Mathematics for Data Management
Grade 12, University Preparation (MDM4U)

 

CourseTitle: Mathematics for Data Management, Grade 12,
University Preparation (MDM4U)

CourseName: Mathematics for DataManagement

CourseCode: MDM4U

Grade: 12

CourseType: University Preparation

CreditValue: 1.0

Prerequisite: Functions, Grade 11, University Preparation or
Functions and Applications – Grade 11, University or
CollegePreparation

Course Description
 
This course extends students’ experience with functions. Students will investigate the propertiesof polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidatetheir understanding of mathematics before proceeding to any one of a variety of universityprograms.
Outline of Course Content
 

Unit

Titles and Descriptions

Time and Sequence

Unit 1

Solving Problems with Matrices and Graphs

 

In this unit students will demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data; describe the characteristics of a good sample, some sampling techniques, and principles of primary data collection, and collect and organize data to solve a problem; demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.

16 hours

Unit 2

Permutations and organized counting

 

Combinatorics is the branch of mathematics dealing withideas andmethodsforcounting,especiallyincomplexsituations.The techniques and mathematical logic for counting possible arrangements or outcomes are useful for a wide variety of applications. A computer programmer writing software for a game or industrial process would use these techniques,as would a basketball coach planning potential line-ups for a game, or a school board trying to make the most efficient use of its buses. In this unit students will demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data; describe the characteristics of a good sample, some sampling techniques, and principles of primary datacollection, and collect and organize data to solve aproblem.

16 hours

Unit 3

Combinations and Binomial Theorem

In this unit students will solve problems involving the probability of an event or a combination of events for discrete sample spaces; solve problems involving the application of permutations and combinations to determine the probability of an event. The Binomial Theorem is an important formula giving the expansion of powers of sums. This formula and the triangular arrangement of the binomial coefficients are often attributed to Pascal who described them in the 17th century. This triangle is referred to as Pascal's Triangle. Pascal's method for building his triangle is a simple iterative process similar to those described in Unit 1. Pascal made the triangle famous by finding many applications for it. In this unit students will demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications using the Binomial theorem and Pascal's triangle.

 

Unit 4

Introduction to Probability

In this unit students will solve problems involving the probability of an event or a combination of events for discrete sample spaces; solve problems involving the application of permutations and combinations to determine the probability of an event; demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications; demonstrate an understanding of continuous probability distributions, make connections to discrete probability distributions, determine standard deviations, describe key features of the normal distribution, and solve related problems from a variety of applications.

24 hours

Unit 5

Probability Distribution

In this unit students will solve problems involving the probability of an event or a combination of events for discrete sample spaces; solve problems involving the application of permutations and combinations to determine the probability of an event; demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications; demonstrate an understanding of continuous probability distributions, make connections to discrete probability distributions, determine standard deviations, describe key features of the normal distribution, and solve related problems from a variety of applications.

12 hours

Unit 6

Normal Distribution

 

This unit will cover three discrete probability distributions:

 

·         the binomialdistribution

·         the normaldistribution

·         the standard normaldistribution

 

Students will solve problems involving the probability of an event or a combination of events for discrete sample spaces; solve problems involving the application of permutations and combinations to determine the probability of an event; demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications; demonstrate an understanding of continuous probability distributions, make connections to discrete probability distributions, determine standard deviations, describe key features of the normal distribution, and solve related problems from a variety of applications.

 

 

Culminating Project

8 hours

 

Final Evaluation

The final assessment task is a three hour exam worth 30% of the student’s final mark.

3 hours

 

Total

110 hours