Playlist for Core Maths / Pure Maths
Other Playlists and Main Index
Algebra and Functions
- Introduction
- Multiplication rule 1
- Multiplication rule 2
- Division
- Negative indices
- Fractions to negative indices
- Fractional type
- Simplifying (negative powers)
- Expressing terms in the form axn
- Exam questions
- multiplication rule
- combining and simplifying
- division rule
- rationalising
- surds on a calculator
- Exam questions
Functions
- Introduction
- HCF types
- Grouping types
- Miscellaneous Exercise
- Exam questions
- How to do it
- Exam questions
- Equations
Graph Transformations
- Learn these base graphs
- Translations
- Reflections
- Stretches
- Exam Questions on transformations
- Elimination method for linear types
- Examples :
- 1 | 2 | 3 | 4 | 5 (method 1) | 5 (method 2)
- Examples :
- Substitution Method for linear and quadratic types
- Exam Questions
Coordinate geometry (1)
- Naming the sides
- Trig ratios sinθ, cosθ and tanθ
- Finding a length (1)
- Finding a length (2)
- Finding an angle
- Trig. ratios for 30, 60 and 90 degrees
- Trig. ratios for 45, 45 and 90 degrees
- Trig. ratios for positive multiples of 30, 45 and 60 degrees
- Trig. ratios for negative multiples of 30, 45 and 60 degrees
Applications
- Area of a triangle
- Sine Rule
- Cosine Rule
- Arcs, Sectors and Segments
- Exam questions
- The quadrant rule
- Equations that factorise
- Two basic trigonometric identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1
- The identities: cos(θ) ≡ cos(-θ), sin(θ) ≡ -sin(-θ)
- Solving equations using identities
- Exam questions
Introduction
- The gradient function dy/dx
- terms of the form axn
- Second Derivatives
- Exam Questions
- Tangents and normals
- Exam Questions
Introduction
Equations of curves
Algebra and Functions (2)
- What do we mean by a log?
- Rules of logs
- Simplifying
- Equations
- Solving equations 1
- Solving equations 2
- Change of base type
- Solving equations 4
- Inequalities
- Exam questions
Transformations of Graphs (Revision)
- Translations y = f(x ± a ) and y= f(x)± a
- Reflections y = - f(x) and y = f(-x)
- Stretches y = a f(x)
- Stretches y = f (ax)
- Exam Questions
- The modulus function
- Graph y=|f(x)|
- Graph y=f(|x|)
- Modulus Equations
- Modulus Inequalities
Modelling Curves of the form y=kxn and y=kax
- Converting to linear form
- numerical example still to come
Trigonometry (2)
Secant, Cosecant and Cotangent
- Pythagorean type: sin²x + cos²x ≡1 ; 1 + tan²x ≡ sec²x ; 1 + cot²x ≡ cosec²x
- Addition type: sin(A±B), cos(A±B) and tan(A±B)
- Addition Formulae (compound angles)
- Using the formulae to get exact values:
- Proving identities :
- Double angle type for sin2A, cos2A and tan2A
- Double angle formulae
- Half angles
- Applications - Triple angles
- Factor Formulae
- A cos x ± B sin x and A sin x ± B cos x type
- the identities for A cos x ± B sin x and A sin x ± B cos x
- Examples : 1 and 2
Miscellaneous Exam Practice
Numerical methods
Algebra and Series (2)
Coordinate Geometry (2)
Differentiation(3)
The exponential functions : ex, eax and e(ax+b)
Reciprocal Functions : 1/x and 1/(ax+b)
Integrals of the form : f'(x)/f(x)
Integrals of the form : f'(x)ef(x)
- sin x, cos x, sec² x
- sin(ax+b), cos(ax+b), sec² (ax+b) types
- Identity types
- sin² x types
- cos² x types
- Exam Questions
- Substitution 1
- Substitution 2
- Substitution 3a
- Substitution 3b
- Substitution 4 (trig types)
- Substitution 5 (exponential types)
- Substitution 6 (using limits)
- Substitution 7 (trig type with limits)
- Exam Questions
Mixed examples
Applications
- Separating the variables
- Forming differential equations
- What is a vector and a scalar quantity?
- Notation
- Position vectors
- Equal and negative vectors
- Addition and subtraction of vectors
- Magnitude of a 2 dimensional vector
- Unit vectors
- Magnitude of a 3 dimensional vector
- Vector equation of a line
- Angle between two lines
- Parallel lines
- Intersecting and skew lines
- Closest point to a line and shortest distance from the origin
Exam Questions