This document provides information about a book that is designed to help students achieve their best possible grade in Edexcel GCE Mathematics Core 1 and Core 2 units. It separates the material into the two units and includes features like key points, worked examples, exercises and revision questions to aid learning. At the end, it provides full solutions, a glossary and list of formulae to support student understanding and exam preparation.
English for Writing Research Papers by Adrian WallworkSina Radfar
Publishing your research in an international journal is key to your success in academia. This guide is based on a study of referees' reports and letters from journal editors on reasons why papers written by non-native researchers are rejected due to problems with English usage. It draws on English-related errors from around 5000 papers written by non-native authors, 500 abstracts by PhD students, and over 1000 hours of teaching researchers how to write and present research papers.
With easy-to-follow rules and tips, and with examples taken from published and unpublished papers, you will learn how to:
- prepare and structure a manuscript
- increase readability and reduce the number of mistakes you make in English by
writing concisely, with no redundancy and no ambiguity
- plan and organize your paper, and structure each paragraph and each sentence so
that the reader can easily follow the logical build-up towards various conclusions
- write a title and an abstract that will attract attention and be read
- decide what to include in the various parts of the paper (Introduction, Methodology,
Discussion etc)
- select from over 700 useful phrases
- highlight your claims and contribution
- avoid plagiarism and make it 100% clear whether you are referring to your own work
or someone else’s
- choose the correct tenses and style (active or passive)
123 essays - The Writing Center.. 123 Essay Help Com, 123 essay help me. 123 essay help free. Essay Writer 123 - Paper Writing Service Which Keeps Your Academic .... 123 essay help me review my - autravanastenerifees.x.fc2.com. Essay No. 1. Custom Admission Essay Dnp — Reflection on the Doctor of Nursing .... Eng 121 week 1 assignment practice essay / eng121mart.com by nakskro .... What You need to know About 123 Essay – Alder Creek Kennel. Addictionary. Essay 123 help - College Homework Help and Online Tutoring.. #1 123 essay help. Homework Help Sites.. essay examples: importance of education essay. Buy essays 123 - 123 term papers. essay examples: hero definition essay. (DOC) Engl 123 Essay 2 | cin le - Academia.edu. Free essays 123 by Willoughby Amanda - Issuu. Help essay 123 - College Homework Help and Online Tutoring.. ENG 123 Mod 7-3 Essay Project 2 - 1 Modular 7: Essay-Technology in the ....
English for Writing Research Papers by Adrian WallworkSina Radfar
Publishing your research in an international journal is key to your success in academia. This guide is based on a study of referees' reports and letters from journal editors on reasons why papers written by non-native researchers are rejected due to problems with English usage. It draws on English-related errors from around 5000 papers written by non-native authors, 500 abstracts by PhD students, and over 1000 hours of teaching researchers how to write and present research papers.
With easy-to-follow rules and tips, and with examples taken from published and unpublished papers, you will learn how to:
- prepare and structure a manuscript
- increase readability and reduce the number of mistakes you make in English by
writing concisely, with no redundancy and no ambiguity
- plan and organize your paper, and structure each paragraph and each sentence so
that the reader can easily follow the logical build-up towards various conclusions
- write a title and an abstract that will attract attention and be read
- decide what to include in the various parts of the paper (Introduction, Methodology,
Discussion etc)
- select from over 700 useful phrases
- highlight your claims and contribution
- avoid plagiarism and make it 100% clear whether you are referring to your own work
or someone else’s
- choose the correct tenses and style (active or passive)
123 essays - The Writing Center.. 123 Essay Help Com, 123 essay help me. 123 essay help free. Essay Writer 123 - Paper Writing Service Which Keeps Your Academic .... 123 essay help me review my - autravanastenerifees.x.fc2.com. Essay No. 1. Custom Admission Essay Dnp — Reflection on the Doctor of Nursing .... Eng 121 week 1 assignment practice essay / eng121mart.com by nakskro .... What You need to know About 123 Essay – Alder Creek Kennel. Addictionary. Essay 123 help - College Homework Help and Online Tutoring.. #1 123 essay help. Homework Help Sites.. essay examples: importance of education essay. Buy essays 123 - 123 term papers. essay examples: hero definition essay. (DOC) Engl 123 Essay 2 | cin le - Academia.edu. Free essays 123 by Willoughby Amanda - Issuu. Help essay 123 - College Homework Help and Online Tutoring.. ENG 123 Mod 7-3 Essay Project 2 - 1 Modular 7: Essay-Technology in the ....
