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Mathematical Studies – Standard Level
Mathematical Studies – Standard Level
Stuart the ExamSolutions Guy
2016-09-27T22:24:52+00:00
Mathematical Studies – Standard Level
Prior Knowledge
Surds
Surds - introduction & simplifying
Addition and subtraction of surds
Multiplying surds
Dividing surds
Rationalising surds
Exam Questions - Surds
Number
Approximations and errors
Types of number
Approximations and error
Standard Form (Scientific Notation)
Expressing a number in standard form or scientific form
SI units of measurement
Money Problems
Currency conversions
Compound interest
Representing Data
Descriptive statistics
Using a graphical display calculator for descriptive statistics
Coordinate Geometry
Gradient
Line segment
Parallel lines
Perpendicular lines
Lines
Equation of a straight line: y=mx+c
Distance between two points
Mid-point of a line segment
Equation of a parallel line
Equation of a perpendicular bisector
Trigonometry
Trigonometry: Right-Angled Triangles
Introduction to trigonometry
Finding the length of a side
Finding an angle
Applications of Trigonometry
Sine rule
Exam Questions - Sine rule
Cosine rule
3D Trigonometry and Geometry
Geometry of three-dimensional solids
Distance between points in a solid
Angles between two lines, or between a line and a plane
The Normal Distribution
The Normal Distribution
The normal distribution
The standard normal distribution Z~N(0,1) - Using tables or calculator
Calculating probabilities from a normal distribution
Correlation and Linear Regression
Correlation
Correlation
Product moment correlation coefficient (pmcc)
Exam Questions - Correlation
Regression
Regression
Interpreting the regression line constants, explanatory and response variables
Making predictions and reliability of predicted values
Exam Questions - Regression
Hypothesis Tests
Hypothesis Tests – Contingency Tables
Chi squared test for contingency tables
Differentiation
Differentiation – Introduction
The gradient function dy/dx
Differentiation - terms of the form ax
^{n}
The second derivative
Exam Questions - Differentiation: introduction
Tangents and Normals
Equations of tangents and normals
Exam Questions - Tangents and normals
Stationary Points
Stationary points
Nature of a stationary point
Exam Questions - Stationary points
Applications of stationary points
Exam Questions - Applications of stationary points
Sequences and Series
Working with Sequences and Series
Definition and finding the nth term
Sigma notation
Exam Questions - Sigma notation
Arithmetic Progressions
Arithmetic progressions
Sum of the first n terms
Exam Questions - Arithmetic sequences and series
Examsolutions Beastie - Arithmetic progressions
Geometric Series
Geometric series
Proof of sum of first n terms, S
_{n}
Sum to infinity
Exam Questions - Geometric series
Probability
Possibility Space (Sample Space)
Possibility space diagrams
Tree Diagrams
Probability tree diagrams
Combining probabilities
Conditional probability in tree diagrams
Exam Questions - Tree diagrams
Venn Diagrams
Venn diagrams
Probability in Venn diagrams
Conditional probability in Venn diagrams
P(A∪B) and mutually exclusive events
Independent, Dependent and Mutually Exclusive Events
Independent, dependent and mutually exclusive events
Logic
Logic
Introduction to logic
Compound statements and symbols
Truth tables : negation
Truth tables : conjunction (and)
Truth tables : resolving an ambiguity - the 'or' connective
Logical equivalence, tautologies and contradictions
Compound statements made up from three simple statements
Arguments