Binomial expansion Study guides, Revision notes & Summaries
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![Test Bank for Corporate Finance, 8th Edition by Ehrhardt Brigham](/docpics/3042158/64abb6cb3d85a_3042158_121_171.jpeg)
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Test Bank for Corporate Finance, 8th Edition by Ehrhardt Brigham
- Exam (elaborations) • 419 pages • 2023
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Test Bank for Corporate Finance: A Focused Approach 8th Edition 8e by Michael C. Ehrhardt; Eugene F. Brigham. ISBN 4638 
 
Full Chapters test bank included 
 
Chapter 1: An Overview of Financial Management and the Financial Environment 
1-1 The Five-Minute MBA 
1-2 Finance From 40,000 Feet Above 
1-3 The Corporate Life Cycle 
1-4 Governing a Corporation 
1-5 An Overview of Financial Markets 
1-6 Types of Claims on Future Cash Flows: Financial Instruments, Financial Assets, and Financial Sec 
1-7...
![Binomial expansion, Algebraic Functions- A* A level Mathematics Edexcel Notes](/docpics/5734420/66802320b0452_5734420_121_171.jpeg)
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Binomial expansion, Algebraic Functions- A* A level Mathematics Edexcel Notes
- Summary • 13 pages • 2024
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Pure Mathematics 
 
This document includes summaries of key mathematical concepts and thought-out examples with corrections made where necessary 
 
A* achieved using these notes in 2022 exams 
 
Relevant to the Edexcel exam board 
•	Mathematical Proof 
•	Algebraic functions 
•	Dividing polynomials 
•	Equating coefficients 
•	Factor theorem 
•	Pascal’s triangle 
•	Factorial notation 
•	Binomial expansion 
•	Binomial estimations
![AS-level Edexcel Pure Maths - Module 8: The binomial expansion|2023 LATEST UPDATE|GUARANTEED SUCCESS](/docpics/2958879/64975746e5826_2958879_121_171.jpeg)
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AS-level Edexcel Pure Maths - Module 8: The binomial expansion|2023 LATEST UPDATE|GUARANTEED SUCCESS
- Exam (elaborations) • 2 pages • 2023
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Pascal's triangle 
A triangle where the the two numbers above to make the number below. 
- The numbers are the coefficients of the expansion of (a+b)ⁿ 
- The (n+1)th row gives the coefficients of (a+b)ⁿ 
 
 
 
Binomial 
The sum or difference of two terms 
 
 
 
Expanding brackets 
Multiply every term in bracket a by every term in bracket b 
 
 
 
Factorial 
n! is the product of consecutively decreasing natural numbers from n to 1 
- n! = n(n-1)(n-2)(n-3)...3x2x1 
- n! is also the number of ...
![MAA-HL_paper3-practice_26-practice-questions EXTD 123IBDP Mathematics: Analysis and Approaches, Higher Level Paper 3 Practice Questions|ALL ANSWERS CORRECT](/docpics/638b53dc3d50b_2152465.jpg)
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MAA-HL_paper3-practice_26-practice-questions EXTD 123IBDP Mathematics: Analysis and Approaches, Higher Level Paper 3 Practice Questions|ALL ANSWERS CORRECT
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IBDP Mathematics: Analysis and Approaches, Higher Level 
Paper 3 
Practice Questions 
Daniel Hwang 
 
Suggestions and corrections are welcome. 
Updated March 18, 2021 
Question number 
 
1 
2 
3 
4 
5 
6 
7 
8 
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 
2 
5 
2 
6 
Maximum mark 
 
3 
1 
3 
1 
2 
7 24 31 
2 
3 
2 
9 31 
2 
7 26 
2 
3 31 29 
2 
8 23 
2 
5 30 
2 
4 23 32 
2 
4 
2 
3 29 23 
2 
7 
3 
2 
Number & algebra 
Sequences & series 
x x x x x x 
x 
Exponents & logs x x x x 
x 
x x ...
![Sequence, Partial Functions- A* A level Mathematics Edexcel Notes](/docpics/5734639/66802e6e81259_5734639_121_171.jpeg)
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Sequence, Partial Functions- A* A level Mathematics Edexcel Notes
- Summary • 24 pages • 2024
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- £3.49
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Pure Mathematics 
 
This document includes summaries of key mathematical concepts and thought-out examples with corrections made where necessary 
 
