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A-Level Maths
AS ONLY
A: Proof
A1. Proof
B: Algebra & Functions
B1. Indices
B2. Surds
B3: Quadratics
B4: Simultaneous Equations
B5: Inequalities
B6: Polynomials
B7: Graphs & Proportion
B9: Graph Transformations
C: Coordinate Geometry
C1: Coordinate Geometry
C2: Circles
D: Sequences & Series
D1: Binomial Expansion
E: Trigonometry
E1: Trigonometry
E3: Trig Graphs
E5: Trigonometric Identities
E7: Trig Equations
F: Exponentials & Logarithms
F1: Exponentials
F2: Exponential Models
F3: Logarithms
F4: Laws of Logarithms
F5: Exponential & Logarithmic Equations
F6: Reduction to Linear Form
F7: Exponential Growth & Decay
G: Differentiation
G1: Differentiation from First Principles
G2: Differentiation
G3: Gradients
H: Integration
H1: Fundamental Theorem of Calculus
H2: Indefinite Integrals
H3: Definite Integrals
J: Vectors
J1: Introducing Vectors
J2: Magnitude & Direction of a Vector
J3: Resultant & Parallel Vectors
J4: Position Vectors
J5: Vector Problems
K: Statistical Sampling
K1: The Large Data Set & Sampling Methods
L: Data Presentation & Interpretation
L1: Box Plots, Cumulative Frequency & Histograms
L2: Scatter Graphs
L3: Central Tendency & Variation
L4: Outliers & Cleaning Data
M: Probability
M1: Venn Diagrams, Tree Diagrams & Two-Way Tables
N: Statistical Distributions
N1: Discrete Random Variables & The Binomial Distribution
O: Hypothesis Testing
O1: Introducing Hypothesis Testing
O2: Binomial Hypothesis Testing
P: Quantities & Units in Mechanics
P1: Quantities & Units in Mechanics
Q: Kinematics
Q1: Displacement, Velocity & Acceleration
Q2: Graphs of Motion
Q3: SUVAT
Q4: Calculus in Kinematics
R: Forces & Newton's Laws
R1: Introducing Forces & Newton's First Law
R2: Newton's Second Law
R3: Weight and Tension
R4: Newton's Third Law and Pulleys
2nd Year ONLY
A: Proof
A1: Proof
B: Algebra & Functions
B6: Polynomials & Rational Expressions
B7: Graphs & Proportion
B8: Functions
B9: Graph Transformations
B10: Algebraic Fractions
B11: Modelling
C: Coordinate Geometry
C3: Parametric Equations
C4: Parametric Equation Modelling
D: Sequences & Series
D1: Binomial Expansion
D2: Sequences
D3: Sigma Notation
D4: Arithmetic Sequences
D5: Geometric Sequences
D6: Modelling with Sequences
E: Trigonometry
E1: Trigonometry
E2: Small Angle Approximation
E3: Trig Graphs
E4: Further Trigonometry
E5: Trigonometric Identities
E6: Compound Angles & Equivalent Forms
E7: Trig Equations
E8: Proving Trigonometric Identities
E9: Trigonometry in Context
G: Differentiation
G1: Differentiation from First Principles
G2: Differentiation
G3: Gradients
G4: Further Differentiation
G5: Implicit Differentiation & Parametric Differentiation
G6: Forming Differential Equations
H: Integration
H2: Indefinite Integrals
H3: Definite Integrals & Parametric Integration
H4: Integration as the Limit of a Sum
H5: Further Integration
H6: Integration with Partial Fractions
H7: Differential Equations
H8: Differential Equations in Context
I: Numerical Methods
I1: The Change of Sign Method
I2: The x=g(x) Method & The Newton-Raphson Method
I3: Numerical Integration
I4: Numerical Methods in Context
J: Vectors
J1: Introducing Vectors
J2: Magnitude & Direction of a Vector
J5: Vector Problems
M: Probability
M2: Conditional Probability
M3: Modelling with Probability
N: Statistical Distributions
N2: The Normal Distribution
N3: Appropriate Distributions
O: Hypothesis Testing
O1: Introducing Hypothesis Testing
O3: Sample Means Hypothesis Testing
P: Quantities & Units in Mechanics
P1: Quantities & Units in Mechanics
Q: Kinematics
