Trigonometric integration - Study guides, Class notes & Summaries
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OCR 2023 GCE MATHEMATICS B MEI H640/02: PURE MATHEMATICS AND STATISTICS A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)
- Exam (elaborations) • 66 pages • 2024
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2 
© OCR 2023 H640/02 Jun23 
^ h 
= 
e 
n+1 
2 
n 2 2 
L P 
Formulae A Level Mathematics B (MEI) (H640) 
Arithmetic series 
S = 
1 
n^a + lh = 
1 
n"2a +^n - 1hd, 
Geometric series 
Sn 
= 
a 1-r 
n 
1 -r 
 a 
3 1-r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2 +f+ 
nCr 
a 
n-r 
b 
r +f+b 
n 
n e N , 
n 
J 
n 
N n! 
where Cr 
= n 
Cr 
= K 
r 
O = 
r!^n -rh! 
^1+xh 
n 
= 1+nx+ 
n^n -1h 
x 
2 
+f+ 
n^n -1hf^n -r+1h 
x 
r 
+f 
x 1 1, n e R 
2! 
Differentiation...
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OCR 2023 GCE MATHEMATICS B MEI H640/01: PURE MATHEMATICS AND MECHANICS A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)
- Exam (elaborations) • 62 pages • 2024
- Available in package deal
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- $7.99
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2 
© OCR 2023 H640/01 Jun23 
= 
r n r Kr 
O 
e 
n+1 
2 
Formulae A Level Mathematics B (MEI) (H640) 
Arithmetic series 
S = 
1 
n^a+lh = 
1 
n"2a+^n-1hd, 
n 2 2 
Geometric series 
Sn 
= 
a^1-r 
nh 
1 -r 
 a 
3 1 -r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2 +f+ 
nCr 
a 
n-r 
b 
r +f+ b 
n ^n e Nh, 
where 
nC = C = 
J 
n 
N 
= 
L P 
n! 
r!^n -rh! 
^1+xh 
n 
= 1+nx+ 
n^n -1h 
x 
2 
+f+ 
n^n - 1hf^n -r+1h 
x 
r 
+f 
^x 1 1, n e Rh 
2! 
Differentiation 
f^x...
-
OCR 2023 GCE MATHEMATICS A H240/01: PURE MATHEMATICS A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)
- Exam (elaborations) • 68 pages • 2024
- Available in package deal
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- $7.99
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2 
© OCR 2023 H240/01 Jun23 
^ h 
= 
n+1 
2 
n 2 2 
L P 
2! r! 
dx dx 
Formulae 
A Level Mathematics A (H240) 
Arithmetic series 
S = 
1 
n^a + lh = 
1 
n"2a +^n - 1hd, 
Geometric series 
Sn 
= 
a 1-r 
n 
1 -r 
 a 
3 1-r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2 +f+ 
nCr 
a 
n-r 
b 
r +f+b 
n ^n e Nh 
n 
J 
n 
N n! 
where Cr 
= n 
Cr 
= K 
r 
O = 
r!^n -rh! 
^1+xh 
n 
= 1+nx+ 
n^n -1h 
x 
2 
+f+ 
n^n -1hf^n -r+1h 
x 
r 
+f ^ x 1 1,n e Rh 
Differentiati...
-
OCR 2023 GCE MATHEMATICS B MEI H640/03: PURE MATHEMATICS AND COMPREHENSION A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)
- Exam (elaborations) • 66 pages • 2024
- Available in package deal
-
- $7.99
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2 
© OCR 2023 H640/03 Jun23 
= 
e 
n+1 
2 
Formulae A Level Mathematics B (MEI) (H640) 
Arithmetic series 
S = 
1 
n^a+lh = 
1 
n"2a+^n-1hd, 
n 2 2 
Geometric series 
Sn 
= 
a^1-r 
nh 
1 -r 
 a 
3 1 -r 
for r 1 1 
Binomial series 
^a+bh 
n 
= a 
n + 
nC1 
a 
n-1 
b+ 
nC2 
a 
n-2 
b 
2 +f+ 
nCr 
a 
n-r 
b 
r +f+ b 
n ^n e Nh, 
n 
Jn 
N n! 
where 
Cr 
= n 
Cr 
= K 
r 
O = 
r!^n -rh! 
L P 
^1+xh 
n 
= 1+nx+ 
n^n -1h 
x 
2 
+f+ 
n^n - 1hf^n -r+1h 
x 
r 
+f 
^x 1 1, n e Rh 
2! 
Differentiation 
f^x...
-
SMA 2101: CALCULUS I c Francis O. Ochieng francokech@gmail.com Department of Pure and Applied Mathematics Jomo Kenyatta University of Agriculture and Technology
- Class notes • 59 pages • 2023
-
- $8.39
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SMA 2101: CALCULUS I 
c Francis O. Ochieng 
 Department of Pure and Applied Mathematics Jomo Kenyatta University of Agriculture and Technology 
Course content 
• Functions: definition, domain, range, codomain, composition (or composite), inverse. • Limits, continuity and differentiability of a function. • Differentiation by first principle and by rule for x 
n 
(integral and fractional n). • Other techniques of differentiation, i.e., sums, products, quotients, chain rule; their applic...
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Mathematics 114 summaries
- Summary • 80 pages • 2022
- Available in package deal
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- $13.12
- 2x sold
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Aesthetic digital concise summaries of all the theory and some examples you need to know for mathematics 114. 
The whole semester's content for mathematics 114 is summarised. 
Self-study: Revision of coordinate geometry & straight lines 
These are topics that you should be familiar with from school. Some students forget some of this material by the time they start their first year, and therefore need to revise them. These topics are all required for Calculus topics later on. 
 
