Mathematical Studies – Standard Level

Prior Knowledge

Surds

  1. Surds - introduction & simplifying
  2. Addition and subtraction of surds
  3. Multiplying surds
  4. Dividing surds
  5. Rationalising surds
  6. Exam Questions - Surds

Number

Approximations and errors

  1. Types of number
  2. Approximations and error

Standard Form (Scientific Notation)

  1. Expressing a number in standard form or scientific form
  2. SI units of measurement

Money Problems

  1. Currency conversions
  2. GCSE Compound interest

Representing Data

Descriptive statistics

  1. Using a graphical display calculator for descriptive statistics

Coordinate Geometry

Gradient

  1. Line segment
  2. Parallel lines
  3. Perpendicular lines

Lines

  1. Equation of a straight line: y=mx+c
  2. Distance between two points
  3. Mid-point of a line segment
  4. Equation of a parallel line
  5. Equation of a perpendicular bisector

Trigonometry

Trigonometry: Right-Angled Triangles

  1. Introduction to trigonometry
  2. Finding the length of a side
  3. Finding an angle

Applications of Trigonometry

  1. Sine rule
  2. Exam Questions - Sine rule
  3. Cosine rule

3D Trigonometry and Geometry

  1. Geometry of three-dimensional solids
  2. Distance between points in a solid
  3. Angles between two lines, or between a line and a plane

The Normal Distribution

The Normal Distribution

  1. The normal distribution
  2. The standard normal distribution Z~N(0,1) - Using tables or calculator
  3. Probabilities from a normal distribution using tables
  4. Sampling distribution of the sample means (Normal distribution)
  5. Sampling distribution of the sample means (Normal distribution) proof
  6. Introduction to Hypothesis testing for Normal distribution
  7. Hypothesis testing for Normal distribution (One tailed and 2 tailed test)
  8. Understanding Critical values (Hypothesis testing for Normal Distribution)
  9. Hypothesis testing for Normal Distribution - Critical values method (3 examples)

Correlation and Linear Regression

Correlation

  1. Correlation
  2. Product moment correlation coefficient (pmcc)
  3. Exam Questions - Correlation

Regression

  1. Regression
  2. Interpreting the regression line constants, explanatory and response variables
  3. Making predictions and reliability of predicted values
  4. Exam Questions - Regression

Hypothesis Tests

Hypothesis Tests – Contingency Tables

  1. Chi squared test for contingency tables

Differentiation

Differentiation – Introduction

  1. The gradient function dy/dx
  2. Differentiation - terms of the form axn
  3. The second derivative
  4. Exam Questions - Differentiation: introduction

Tangents and Normals

  1. Equations of tangents and normals
  2. Exam Questions - Tangents and normals

Stationary Points

  1. Stationary points
  2. Nature of a stationary point
  3. Exam Questions - Stationary points
  4. Applications of stationary points
  5. Exam Questions - Applications of stationary points

Sequences and Series

Working with Sequences and Series

  1. Definition and finding the nth term
  2. Sigma notation

Arithmetic Progressions

  1. Arithmetic progressions
  2. Sum of the first n terms
  3. Exam Questions - Arithmetic sequences and series
  4. Examsolutions Beastie - Arithmetic progressions

Geometric Series

  1. Geometric series
  2. Proof of sum of first n terms, Sn
  3. Sum to infinity
  4. Exam Style Questions - Geometric Series and Progressions
  5. Exam Questions - Geometric series

Probability

Possibility Space (Sample Space)

  1. Possibility space diagrams

Tree Diagrams

  1. Tree Diagrams
  2. Probability Tree Diagrams for Independent Events
  3. And Rule (multiplication) / Or Rule (addition for mutually exclusive events)
  4. Probability Tree Diagrams for Dependent Events
  5. Conditional probability in tree diagrams
  6. Exam Questions - Tree diagrams

Venn Diagrams

  1. Venn diagrams
  2. Probability in Venn diagrams
  3. Conditional probability in Venn diagrams
  4. P(A∪B) and mutually exclusive events

Independent, Dependent and Mutually Exclusive Events

  1. Independent, dependent and mutually exclusive events

Logic

Logic

  1. Introduction to logic
  2. Compound statements and symbols
  3. Truth tables : negation
  4. Truth tables : conjunction (and)
  5. Truth tables : resolving an ambiguity - the 'or' connective
  6. Logical equivalence, tautologies and contradictions
  7. Compound statements made up from three simple statements
  8. Arguments