Q3: SUVAT
Q4: Calculus in Kinematics
Q5: Projectiles
R: Forces and Newton's Laws
R1: Introducing Forces & Newton's First Law
R2: Newton's Second Law
R4: Newton's Third Law and Pulleys
R5: F=ma & Differential Equations
R6: The Coefficient of Friction
S: Moments
S1: Moments
FULL A-Level
A: Proof
A1: Proof
B: Algebra & Functions
B1: Indices
B2: Surds
B3: Quadratics
B4: Simultaneous Equations
B5: Inequalities
B6: Polynomials & Rational Expressions
B7: Graphs & Proportion
B8: Functions
B9: Graph Transformations
B10: Algebraic Fractions
B11: Modelling
C: Coordinate Geometry
C1: Coordinate Geometry
C2: Circles
C3: Parametric Equations
C4: Parametric Equation Modelling
D: Sequences & Series
D1: Binomial Expansion
D2: Sequences
D3: Sigma Notation
D4: Arithmetic Sequences
D5: Geometric Sequences
D6: Modelling with Sequences
E: Trigonometry
E1: Trigonometry
E2: Small Angle Approximation
E3: Trig Graphs
E4: Further Trigonometry
E5: Trigonometric Identities
E6: Compound Angles & Equivalent Forms
E7: Trig Equations
E8: Proving Trigonometric Identities
E9: Trigonometry in Context
F: Exponentials & Logarithms
F1: Exponentials
F2: Exponential Models
F3: Logarithms
F4: Laws of Logarithms
F5: Exponential & Logarithmic Equations
F6: Reduction to Linear Form
F7: Exponential Growth & Decay
G: Differentiation
G1: Differentiation from First Principles
G2: Differentiation
G3: Gradients
G4: Further Differentiation
G5: Implicit Differentiation & Parametric Differentiation
G6: Forming Differential Equations
H: Integration
H1: Fundamental Theorem of Calculus
H2: Indefinite Integrals
H3: Definite Integrals & Parametric Integration
H4: Integration as the Limit of a Sum
H5: Further Integration
H6: Integration with Partial Fractions
H7: Differential Equations
H8: Differential Equations in Context
I: Numerical Methods
I1: The Change of Sign Method
I2: The x=g(x) Method & The Newton-Raphson Method
I3: Numerical Integration
I4: Numerical Methods in Context
J: Vectors
J1: Introducing Vectors
J2: Magnitude & Direction of a Vector
J3: Resultant & Parallel Vectors
J4: Position Vectors
J5: Vector Problems
K: Statistical Sampling
K1: The Large Data Set & Sampling Methods
L: Data Presentation & Interpretation
L1: Box Plots, Cumulative Frequency & Histograms
L2: Scatter Graphs
L3: Central Tendency & Variation
L4: Outliers & Cleaning Data
M: Probability
M1: Venn Diagrams, Tree Diagrams & Two-Way Tables
M2: Conditional Probability
M3: Modelling with Probability
N: Statistical Distributions
N1: Discrete Random Variables & The Binomial Distribution
N2: The Normal Distribution
N3: Appropriate Distributions
O: Hypothesis Testing
O1: Introducing Hypothesis Testing
O2: Binomial Hypothesis Testing
O3: Sample Means Hypothesis Testing
P: Quantities & Units in Mechanics
P1: Quantities & Units in Mechanics
Q: Kinematics
Q1: Displacement, Velocity & Acceleration
Q2: Graphs of Motion
Q3: SUVAT
Q4: Calculus in Kinematics
Q5: Projectiles
R: Forces and Newton's Laws
R1: Introducing Forces & Newton's First Law
R2: Newton's Second Law
R3: Weight & Tension
R4: Newton's Third Law and Pulleys
R5: F=ma & Differential Equations
R6: The Coefficient of Friction
S: Moments
S1: Moments
Revision Tips Videos
Enrolment Work
Teaching Order Year 1
101: Linear Graphs
102: Quadratic Graphs
103: Indices & Surds 1
104: Indices & Surds 2
105: Exponentials and Logarithms
106: Logarithms 1
107: Logarithms 2
108: e^x and ln(x)
109: Logarithms 3
110: Exponential Growth & Decay 1
111: Exponential Growth & Decay 2
112: Polynomials 1
113: Polynomials 2
114: Graph Sketching Polynomials