Week 1: Numbers,...
-
Pure Mathematics Revision Notes (Mathematics Edexcel A-Level)
- Summary • 12 pages • 2024
- Available in package deal
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- $8.26
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Pure Mathematics Edexcel A-Level Year 1 and 2 revision notes, written by a straight A* student. Includes diagrams and explanations for concepts. Well organised and in order. 
Includes collated information from class, textbooks and online. Topics include: Quadratics, Graphs and transformations, Functions and graphs, Circles, Algebraic methods, The binomial expansion, Trigonomic ratios, Trigonomic identities and equations, Trigonometric functions, Trigonometry and modelling, Vectors, Differentiat...
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Test Banks For Essential Calculus 2nd Edition by James Stewart, 9781133112297, Chapter 1-13 Complete Guide
- Exam (elaborations) • 298 pages • 2023
-
- $25.11
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Essential Calculus 2nd Edition 
 
2297 
 
0875 
 
0, 3, 4, 0, 2467, 3011, 9067, 6609 
 
1: Functions and Limits 
 
1.1: Functions and Their Representations 
 
1.2: A Catalog of Essential Functions 
 
1.3: The Limit of a Function 
 
1.4: Calculating Limits 
 
1.5: Continuity 
 
1.6: Limits Involving Infinity 
 
2: Derivatives 
 
2.1: Derivatives and Rates of Change 
 
2.2: The Derivative as a Function 
 
2.3: Basic Differentiation Formulas 
 
2.4: The Product and Quotient Rules 
 
2.5: The Chain ...
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Test Bank For Essential Calculus 2nd Edition by James Stewart 9781133112297 Chapter 1-13 Complete Guide.
- Exam (elaborations) • 298 pages • 2023
-
- $29.88
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Test Bank For Essential Calculus 2nd Edition by James Stewart 2297, 3, 0875, 5 
 
1: Functions and Limits 
 
2: Derivatives 
 
3: Applications of Differentiation 
 
4: Integrals 
 
5: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric 
 
6: Techniques of Integration 
 
7: Applications of Integration 
 
8: Series 
 
9: Parametric Equations and Polar Coordinates 
 
10: Vectors and the Geometry of Space 
 
11: Partial Derivatives 
 
12: Multiple Integrals 
 
13: Vector Calculus
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COMPLETE MATHEMATICS NOTES
- Class notes • 662 pages • 2023
- Available in package deal
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- $35.00
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Natural Numbers --------------------------------------------------------------------------11 
Factors -------------------------------------------------------------------------------------18 
Divisibility test ----------------------------------------------------------------------------23 
G.C.D ---------------------------------------------------------------------------------------26 
L.C.M ---------------------------------------------------------------------------------------29 
Integers---------...
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