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The document outlines key topics in mathematics, mechanics, and statistics, including proof techniques, algebra, trigonometry, differentiation, and integration in mathematics; kinematics and forces in mechanics; and statistical sampling, data presentation, and probability in statistics. Each section contains specific concepts and methods such as Newton's laws, regression lines, and hypothesis testing. The content serves as a comprehensive guide for understanding fundamental principles across these subjects.

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Sarah Daisy
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16 views3 pages

Text

The document outlines key topics in mathematics, mechanics, and statistics, including proof techniques, algebra, trigonometry, differentiation, and integration in mathematics; kinematics and forces in mechanics; and statistical sampling, data presentation, and probability in statistics. Each section contains specific concepts and methods such as Newton's laws, regression lines, and hypothesis testing. The content serves as a comprehensive guide for understanding fundamental principles across these subjects.

Uploaded by

Sarah Daisy
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as TXT, PDF, TXT or read online on Scribd
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Maths

Pure
◦ 1: Proof
◦ Proof by deduction
◦ Proof by exhaustion
◦ Proof by counter example
◦ 2: Algebra and functions
◦ Laws of indices
◦ Surds
◦ Quadratic functions and graphs
◦ Discriminant
◦ Complete the square
◦ Binomial expansion
◦ Binomial estimation
◦ Algebraic division and Factor theorem
◦ Solving quadratic equations
◦ Simultaneous equations
◦ Solve linear and quadratic inequalities and interpret graphically
◦ Bracketed and franctional inequalities
◦ Proportionality
◦ Graph transformations
◦ Completing the square
◦ Discriminant
◦ 3: Coordinate geometry in (x,y) plane
◦ Different graphs
◦ Straight line graphs and equations
◦ Gradients
◦ Parallel; and perpendicular lines
◦ Midpoints and perpendicular bisectors
◦ Length between points and area
◦ Circles
◦ Graph intersections
◦ Graph transformations
◦ Graphical inequalities
◦ Tangents and normals
◦ 4: Sequences and series:
◦ Binomial expansion
◦ Sigma notation
◦ Arithmetic sequences (nth term)
◦ 5: Trigonometry
◦ Sin and cosine rules
◦ Area of triangle
◦ Identities
◦ Double angle formulae
◦ Trigonometric equations
◦ Trigonometric proof
◦ Trigonometric graphs and transformations
◦ 6: Exponentials and logarithms
◦ Logarithms
◦ Exponentials
◦ Ln and e
◦ 7: differentiation
◦ Graphical application
◦ Second derivatives
◦ First principles
◦ Stationary points
◦ 8: Integration
◦ Simple integration
◦ Integrals for area of curve
◦ Lim
◦ Fractional integration
◦ 9: Numerical methods
◦ Solve equations with Newton-Raphson method
◦ Problem solving questions
◦ 10: Vectors
◦ 2D vectors
◦ 3D vectors
◦ Magnitude of vector
◦ Parallel vectors
◦ Position vectors
◦ Distance between 2 points
Mechanics
◦ 1: Quantities and units in mechanics
◦ SI units
◦ Velocity, acceleration, force, weight, moment
◦ 2: Kinematics
◦ Position, displacement, distance travelled, velocity, speed,
acceleration
◦ Velocity-time graphs
◦ Displacement-time graphs
◦ Vectors in mechanics (I and j)
◦ Calculus
◦ Differentiation and integration
◦ Projectiles
◦ 3: Forces and Newton’s Law
◦ Newton’s first law
◦ Newton’s 2nd law - resolving forces
◦ Movement of particle under gravity
◦ Newton’s 3rd law - equilibrium of forces
◦ Resultant forces
◦ Friction
◦ 4: Moments
◦ Simple moments
Statistics
◦ 1: Statistical sampling
◦ Definitions
◦ Critique an experiment
◦ 2: Data presentation and interpretation
◦ Histograms
◦ Scatter diagrams
◦ Regression lines for bivariate data
◦ Correlation
◦ Standard deviation
◦ 3: Probability
◦ Mutually exclusive and independent events
◦ Vent diagrams
◦ Conditional probability
◦ Two-way tables
◦ Tree diagrams
◦ 4: Statistical distribution
◦ Simple, discrete probability distributions ( binomial distribution)
◦ Normal distribution
◦ 5: Hypothesis testing
◦ correlation coefficients
◦ P value
◦ Hypothesis testing and rejection (null hypothesis)

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