115. Graph Sketching Rational Functions
116: Graph Transformations
117: Coordinate Geometry
118: Equation of a Circle 1
119: Equation of a Circle 2
120: Reduction to Linear Form 1
121: Reduction to Linear Form 2
122: Inequalities 1
123 Inequalities 2
124: Differentiation from First Principles
125: Graphs of Motion
126: Constant Acceleration SUVAT 1
127: Constant Acceleration SUVAT 2
128: Differentiation
129: Differentiation - Tangents & Normals
130: Differentiation - Stationary Points
131: Second Derivatives and Points of Inflection 1
132: Second Derivatives and Points of Inflection 2
133: Differentiation - Optimisation
134: Linear Regression & PMCC
135: Probability 1
136: Probability 2
137: Mean and Standard Deviation
138: Outliers and Using Statistical Diagrams
139: Pascal's Triangle & nCr
140: Binomial Expansion
141: Discrete Random Variables
142: Binomial Distribution
143: Binomial Hypothesis Testing 1
144: Binomial Hypothesis Testing 2
145: Integration
146: Integration - Finding Areas
147: The Trapezium Rule
148: Integration - Areas between Curves
149: Variable Acceleration 1
150: Variable Acceleration 2
151: Proof
152: Basic Trigonometry
153: Radians, Sectors & Arc Length
154: Vectors
155: Introducing Forces & Equilibrium
156: Newton's 2nd Law
157: Connected Particles 1
158: Connected Particles 2
159: Trigonometric Equations 1
160: Trigonometric Equations 2
161: Trigonometric Identities 1
162: Trigonometric Identities 2
163: Trigonometric Modelling
164: The Coefficient of Friction
165: Blocks on a Slope
166: Blocks and Pulleys on a Slope
Teaching Order Year 2
201: Domain and Range
202: Domain, Range & Composite Functions
203: Even, Odd and Periodic Functions
204: Graph Transformations
205: Inverse Functions
206: Modulus Functions
209: Sequences - Inductive Definitions
210: Arithmetic Sequences
211: Moments 1
212: Moments 2
213: Geometric Sequences
214: Sequences and Series
215: Inverse Trigonometric Functions
216: sec(x), cosec(x) & cot(x) 1
217: sec(x), cosec(x) & cot(x) 2
218: Compound Angle Formulae
219: Double Angle Formulae 1
220: Double Angle Formulae 2
221: Differentiation - Standard Functions
222: Differentiation - The Chain Rule
223: Differentiation - Connected Rates of Change
224: Differentiation - The Product Rule
225: Differentiation - The Quotient Rule
226: Choosing Differentiation Methods
227: Implicit Differentiation 1
228: Implicit Differentiation 2
229: Reversing the Chain Rule
230: Integration by Substitution 1
231: Integration by Substitution 2
232: Integration by Parts 1
233: Integration by Parts 2
234: Partial Fractions 1
235: Partial Fractions 2
236: Choosing Integration Methods
237: Numerical Methods - Change of Sign Method
238: Numerical Methods - x=g(x) Method
239: Numerical Methods - Newton-Raphson Method
240: Differential Equations 1
241: Differential Equations 2
242: Forming Differential Equations
243: 2D Constant Acceleration - SUVAT
244: 2D Variable Acceleration
245: Projectiles 1
246: Projectiles 2
247: Binomial Expansion 1
248: Binomial Expansion 2
249: 3D Vectors
250: Trigonometry - Harmonic Forms 1
251: Trigonometry - Harmonic Forms 2
252: Small Angle Approximation
253: The Normal Distribution - Finding Probabilities
254: The Normal Distribution - Inverse Normal
255: The Normal Distribution - Approximations
256: Parametric Equations
257: Parametric Differentiation 1
258: Parametric Differentiation 2
259: Parametric Integration
260: Proof by Contradiction
261: Sample Means Hypothesis Testing
262: PMCC Hypothesis Testing
Casio Classwiz How To
Bumper Book of Integrals
A-Level Further Maths
PURE
