Math Module

Further Pure Core Maths A-Level OCR

Video lessons and worked examples for Further Pure Core Maths A-Level OCR - free maths revision from ExamSolutions.

164 lessonsQuestion + answer PDFs
1
Complex numbers specimen questions (mixed exam boards)
Open
2
Systems of differential equations
Open
3
Damped Oscillations
Open
4
The identity: cosh<sup>2</sup>x-sinh<sup>2</sup>x ≡ 1
Open
5
Exam Questions – Partial Fractions (Improper type)
Open
6
Invariant points
Open
7
3D matrix transformations
Open
8
Convergent and Divergent Integrals
Open
9
Solving three linear simultaneous equations
Open
10
Mixed examples : Differentiating inverse trig functions
Open
11
Angle between a line and a plane
Open
12
The mean value of a function
Open
13
Exam Questions – Trig Type
Open
14
Exam Questions – Exponential Type ke<sup>px</sup> (exponential types)
Open
15
Exam Questions – Matrix transformations
Open
16
Exam Questions – Finding roots
Open
17
Shortest distance of a point to a line
Open
18
Shortest distance from a point to a plane
Open
19
Geometrical effects of conjugating a complex number
Open
20
Modulus-argument form of a complex number
Open
21
Transposed and symmetric matrices
Open
22
Shortest distance between two skew lines
Open
23
Vector product (cross product)
Open
24
Standard integrals relating to hyperbolic functions
Open
25
Integrating inverse trigonometric and hyperbolic functions using integration by parts
Open
26
Using trigonometric and hyperbolic substitutions
Open
27
Integrating expressions involving hyperbolic functions
Open
28
Finding the inverse of a 3×3 matrix where it exists
Open
29
Finding the determinant of a 3×3 matrix
Open
30
Derivatives of sin<sup>-1</sup>(x), cos<sup>-1</sup>(x) and tan<sup>-1</sup>(x)
Open
31
Denominator contains 1 linear and 1 quadratic factor
Open
32
Relationships between the roots and coefficients of a quartic equation
Open
33
Relationships between the roots and coefficients of a cubic equation
Open
34
Relationships between the roots and coefficients of a quadratic equation
Open
35
Exam Questions – Volume of Revolution about the y-axis
Open
36
Volume of revolution about the x-axis generated between curves
Open
37
Volume of Revolution about the y-axis generated between curves
Open
38
Volume of Revolution about the y-axis
Open
39
Exam Questions – Maclaurin’s series
Open
40
Exam Questions – General solutions where f(x) = kx (linear types)
Open
41
Exam Questions – Matrix proofs
Open
42
Exam Questions – Vectors
Open
43
Exam Questions – Parallel intersecting and skew lines
Open
44
Exam Questions – Scalar product
Open
45
Exam Questions – Volume of revolution about the x-axis
Open
46
Integrals of the form 1/(a<sup>2</sup>+x<sup>2</sup>) and 1/√(a<sup>2</sup>-x<sup>2</sup>)
Open
47
Solving quartic equations
Open
48
Solving cubic equations
Open
49
Solving quadratic equations with complex roots
Open
50
Square roots of a complex number
Open
51
Exam Questions – Area bounded by a polar curve
Open
52
Exam Questions – Particular solutions using boundary conditions
Open
53
Exam Questions – Substitution types
Open
54
Exam Questions – Exact equations (integrating factors)
Open
55
Exam Questions – nth roots of a complex number
Open
56
Exam Questions – Further complex numbers
Open
57
Exam Questions – Method of differences
Open
58
Exam Questions – Divisibility and multiple tests
Open
59
Exam Questions – Sum of series
Open
60
Exam Questions – Series
Open
61
Exam Questions – Identity and inverse of a 2×2 matrix
Open
62
Exam Questions – Complex numbers
Open
63
Exam Questions – Volume of revolution: parametric form
Open
64
Exam Questions – Integrals involving partial fractions
Open
65
The angle between two planes
Open
66
Finding the point of intersection between a line and a plane
Open
67
Scalar product forms of a plane
Open
68
Cartesian form of a plane
Open
69
Parametric vector form of a plane
Open
70
Cartesian form of a line
Open
71
Differentiation of inverse hyperbolic functions
Open
72
Differentiation of hyperbolic functions
Open
73
Solving hyperbolic equations using hyperbolic identities
Open
74
Expressing inverse hyperbolic functions as natural logarithms
Open
75
Solving equations using inverse and exponential functions
Open
76
Graphs of sinh(x), cosh(x) and tanh(x)
Open
77
Definitions
Open
78
Area bounded by a cardioid and a loop
Open
79
Area bounded by a polar curve
Open
80
Sketching curves the curve r = asin 2θ
Open
81
Sketching curves the cardioid r = a (1+cosθ)
Open
82
Sketching curves a circle and arc
Open
83
Sketching polar curves a half-line
Open
84
Sketching polar curves a spiral
Open
85
Converting the equation of a Cartesian curve to polar form
Open
86
Converting the equation of a polar curve to Cartesian form
Open
87