1 Assessment feedback TOUR 1001 Understanding Tr.docxmercysuttle
1
Assessment feedback
TOUR 1001 Understanding Travel and Tourism Assignment 2 – Summary of article
Length – 2xA4 pages using font 12 Times New Roman (Single line spacing). Due date – Assignment 2, Friday 3
rd
May by 11p.m.
Up to 5% of the marks will be deducted from final mark for incorrect spelling and/or grammar and for failure to follow guidelines for title page. Late
assignments will receive a 10% penalty per day late.
Fail 2 Fail 1 Pass 2 Pass 1 Credit Distinction High Distinction
Understanding of
article content. (75%)
Minimal understanding
of content of the set
article, indicated in
incorrect statements
and excessive
quotation.
Major aspects of the
article completely
omitted.
Some
understanding of
content of the set
article.
No explanation of
theoretical
framework and
methodology used
in the article.
Failure to
discriminate
between
important and
peripheral aspects.
Too much
quotation.
Most major
aspects
distinguished
from peripheral
aspects.
Excessive use of
quotation, thus
avoiding
explanation.
Major aspects of
the article
identified and
explained.
Some unnecessary
use of quotation,
thus avoiding
explanation.
Major aspects of
the content of the
article identified.
Unnecessary
quotation avoided.
Clear demonstration of
understanding of
content and purpose of
the article, shown in the
links made between
examples and
theoretical framework.
Unnecessary quotation
avoided.
Thorough understanding
of key aspects of the
article, its content and
purpose, shown in the
links made between
examples and
theoretical framework.
Individuality shown in
organisation of the
content of the summary
while remaining true to
the intent of the
content.
Adherence to
summarising
guidelines outlined in
relevant Information
sheet. (25%)
Complete failure to
adhere to guidelines for
summarising an article.
Some adherence
to guidelines.
Errors in
formatting article
reference details.
Failure to provide
page numbers for
Some
adherence to
guidelines.
Formatting of
reference
details error
free.
Page numbers
Complete
adherence to
referencing
guidelines.
Ideas grouped
successfully in
most cases.
Improvement
Complete
adherence to
referencing
guidelines.
Ideas grouped
successfully in well-
constructed
paragraphs.
Complete adherence to
referencing guidelines.
Ideas appropriately
grouped in well-
constructed paragraphs.
Concise words and other
written expressions well
Complete adherence to
referencing guidelines.
Concise written
expression. Ideas
appropriately grouped
in well-constructed
paragraphs.
Demonstrated
2
quotations.
Failure to group
ideas in well-
constru ...
A work in progress - drafts to be updated and completed later. Practice with the the assessment statements from the Core component of the course that require diagrams.
Georgia Common Core Coach, CCGPS Edition, Composition, Level ITriumphLearningNY
Composition exercises support students in constructing more complex, sophisticated writing, as required by the Common Core Georgia Performance Standards.
The first two lessons of Georgia Common Core Coach, CCGPS Edition, Composition provide the foundation for the remaining lessons. With the first lesson walking students through the writing process from start to finish, and the second lesson taking them through the entire research process. The second unit of the book offers lessons on specific writing types that are outlined in the Common Core Georgia Performance Standards.
1 Assessment feedback TOUR 1001 Understanding Tr.docxmercysuttle
1
Assessment feedback
TOUR 1001 Understanding Travel and Tourism Assignment 2 – Summary of article
Length – 2xA4 pages using font 12 Times New Roman (Single line spacing). Due date – Assignment 2, Friday 3
rd
May by 11p.m.
Up to 5% of the marks will be deducted from final mark for incorrect spelling and/or grammar and for failure to follow guidelines for title page. Late
assignments will receive a 10% penalty per day late.
Fail 2 Fail 1 Pass 2 Pass 1 Credit Distinction High Distinction
Understanding of
article content. (75%)
Minimal understanding
of content of the set
article, indicated in
incorrect statements
and excessive
quotation.
Major aspects of the
article completely
omitted.
Some
understanding of
content of the set
article.
No explanation of
theoretical
framework and
methodology used
in the article.
Failure to
discriminate
between
important and
peripheral aspects.