A: Proof
A1: Proof by Induction
B: Complex Numbers
B1: Introducing Complex Numbers
B2: Working with Complex Numbers
B3: Complex Conjugates
B4: Introducing the Argand Diagram
B5: Introducing Modulus-Argument Form
B6: Multiply and Divide in Modulus-Argument Form
B7: Loci with Argand Diagrams
B8: De Moivre's Theorem
B9: z = re^(iθ)
B10: nth Roots of Unity
B11: Geometrical Problems
C: Matrices
C1: Introducing Matrices
C2: The Zero & Identity Matrices
C3: Matrix Transformations
C4: Invariance
C5: Determinants
C6: Inverse Matrices
C7: Simultaneous Equations
C8: Geometrical Interpretation
AQA C9: Factorising Determinants
AQA C10: Eigenvalues and Eigenvectors
AQA C11: Diagonalisation
EXTRA PURE C12: Cayley-Hamilton Theorem
D: Further Algebra & Functions
D1: Roots of Polynomials
D2: Forming New Equations
D3: Summations
D4: Method of Differences
D5: Introducing Maclaurin Series
D6: Standard Maclaurin Series
AQA D7: Limits and l'Hôpital's Rule
AQA D8: Polynomial Inequalities
AQA D9: Rational Function Inequalities
AQA D10: Modulus of Functions
AQA D11: Reciprocal Graphs
AQA D12: Linear Rational Functions
AQA D13: Quadratic Rational Functions
AQA D14: Discriminants
AQA D15: Conic Sections
AQA D16: Transformations
E: Further Calculus
E1: Improper Integrals
E2: Volumes of Revolution
E3: Mean Value
E4: Partial Fractions
E5: Differentiating Inverse Trig
E6: Integrals of the form (a^2-x^2)^(-½) and (a^2+x^2)^(-1)
AQA E7: Arc Length and Sector Area
AQA E8: Reduction Formulae
AQA E9: Limits
F: Further Vectors
F1: Equations of Lines
F2: Equations of Planes
F3: The Scalar Product
F4: Perpendicular Vectors
F5: Intersections
F6: The Vector Product
G: Polar Coordinates
G1: Polar Coordinates
G2: Polar Curves
G3: Polar Integration
H: Hyperbolic Functions
H1: Hyperbolic Functions
H2: Hyperbolic Calculus
H3: Hyperbolic Inverse
H4: Hyperbolic Inverse
H5: Hyperbolic Integration
AQA H6: Hyperbolic Identities
AQA H7: Hyperbolic Identities
I: Differential Equations
I1: 1st Order Differential Equations - Integrating Factors
I2: 1st Order Differential Equations - Particular Solutions
I3: Modelling
I4: 2nd Order Homogeneous Differential Equations
I5: 2nd Order Non-Homogeneous Differential Equations
I6: 2nd Order Non-Homogeneous Differential Equations
I7: Simple Harmonic Motion
I8: Damped Oscillations
I9: Systems of Differential Equations
AQA I10: Hooke's Law
AQA I11: Damping Force
J: Numerical Methods
AQA J1: Mid-Ordinate Rule & Simpson's Rule
AQA J2: Euler's Step by Step Method
AQA J3: Euler's Improved Step by Step Method
OCR MEI Modelling with Algorithms
A: Tracing an Algorithm
B: Bin Packing
C: Sorting Algorithms
D: Graph Theory
E: Minimum Spanning Trees
F: Dijkstra's Algorithm
G: Critical Path Analysis
H: Network Flows
I: Linear Programming
J: Simplex Algorithm
K: LP Solvers
OCR MEI Statistics a / Minor
A: PMCC
B: Linear Regression
C: PMCC Hypothesis Testing
D: Spearman’s Rank
E: Chi-Squared Contingency Table Tests
F: Discrete Random Variables
G: Discrete Uniform Distributions
H: Geometric Distributions
I: Binomial Distribution
J: Poisson Distribution
K: Goodness of Fit Tests
OCR MEI Mechanics a / Minor
A: Energy
B: Power
C: Friction
D: Momentum & Impulse
E: Collisions
F: Moments
G: Centre of Mass
H: Dimensional Analysis
Teaching Order Year 1
01: Core Pure - Matrices: Basics
a. Introducing Matrices
b. The Zero & Identity Matrices
02: Core Pure - Matrices: 2D Transformations
03: Core Pure - Matrices: Invariant Points
04: Core Pure - Matrices: 3D Transformations
05: Modelling with Algorithms - Algorithms and Bin Packing
a. Tracing an Algorithm