Converting polar coordinates to Cartesian coordinates
Open
88
Converting Cartesian coordinates to polar coordinates
Open
89
Defining the position of a point
Open
90
Further series
Open
91
Series expansion for ln(1+x)
Open
92
Series expansion for sin(x) and cos(x)
Open
93
Series expansion for e<sup>x</sup>
Open
94
Maclaurin’s series expansion
Open
95
Using substitution to reduce a differential equation to a known form
Open
96
Particular solutions using boundary conditions to solve differential equations
Open
97
Special types of particular integrals
Open
98
General solutions where f(x) = ke<sup>px</sup> (exponential types)
Open
99
General solutions where f(x) = kx<sup>2</sup> (quadratic types)
Open
100
General solutions where f(x) = kx (linear types)
Open
101
General solutions where f(x) = k (constant types)
Open
102
How to solve second order linear differential equations that equal zero
Open
103
Using substitution to reduce a differential equation to a known form
Open
104
Solving equations of the form dy/dx + Py = Q using an integrating factor
Open
105
Exact equations where one side is the exact derivative of a product
Open
106
Separating the variables and sketching a family of curves
Open
107
Working with constants in log types
Open
108
Differential Equations – Finding a general and a particular solution
Open
109
Using complex numbers to represent regions on an Argand diagram
Open
110
The locus of a point moving along a half-line
Open
111
The locus of a point moving along a perpendicular bisector
Open
112
The locus of a point moving in a circle
Open
113
nth roots of a complex number
Open
114
De Moivre’s theorem
Open
115
Multiplication and division rules for mod and argument of two complex numbers
Open
116
Exponential Form (Euler’s relation)
Open
117
Method of differences
Open
118
Matrix proofs
Open
119
Divisibility and multiple test proofs
Open
120
Proof for other series
Open
121
Proof of the sum of the series ∑r³
Open
122
Proof of the sum of the series ∑r²
Open
123
Proof of the sum of the series ∑r
Open
124
Using known formulae to sum more complex series
Open
125
Sum of the cubes of the first n natural numbers ∑r<sup>3</sup>
Open
126
Sum of the squares of the first n natural numbers ∑r<sup>2</sup>
Open
127
Determinant as the area scale factor of a transformation
Open
128
Inverse matrices to reverse linear transformations
Open
129
Combinations of transformations
Open
130
How well do you know your transformations?
Open
131
Linear transformations – enlargement
Open
132
Linear transformations – reflections
Open
133
Linear transformations – rotations
Open
134
Solving simultaneous linear equations in 2 unknowns
Open
135
Sum of the first n natural numbers ∑r and the results for ∑a and ∑(ar+b)
Open
136
Identity and Inverse of a 2×2 matrix
Open
137
Matrix multiplication
Open
138
Addition and subtraction and multiplying a matrix by a scalar
Open
139
Introduction and dimension of a matrix
Open
140
Solving problems with complex numbers
Open
141
Modulus and argument of a complex number
Open
142
Argand diagrams
Open
143
Division of a complex number by a complex number
Open
144
Complex conjugates
Open
145
Addition, subtraction and multiplying complex numbers and simplifying powers of i
Open
146
Real and imaginary numbers
Open
147
Closest point to a line and shortest distance from the origin
Open
148
Intersecting and skew lines
Open
149
Parallel lines
Open
150
Angle between two lines
Open
151
Vector equation of a line
Open
152
Perpendicular vectors
Open
153
Scalar product
Open
154
Differential Equations – Exponential and trig type
Open
155
Volume of revolution for a curve given in parametric form
Open
156
Volume of revolution about the x-axis
Open
157
Integrals involving partial fractions
Open
158
Improper types
Open
159
Sigma notation
Open
160
Exam Questions – Expressing sin(nθ) and cos(nθ) in terms of sinθ and cosθ
Open
161
Expressing sin(nθ) and cos(nθ) in terms of sinθ and cosθ
Open
162
Expressing sin<sup>n</sup>θ and cos<sup>n</sup>θ in terms of sin(kθ) and cos(kθ)
Open
163
General solutions where f(x) = λ cosωx + µ sinωx (trig types)
Open
164
Solving the differential equation: ẍ = – ω<sup>2</sup>x
Open

Oh … No … A Popup!

Don’t worry, we are not after anything, but remember what these icons mean. If you forget, then just click an icon to get this popup back again.

Calculator: YesCalculator allowed
Calculator: NoNon-calculator question
Difficulty: EasyEasier
Difficulty: MediumHarder
Difficulty: HardChallenging
AXI ANSWER DOOR
Answer it in the app - Axi marks your working
Every lesson ends in a question you answer on the platform - maths keyboard or a photo of written work. Hints from Axi, our AI tutor, are free; marking uses one practice credit, always shown first.
Answer in app Ask Axi