A* achieved using these notes in 2022 exams 
 
Relevant to the Edexcel exam board 
 
•	Arithmetic series and sequences 
•	Geometric sequences and series 
•	Sigma notation 
•	Recurrence relations 
•	Year 13 Binomial Expansion 
•	Year 13 Partial Functions
![AQA AS MATHEMATICS 7356/1 Paper 1 Version: 1.0 Final PB/KL/Jun23/E4 7356/1 AS MATHEMATICSQUESTION PAPER & MARKING SCHEME/ [MERGED] Mark scheme June 2023](/docpics/4377626/65b991fcd9857_4377626_121_171.jpeg)
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AQA AS MATHEMATICS 7356/1 Paper 1 Version: 1.0 Final PB/KL/Jun23/E4 7356/1 AS MATHEMATICSQUESTION PAPER & MARKING SCHEME/ [MERGED] Mark scheme June 2023
- Exam (elaborations) • 47 pages • 2024
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AQA 
AS 
MATHEMATICS 
7356/1 
Paper 1 
Version: 1.0 Final 
PB/KL/Jun23/E4 7356/1 
AS 
MATHEMATICS 
Paper 1 
Time allowed: 1 hour 30 minutes 
Materials 
l You must have the AQA Formulae for A‑level Mathematics booklet. 
l You should have a graphical or scientific calculator that meets the 
requirements of the specification. 
Instructions 
l Use black ink or black ball-point pen. Pencil should only be used for drawing. 
l Fill in the boxes at the top of this page. 
l Answer all questions. 
l You...
![Engineering math 115 Binomial theorem, Antiderivatives, Mathematical inductions, Definite integral & Riemann sums](/docpics/632052514637e_1958223.jpg)
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Engineering math 115 Binomial theorem, Antiderivatives, Mathematical inductions, Definite integral & Riemann sums
- Other • 25 pages • 2022
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These notes are in a pdf format. 
- colour coded 
- step-by-step examples for each topic 
The notes cover the topic: Antiderivatives, Mathematical Induction, Binomial theorem, Definite integral & Riemann sums
![2023 AQA AS MATHEMATICS 7356/1 Paper 1 Question Paper & Mark scheme (Merged) June 2023 [VERIFIED]](/docpics/5301651/6643b7c7408dc_5301651_121_171.jpeg)
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2023 AQA AS MATHEMATICS 7356/1 Paper 1 Question Paper & Mark scheme (Merged) June 2023 [VERIFIED]
- Exam (elaborations) • 50 pages • 2024
- Available in package deal
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- £6.46
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2023 AQA AS MATHEMATICS 7356/1 Paper 1 Question Paper & Mark scheme (Merged) 
June 2023 [VERIFIED] 
AS 
MATHEMATICS 
Paper 1 
Thursday 18 May 2023 afternoon Time allowed: 1 hour 30 minutes 
Materials 
You must have the AQA Formulae for A‑level Mathematics booklet. You should have a graphical or scientific calculator that meets the 
requirements of the specification. 
Instructions 
Use black ink or black ball-point pen. Pencil should only be used for drawing. 
Fill in the boxes at the top of ...
![Solutions for Basic Technical Mathematics with Calculus, 12th Edition Washington (All Chapters included)](/docpics/5757405/6685390eb48ef_5757405_121_171.jpeg)
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Solutions for Basic Technical Mathematics with Calculus, 12th Edition Washington (All Chapters included)
- Exam (elaborations) • 2488 pages • 2024
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Complete Solutions Manual for Basic Technical Mathematics with Calculus, 12th Edition by Allyn J. Washington, Richard Evans ; ISBN13: 9780137582792....(Full Chapters included Chapter 1 to 31)...Chapter 1 Basic Algebraic Operations 
Chapter 2 Geometry 
Chapter 3 Functions and Graphs 
Chapter 4 The Trigonometric Functions 
Chapter 5 Systems of Linear Equations; Determinants 
Chapter 6 Factoring and Fractions 
Chapter 7 Quadratic Equations 
Chapter 8 Trigonometric Functions of Any Angle 
Chapter 9 ...
![2023 AQA AS MATHEMATICS 7356/1 Paper 1 Question Paper & Mark scheme (Merged) June 2023 [VERIFIED]](/docpics/5275378/6640ae9bf1158_5275378_121_171.jpeg)
-
2023 AQA AS MATHEMATICS 7356/1 Paper 1 Question Paper & Mark scheme (Merged) June 2023 [VERIFIED]
- Exam (elaborations) • 50 pages • 2024
- Available in package deal
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- £9.29
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2 
Section A 
Answer all questions in the spaces provided. 
1 At a point P on a curve, the gradient of the tangent to the curve is 
10 State the gradient of the normal to the curve at P 
Circle your answer. 
[1 mark] 
10 0.1 0.1 10 
2 3 
x 
2 Identify the expression below which is equivalent to 5 
Circle your answer. 
[1 mark] 
8x 
3 
125x 
3 
125 8 
125 8 8x 
3 
125x 
3 
Do not write 
outside the 
box 
(02) 
Jun23/7356/1 
3 
The coefficient of x 
2 
in the binomial expansion of (1 þ ax) 
6 ...
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