Time Electric current Temperature Amount of substance Luminous intensity
metre kilogram second ampere kelvin mole candela
Abbrev. m kg s A K mol cd
MASS
Proton Neutron Electron
1 1 negligible
CHARGE +1 0 -1
ELECTR ICITY Charge (Q) = current (I) x time (t) Voltage (V) = energy (E) charge (Q) Potential dividers = voltage (V) out =
LENGTH
1 centimetre (cm) 1 metre (m) 1 kilometre (km) 1 inch (in) 1 yard (yd) 1 mile
= 10 mm = 100 cm = 1,000 m = 36 in = 1,760 yd
= 0.3937 in = 1.0936 yd = 0.6214 mile = 2.5400 cm = 0.9144 m = 1.6093 km
1 litre (l) 1 pint (pt) 1 gallon (gal)
voltage (V) in x Resistance 2 (Resistance 1 + Resistance) 2
voltage (V)
Resistance =
current (I)
Electrical Energy (E) = power (P) x time (t)
VOLUME & CAPACITY = 1,000 ml = 20 fl oz = 8 pt
= 1.76 pt = 0.5683 l = 4.546 l
= 1,000 mg = 1,000 g = 1,000 kg = 437.5 grains = 16 oz = 2,240 lb
= 0.0353 oz = 2.2046 lb = 0.9842 ton = 28.3495 g = 0.4536 kg = 1.0160 t
1.6093 0.6214
= km per hr = miles per hr
WEIGHT
Power (P) = current (I) x voltage (V)
R EFR ACTION Refractive Index (N) =
sin i sin r
Where i is the angle of incidence and r is the angle of refraction
1 gram (g) 1 kilogram (kg) 1 tonne (t) 1 ounce (oz) 1 pound (lb) 1 ton
VELOCITY miles per hr km per hr
PARTICLE
x x
TEMPER ATUR E
To change temperature given in Fahrenheit (F) to Celsius (C) Start with (F) - 32 x 5 ÷ 9 = (C)
To change temperature given in Celsius (C) to Fahrenheit (F) Start with (C) x 9 ÷ 5 + 32 = (F)
NEWTON’S LAWS OF MOTION 1st Law: An object will stay in a state of rest or in uniform motion unless acted on by an external force. 2nd Law: The force acting on a body is directly proportional to the mass of the body and its acceleration and is in the direction of the acceleration. Force = Mass x Acceleration 3rd Law: To every action force, there is an equal and opposite reaction force.
FORCE Moment = force x perpendicular distance of force from pivot Momentum = mass x velocity Change in momentum = impulse = force x time Pressure =
force area
Speed =
distance time
change in velocity
Acceleration =
time taken
ENERGY Gravitational Potential Energy (GPE) = mass(M) x gravity(G) x height(H) Kinetic Energy (KE) = 0.5 x mass(M) x velocity(V)² Change in Gravitational Potential Energy (GPE) = Change in Kinetic Energy (KE) (this is only true for a falling body with no air resistance) Efficiency =
or =
useful power output total power input useful energy output total energy input
x 100%
x 100%
Work done = force x distance moved in force’s own direction
Periodic table
KEY
The Periodic Table is all about trends in the properties of elements. Spotting trends and similarities in all your studies is a great life skill, helping you to build on what you know already.
REVISION success R evision is essential for exam Things to consider in each study session:
1 2 3
Objectives of study session The resources you need e.g. notes, books, internet Where to study – the library or at home?
Being organised puts you in control of your life. You are the only person who can organise it!
1
Get started in plenty of time and, to give your study a focus, create a revision plan, taking into account all your commitments like playing sports or working part-time.
2
Top tips
Find a warm, comfortable place to study that has good lighting and where you will not be distracted.
3
to r evision success
5
4 To keep your recall ability at its peak, study for no longer than 45 minutes at a time, and then allow yourself a break of 5-10 minutes.
Rather than just trying to memorise your notes by writing them out over and over, make your revision active by drawing Mind Maps and making charts.
Review past exam papers to get an overview of how the questions are structured and to give yourself some practice at writing your answers.
R evision Timetable Use the example below to set up your own revision timetable. Remember, everyone’s schedules are different so think about what will work best for you.
day
2
session
1 45
mins
day
3
session
1 45
mins
session
2 45
mins
session
2 45
mins
session
2 45
mins
session
3 45
mins
15
m i n re v ie w
session
3 45
mins
15
m i n re v ie w
session
3 45
mins
15
m i n re v ie w
r
e r b
k
mins
a
1 45
e
session
b
1
a
day
k
Don’t forget to include a reward for yourself at the end of each day!