b. Bin Packing
06: Modelling with Algorithms - Sorting Algorithms
07: Modelling with Algorithms - Graph Theory
08: Modelling with Algorithms - Kruskal's, Prim's & Dijkstra's Algorithms
a. Minimum Spanning Trees
b. Dijkstra's Algorithm
09: Core Pure - Complex Numbers: Basics
a. Introducing Complex Numbers
b. Working with Complex Numbers
c. Complex Conjugates
10: Core Pure - Complex Numbers: Argand Diagrams
a. Introducing the Argand Diagram
b. Introducing Modulus-Argument Form
c. Multiply and Divide in Modulus-Argument Form
d. Loci with Argand Diagrams
11: Modelling with Algorithms - Critical Path Analysis
12: Modelling with Algorithms - Network Flows
13: Modelling with Algorithms - Graphical Linear Programming
14: Modelling with Algorithms - LP Solver: Shortest Path, CPA, Network Flow
15: Modelling with Algorithms - Simplex Algorithm
16: Modelling with Algorithms - LP Solver: Matching, Transportation Problem
17: Core Pure - Series: Using Formulae
18: Core Pure - Series: Method of Differences
19: Core Pure - Matrices: Inverses, Singular Matrices, Simultaneous Equatio
a. Determinants
b. Inverse Matrices
c. Simultaneous Equations
20: Core Pure - Matrices: Invariant Lines
21: Core Pure - Roots of Polynomials
a. Roots of Polynomials
b. Forming New Equations
22: Core Pure - Proof by Induction: Series
23: Core Pure - Proof by Induction: Sequences
24: Core Pure - Proof by Induction: Matrices
25: Core Pure - Vectors: Scalar Product
a. The Scalar Product
b. Perpendicular Vectors
26: Core Pure - Vectors: Planes
a. Geometrical Interpretation
b. Equations of Planes
27: Statistics - PMCC
28: Statistics - Linear Regression
29: Statistics - PMCC Hypothesis Testing
30: Statistics - Spearman's Rank Correlation Coefficient
31: Statistics - Chi-Squared Contingency Table Tests
32: Statistics - Discrete Random Variables
33: Statistics - Discrete Uniform Distribution
34: Statistics - Geometric Distribution
Teaching Order Year 2
01: Core Pure - Polar Curves
a. Polar Coordinates
b. Polar Curves
02: Core Pure - Vectors: Lines
a. Lines
b. Intersections
03: Core Pure - Matrices: Determinant and Inverse of a 3x3 Matrix
a. Determinants
b. Inverse Matrices
c. Simultaneous Equations
04: Mechanics - Energy
11: Core Pure - Vectors: Vector Product
12: Core Pure - Proof by Induction: Divisibility
13: Core Pure - Complex Numbers: De Moivre's Theorem & Roots of Unity
a. De Moivre's Theorem
b. z = re^(iθ)
c. nth Roots of Unity
d. Geometrical Problems
14: Core Pure - Partial Fractions & Series
a. Method of Differences with Partial Fractions
b. Partial Fractions
15: Core Pure - Calculus: Improper Integrals
16: Core Pure - Calculus: Mean Value
17: Core Pure - Calculus: Volumes of Revolution
18: Core Pure - Calculus: Areas with Polar Curves
19: Core Pure - Calculus: Inverse Trig Functions
a. Differentiating Inverse Trig
b. Integrals of the form (a^2-x^2)^(-½) and (a^2+x^2)^(-1)
20: Core Pure - Hyperbolic Functions
a. Hyperbolic Functions
b. Hyperbolic Calculus
c. Hyperbolic Inverse
d. More Hyperbolic Inverse
e. Hyperbolic Integration
21: Core Pure - Series: Maclaurin Series
a. Introducing Maclaurin Series
b. Standard Maclaurin Series
22: Core Pure - Differential Equations: First Order
a. Integrating Factors
b. Particular Solutions
c. Modelling
23: Core Pure - Differential Equations: Second Order
a. 2nd Order Homogeneous Differential Equations
b. 2nd Order Non-Homogeneous Differential Equations
c. Examples
24: Core Pure - Differential Equations: Damped Simple Harmonic Motion
a. Simple Harmonic Motion
b. Damped Oscillations
25: Core Pure - Differential Equations: Systems of DEs