Too much
quotation.
Most major
aspects
distinguished
from peripheral
aspects.
Excessive use of
quotation, thus
avoiding
explanation.
Major aspects of
the article
identified and
explained.
Some unnecessary
use of quotation,
thus avoiding
explanation.
Major aspects of
the content of the
article identified.
Unnecessary
quotation avoided.
Clear demonstration of
understanding of
content and purpose of
the article, shown in the
links made between
examples and
theoretical framework.
Unnecessary quotation
avoided.
Thorough understanding
of key aspects of the
article, its content and
purpose, shown in the
links made between
examples and
theoretical framework.
Individuality shown in
organisation of the
content of the summary
while remaining true to
the intent of the
content.
Adherence to
summarising
guidelines outlined in
relevant Information
sheet. (25%)
Complete failure to
adhere to guidelines for
summarising an article.
Some adherence
to guidelines.
Errors in
formatting article
reference details.
Failure to provide
page numbers for
Some
adherence to
guidelines.
Formatting of
reference
details error
free.
Page numbers
Complete
adherence to
referencing
guidelines.
Ideas grouped
successfully in
most cases.
Improvement
Complete
adherence to
referencing
guidelines.
Ideas grouped
successfully in well-
constructed
paragraphs.
Complete adherence to
referencing guidelines.
Ideas appropriately
grouped in well-
constructed paragraphs.
Concise words and other
written expressions well
Complete adherence to
referencing guidelines.
Concise written
expression. Ideas
appropriately grouped
in well-constructed
paragraphs.
Demonstrated
2
quotations.
Failure to group
ideas in well-
constru ...
A work in progress - drafts to be updated and completed later. Practice with the the assessment statements from the Core component of the course that require diagrams.
Georgia Common Core Coach, CCGPS Edition, Composition, Level ITriumphLearningNY
Composition exercises support students in constructing more complex, sophisticated writing, as required by the Common Core Georgia Performance Standards.
The first two lessons of Georgia Common Core Coach, CCGPS Edition, Composition provide the foundation for the remaining lessons. With the first lesson walking students through the writing process from start to finish, and the second lesson taking them through the entire research process. The second unit of the book offers lessons on specific writing types that are outlined in the Common Core Georgia Performance Standards.
5. 1 Indices and surds
Test this rule for yourself by using
1.1 Integer indices Generally, for any number a, a0 = 1 different values of a.
In the quantity 23, the base is 2 and the index is 3. index
23
23 is evaluated as 23 = 2 ´ 2 ´ 2 = 8 base Consider
3
33 ÷ 35 = 35 = 3×3×3 = 1 = 1
3 3 × 3 × 3 × 3 × 3 3 × 3 32
Generally, for any number a, the quantity an index From the general rule for dividing indices you know that
has base a and index n. an 33 ¸ 35 = 33-5 = 3-2
base
an is evaluated as an = a ´ a ´ . . . ´ a
Hence it follows that 3−2 = 12
3
n times
There are rules to help you perform arithmetic using indices. Indices is the plural of index.
A negative index is equivalent to
Generally, for any number a, a −n = 1n
− a positive reciprocal index.
a
Consider 23 ´ 22 = (2 ´ 2 ´ 2) ´ (2 ´ 2) = 25 5=3+2
3 ´ 33 = 3 ´ (3 ´ 3 ´ 3) = 34 4=1+3
5´ 53 × 52 = 5 ´ (5 ´ 5 ´ 5) ´ (5 ´ 5) = 56 6=1+3+2
Consider (32)3 = (32) ´ (32) ´ (32)
= (3 ´ 3) ´ (3 ´ 3) ´ (3 ´ 3)
This result is true for = 36 6=2´3
Generally, for any number a, am × an = am+n any numbers m and n.
C1
C1
Generally, for any number a, (am)n = am´n Test this rule for yourself by using
2 ÷ 2 = 22 = 2 × 2 × 2 × 2 × 2 = 2 × 2 × 2 = 23
5
5 2
Consider 3=5-2 different values of a, m and n.
2 2×2
54 ÷ 22 = 52 = 5 × 5 × 5 × 5 = 5 × 5 = 52
4
2=4-2
You can use the laws of indices to evaluate numerical quantities.