CONTINUE EACH DAY FROM NOW ON IN THE SAME WAY day
6
day off
-
day
7
review the week ’ s revision
day
28
review the month ’ s revision
give yourself a reward
- 15
mins per subject
- 15
You can get more help with
mins per subject
Revision at
www.academictips.co.uk
NG
I WELL-BE
Being comfortable, healthy and happy is what everyone wants in life. Having this sense of well-being can help us to build the life we want and achieve our goals. Yet well-being isn’t a given – it’s something we have to work at. Well-being has different features. There’s physical well-being (being healthy and fit, eating good food and taking exercise, not smoking or drinking to excess), emotional well-being (feeling balanced and being able to express emotions appropriately), mental and intellectual well-being (using your mind and intellect, thinking critically, being interested in learning) and spiritual well-being (having a sense of awe and wonder and an awareness that life extends beyond the material world regardless of your religious beliefs). But how can you make sure you give time to each feature of overall well-being?
Here are just some ideas:
Physical well-being Getting at least five fruits and vegetables a day, drinking plenty of water, not eating too much saturated fat and taking a little exercise each day will boost your physical well-being.
Emotional well-being Getting into the habit of talking to a trusted friend or family member about how you feel will help you express your emotions in a healthy way.
Mental and intellectual well-being Get your brain fit for learning by getting plenty of sleep, by being switched on in lessons and by having a positive attitude to studying. The more you use your brain, the more you will want to use it. Mental well-being is about life-long learning as much as anything!
Spiritual well-being It doesn’t matter whether you are religious or regularly go to religious services or not, you can still look after your spiritual well-being by having an awareness that you are a part of a bigger whole. It’s about the connection you feel to others and to life itself, your philosophy of life and the sense of hope you feel (among others). Taking part in music, singing, being in nature, having an inner sense of peace and building great relationships with others can all support our spiritual well-being.
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© Oxford Cartographers +44 (0) 1865 882 884 E & OE
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0°
© Oxford Cartographers E&OE +44 (0) 1865 882 884 info@oxfordcartographers.com Tórshavn
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Knowing how to use maps is an incredibly important life skill. Not only can they help us find our way, but they can also tell us about terrain and political borders, about history and how the world is changing.
80º
Arctic Circle RUSSIA
180º
Beaufort
Alaska (U.S.A.)
160º
Sea
140º 120º
100º
C A N A D A
80º
60º 40º
(Denmark)
(Greenland)
Kalaallit Nunaat
N O RT H
ait is Str
20º 0º
Svalbard (Norway)
Greenland Sea AY
20º
W
40º
D
80º
O C E A N
Kara Sea
We s t Siberian Plain
100º
120º
Central Siberian Plateau
sp Ca
ea ian S
AN
d
Se
140º
VI
ETN
SINGAPORE
BRUNEI
AM
Su
Jakarta
a
I n te r n ation al D at e Line
120º
140º
160º
he
rs
kiy
e
180º
nge
Ko ly m a Plain
Ra
Gy
Sea of Okhotsk
da
Sakhalin
ang nR
e
Ana
dyr
Ran
ge
80º
60º
Bering Sea
PACIFIC
K IRIBATI
MARSHALL ISLANDS
OCEAN
MICRO N ES IA
ISLANDS
VANUATU
Port Moresby
PAPUA NEW GUINEA SOLOMON
Coral Sea
New Caledonia (Fr.)
MIDNIGHT
20º
0º
20º
FIJI
40º
80º
60º
Wellington NEW ZEALAND
Ta s m a n Sea
Canberra
Tasmania
97089 Modified Gall Projection
180º
P.M.
© Oxford Cartographers E&OE +44 (0) 1865 882 884 info@oxfordcartographers.com
160º
Gt.Vi ctor ia Des ert
AUSTRALIA
Grea t Sa ndy Des ert
EAST TIMOR
Bandar Sea
IN D O NE S I A
tra ma
c
on a l D at e Line
a
n d e s
100º
I nt e rn at i
Re
A RU PE
i
Ce l e b e s Sea
NEPAL Kathmandu BHUTAN Taipei BANG. Dhaka MYANMAR TAIWAN Hanoi (BURMA) INDIA LAOS Naypyidaw Vientiane S o u t h Manila Philippine THAILAND C h i na S e a PHILIPPINES BangkokCAMB. Sea Phnom Penh
JAPAN Tokyo
N. KOREA Pyongyang Seoul S. KOREA
g Stanovoy Ran
Laptev Sea
C H I N A
Ulan Bator MONGOLIA G o b i Beijing (Peking)
Lake Baikal
R U S S I A Astana Aral Sea
K A Z A K H STA N
Tehran IRAN
80º
t
SOUTHERN OCEAN
Kerguelen (Fr.)