Core Maths Level 3 Certificate
Core Maths Resources
Teaching Videos
AQA Mathematical Studies Paper 1
AQA Mathematical Studies Paper 2A
Basics
GCSE to A-Level Maths Bridging the Gap
GCSE Maths
N: Number
N1
N2
N3
N4
N5
N6
N7
N8
Legacy A-Level Maths 2004
AQA C1
1. Coordinate Geometry
2. Surds
3. Quadratics
4. Inequalities
5. Polynomials
6: Equations of Circles
7: Differentiation
8: Integration
AQA C2
1. Indices
2. Differentiation & Integration
3. Logarithms
4. Graph Transformations
5. Sequences & Series
6: Binomial Expansion
7: Trigonometry 1
8: Trigonometry 2
AQA C3
1. Exponentials & Logarithms
2. Functions
3. Modulus Functions
4. Graph Transformations
5. Trigonometry
6. Differentiation
7. Integration
8. Solids of Revolution
9. Numerical Methods
AQA C4
1. Partial Fractions
2. Parametric Equations
3. Binomial Expansion
4. Trigonometry
5. Differential Equations
6. Implicit Equations
7. Vectors
AQA D1
1. Tracing an Algorithm
2. Sorting Algorithms
3. Graph Theory
4. Kruskal's Algorithm & Prim's Algorithm
5. Dijkstra's Algorithm
6. Bipartite Graphs
7. Chinese Postman Algorithm
8. The Travelling Salesperson Problem
9. Linear Programming
AQA S1
1. Mean & Standard Deviation
2. Probability
3. Binomial Probability
4. The Normal Distribution
5. Central Limit Theorem & Estimation
6. Confidence Intervals
7. Linear Regression
8. The Product Moment Correlation Coefficient
OCR MEI C1
1. Surds
2. Coordinate Geometry
3. Quadratics
4. Inequalities
5. Indices
6. Translations
7. Polynomials
8. Binomial Expansion
9. Equations of Circles
10. Proof
OCR MEI C2
1. Exponentials & Logarithms
2. Trigonometry 1
3. Differentiation 1
4. The Trapezium Rule & Integration
5. Sequences & Series
6. Graph Transformations
7. Trigonometry 2
8. Differentiation 2
OCR MEI C3
1. Exponentials & Logarithms
2. Functions
3. Modulus Functions
4. Differentiation Rules
5. Differentiating Functions
6. Implicit Differentiation
7. Integration
8. Proof
OCR MEI C4
1. Trigonometry
2. Parametric Equations
3. Binomial Expansion
4. Vectors
5. Partial Fractions
6. Differential Equations
7. The Trapezium Rule & Volumes of Revolution
8. Comprehension
OCR MEI S1
1. Probability
2. Mean & Standard Deviation
3. Discrete Random Variables
4. Permutations & Combinations
5. Binomial Probabilities
6. Hypothesis Testing
7. GCSE Recap & Odd and Ends
OCR MEI S2
1. Correlation & Regression
2. The Poisson Distribution
3. The Normal Distribution
4. The Chi-Squared Contingency Table Test
Legacy GCSE Maths Foundation
01. Addition, Subtraction, Multiplication & Division
02. Rounding & Negative Numbers
03. Fractions
04. Primes, Factors, Multiples, Squares, Cubes & Reciprocals
05. Fractions, Decimals & Percentages
06. Time, Money, Best Buys, Currency Exchange & Simple Interest
07. Ratio & Speed, Distance, Time
08. Types of Data, Questionnaires & Bar Charts
09. Mean, Median, Mode & Range
10. Pie Charts & Stem and Leaf Diagrams
11. Frequency Polygons, Histograms & Scatter Graphs
12. Probability
13. Algebraic Expressions
14. Solving Equations & Trial and Improvement
15. Coordinates & Plotting Graphs
16. Sequences & Inequalities
17. Angles & Parallel Lines
18. Triangles & Symmetry
19. Quadrilaterals, Polygons & Tessellation
20. Bearings & Constructions
21. Circles
22. Compound Shapes, 3D Shapes, Elevations & Nets
23. Translations, Reflections, Rotations & Enlargement
24. Pythagoras' Theorem & Metric to Imperial Conversion
TLMaths
AS ONLY
D: Sequences & Series
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D1: Binomial Expansion
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