5 5×5
EXAMPLE 1
Simplify
m n m- n
This result is true for
Generally, for any number a, a ¸ a = a any numbers m and n. a 32 ´ 33
Some important results follow from these two index laws. b 27 ¸ 24
••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
a Use am ´ an = a m+n: 32 ´ 33 = 32+3 a = 3, m = 2 and n = 3
2 3
2×2×2 = 35
Consider 23 ¸ 23 = 3 = 2×2×2 =1
2
b Use am ¸ an = a m-n: 27 ¸ 24 = 27-4 a = 2, m = 7 and n = 4
From the general rule for dividing indices you know that = 23
23 ¸ 23 = 23-3 = 20 Using am ¸ an = am-n
with a = 2, m = 3 and n = 3.
Hence it follows that 20 = 1
2 3
6. 1 Indices and surds 1 Indices and surds
EXAMPLE 2
EXAMPLE 4
Evaluate Simplify
a (0.2)3 a (3a2)3
(2)
−2
b 3
b (2a3)-2
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a (0.2)3 = (0.2 ´ 0.2) ´ 0.2 Breaking down the calculation a Use the rule (am)n = am´n on both terms:
makes the multiplication easier (3a2)3= (3)3 ´ (a2)3 = 27 ´ a2´3 Splitting the 3 and the a² may
= 0.04 ´ 0.2 help you to simplify the problem.
= 0.008 to do without a calculator. = 27 ´ a6
= 27a6 Remember that both the 3 and
()
−2 the a² need to be cubed.
3
b 2 b Use the rule a-n = 1n :
()
−2 a
3 1
Use a-n = 1n : = a = 3 and n = 2
()
a 2 2 2 (2a3)-2 = 1
3
2 ( 2a3 )2
= 1 Remember that 1 = b Now use the rule (am)n = am´n in the denominator:
(9)
4
()a
b
a
1 = 1 Remember that both the 2 and
(2a ) 3 2 22 × (a3)2 the a3 need to be squared.
= 4 = 2 1 3×2
9
2 ×a
= 1 6
4×a
You can also use the laws of indices to simplify algebraic expressions.
C1
C1
= 16
4a
EXAMPLE 3
Simplify
a p2 ´ p3
EXAMPLE 5
Simplify each expression giving the final answer in the
b t5 ¸ t3 form kxn where k is a constant and n an integer.
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a Use am ´ an = am+n: p2 ´ p3 = p2+3 a 3a3 ´ (4a)2
−3
= p5
b ⎛ 2⎞
3
⎜ ⎟
⎝x ⎠
b Use am ¸ an = am-n: t5 ¸ t3 = t5-3 ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
= t2
a 3a3 ´ (4a)2 = 3a3 ´ 16a2 Using the rule (am)n = am´n
= 3 ´ 16 ´ a3 ´ a2 Using the rule am ´ an = am+n
You can apply the index laws to simplify expressions which = 48a5
contain numbers and variables. −3
b ⎛ 32 ⎞
⎜ ⎟ = 1
3
Using the rule a-n = 1n
⎝x ⎠ ⎛ 3 ⎞ a
⎜ 2⎟
⎝x ⎠
= 1 Using the rule (am)n = am´n
27
x6 ( ) to simplify the denominator.
6
=x Since 1 = b
27 ( ba ) a
4 5
7. 1 Indices and surds 1 Indices and surds
Exercise 1.1 5 Simplify these expressions.
1 Evaluate the following quantities. 2
7 5 a ⎛ 5a ⎞
⎜ 2⎟ b (-2a2b)4
a 2 b 3 ⎝b ⎠
c 132 d 23 + 42
c (5t2)3 - (5y2)3 d (2y)3 ´ (3z)3
e 25 + 52 f 92 - 34 3
e (3a)-2 f 2
(4) r2
3
g (22)3 h
3
( 3b )
1 −2
g 2z 2 h (4b)−3 × 1
3 2 2
i (0.4) j (1.01) - (0.99) 3y
k (98)2 - (2)2 l (0.4)2 - (9.6)2 i 4(y2)-3 ¸ (2y)-2 j (3y2t)2 ¸ (3yt2)-2
2 Write each of the following quantities in an index form. 6 Simplify each of the following expressions where possible.
a 32 b 81 c 125 a 4a2 + 9a2 b 9a2 + 4a3
d 0.001 e 25 f 0.04 c 4a2 ´ 9a3 d 4a2 ¸ 9a3
64
e 9a2 - 4a3 f 9a2 ¸ 4a3
g 1 h 441 i 128
10 000 400 243 g 9 ¸ 4a2 h 4a - 9a
C1
C1
3 Evaluate these quantities. i 9a2 ´ 4a - 9a2 j 4a2 ¸ 9a - 4a
a 4-1 b 6-2
INVESTIGATIONS
3
c 70 d (1)
2
7 Which of these numbers can be expressed either as
a power of 3 or as a power of 4?