Putrajaya MALAYSIA
Bay of Bengal
SRI
OCEAN
IND IAN
MALDIVES
Sea
New Delhi
UZ B E K I Tashkent T S U KYRGYZSTAN T AZER. RKME NI TAJIKISTAN ST A Ashgabat N TAN S NI Kabul Islamabad
I R AQ JORDAN
T KUWAIT IS AK QATAR Abu DhabiP U.A.E. Muscat
A R A BI A
c
Colombo LANKA
Arabian
SEYCHELLES
60º
Réunion (Fr.)
COMOROS
DEM. RWANDA Nairobi REP. OF BURUNDI Dodoma Kinshasa CONGO TANZANIA
a 40º
C
ISRAEL
Lake Nasser
EGYPT SAU D I Riyadh
Cairo
60º
Barents Sea
A RC T I C
North Cape
L I BYA
See Europe Map
t
Sahara Desert
A LG E R I A
MOROCCO s M a Atl
ICELAND Reykjavik
N LA
Canary Is. (Sp.)
Western Sahara Nouakchott
CAPE
FIN
Hudson Bay
Dav
60º Bering Sea Gulf of Alaska
OCEAN
Azores (Port.)
AT L A N T I C
Newfoundland
Washington D.C.
Bermuda (U.K.)
Nassau BAHAMAS CUBA
Luanda
Brazzaville CABINDA (ANGOLA)
t
Maputo Tshwane SWAZILAND (Pretoria) SOUTH LESOTHO AFRICA
Cape of Good Hope
P.M.
20º
n
r
Antananarivo MADAGASCAR MAURITIUS
MALAWI ANGOLA Lilongwe ZAMBIA Lusaka Harare ZIMB. NAMIBIA BOTSWANA Windhoek Gaborone
A
at k a
N DE
R
NO
Khartoum ERITREA M A L I NIGER VERDE SENEGAL YEMEN Niamey CHAD SUDAN Asmara San’a’ GAMBIA BURKINA DJIBOUTI FASO GUINEA N’Djamena NIGERIA BISSAU GUINEA Addis Ababa SIERRA LEONE CÔTE D' CEN. Abuja IVOIRE ETHIOPIA AF. REP. LIBERIA CAM. Accra Bangui UGANDA S Mogadishu EQ. GUI. Kampala KENYA GABON
Ascension (U.K.)
SOUTH
St Helena (U.K.)
0º
NOON
Tristan da Cunha (U.K.)
AT L A N T I C
20º
A.M.
OCEAN South Georgia (U.K.)
40º
N A
HA
AF G
The Ottawa Great Lakes
Havana
U N I T E D S TAT E S OF AMERICA
M E XICO
Caracas TRINIDAD & TOBAGO VENEZUELA GUYANA SUR. French Guiana
BRAZIL Brasilia
URUGUAY Montevideo
60º
Falkland Islands (U.K.)
Buenos Aires
Cape Horn
80º
Asunción
PARAGUAY
La Paz BOLIVIA
Bogotá COLOMBIA Quito ECUADOR
COSTA RICA PANAMA
HAITI DOM. REP. Mexico City BELIZE JAMAICA GUATEMALA HONDURAS Caribbean EL SALVADOR NICARAGUA Sea
Galapagos Is. (Ecu.)
Lima
Santiago
100º
O
40º
Hawaii (U.S.A.)
P A C I F I C
O C E A N
Easter Is. (Chile)
120º
AL
M
O
20º
KI RI BATI
French Polynesia
140º
U ral M o u n t a i n s AN
M
IA RIT AN
SW E
O
NG
CO
Tropic of Cancer
Equator
SAMOA
Cook Is. (N.Z.)
160º
E
MB IQ U
MOZ A
0º
20º
A.M.
180º
IA
s. GHANA TOG BENIO N
Ka m ch
. . D i i n g Ra vid
Gt
Tropic of Capricorn
40º
60º
MIDNIGHT
Antarctic Circle
80º
H I L E ARGE NTI NA C
MAU
cky Ro ntain s u Mo
WORLD