3 1 1 64 12 1 1 24 81 36
e (2)
3
f (0.5)-2 9 24 16 27
4 8
8 Which of these expressions simplify to give the
g ()
1
3
h ()
1
2 answer, a?
( a25 )
−1
3 3 −1 3
4 Simplify each expression. 5a 4a 2a 3a 4a
a2 (2a)2 2a2 3a −2 2a2 (5a)−2
a p ´ p3 b 3a ´ 4a2 ´ 5a3
c 12b ¸ 3b4 d (3y2)2 9 A saver deposits £80 with a bank giving an interest rate of
5%. Use your knowledge of indices to express as a ´ bn
e 7p2 + 9p2 f (5a)2 ¸ 5a3 the value of the investment
g (-4b3)2 ´ 5b2 h (3a3)2 ¸ (3a2)3 a after five years
i 4p3(3p3 ¸ 2p3) j (-3y)3 ´ (-2y)2 b after n years.
After how many years and months will the investment
reach £100?
6 7
8. 1 Indices and surds
1.2 Fractional indices
Generally, for any number a, (a ) 1 m
n = (am)n = a n
1 m
( n a )m = n
am = a n
m
The index laws also apply to fractional indices.
You can use the index laws to evaluate expressions involving
fractional indices.
Consider 3 × 3 =3
1 1 1+1
You know that 3 2 × 3 2 = 3 2
EXAMPLE 1
2 Using am ´ an = am+n 2
1
Evaluate a (27)3 b (9)−0.5
=3 ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
=3
You can deduce that 3 is written as
1
32 in index notation. a Rewrite the expression: (272)3
1
or (27 ) 1 2
3 Choose ( 27 )
1 2
3 as this is simpler
1 1 to work with.
1
Similarly 4 = 42 and 5 = 52 You can follow the steps above You know that 27 3 = 3 27 = 3
to show this for yourself.
= (27 )
2 1 2
Hence (27)3 3
= (3)2 = 9 You should recognise that
Now consider 3
2× 2× 2 =2
3 3 3
2 is the cube root of 2. 1
27 3 = 3
27 = 3
1 1 1 1+1+1 b (9) −0.5
= 11
You know that 23 × 23 × 23 = 23 3 3 You can deduce this for yourself (9)2
1
by considering am ´ an ´ ap and 92 = 9 = 3
= 21
using the index laws. =1
=2 3
C1
C1
1
You can deduce that 3 2 is written as 2 3 in index notation. Sometimes the expression will involve a fraction as the
1 1
Similarly 5 =3
53 and 3
7 = 73 base number.
EXAMPLE 2
Evaluate
( ) ( )
1 2 3
−
Generally, for any number a, n
a = an This is the nth root of a. a 125 3
b 256 4
8 81
••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
The other index laws also apply to fractional indices.
( 1)
2 m
⎡ 1⎤
( ) ( )
2 m
125 3
⎢ 125 ⎥
3
Using a n = a n
a =
8 ⎣ 8 ⎦
= (5)
3
Consider ( 8 )2 2
Since 3 125 = 5 and 3 8 = 2
This can be rewritten as ( )
1 2
83 Using (am)n = am´n
2
1 ×2 = 25 Remember to square both
4
= 83 the top and bottom numbers.
( ) ( )
−
3 3
2 −n
= 83 b 256 4
= 81 4
Using the rule a = 1n
81 256 a
1 2
( ) =
Similarly 82 3 83 Using (am)n = am´n ⎡
= ⎢ 81 ⎥ ( )
1 ⎤3
4
Using a n =
m
( )
1 m
an = n am
Hence ( )
1 2
83 =
1
( ) =
82 3
2
83
⎣ 256 ⎦
(4)
3
= 3
= 27 Remember to cube both the
64 top and bottom numbers.
8 9