# Mathematics Of Data Management – Grade 12

This course broadens students’ understanding of mathematics as it relates to managing data. Students will apply methods for organizing and analyzing large amounts of information; solve problems involving probability and statistics; and carry out a culminating investigation that integrates statistical concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. Students planning to enter university programs in business, the social sciences, and the humanities will find this course of particular interest.

From: $500.00

### Overall curriculum expectations

**Rate of Change**

By the end of this course, students will:

**Counting and Probability **

• 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.

**Probability Distributions **

• 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.

**Organization of Data for Analysis **

• 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.

**Statistical Analysis **

• analyse, interpret, and draw conclusions from one-variable data using numerical and graphical summaries;

• analyse, interpret, and draw conclusions from two-variable data using numerical, graphical, and algebraic summaries;

• demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.

**Culminating Data Management Investigation **

• design and carry out a culminating investigation* that requires the integration and application of the knowledge and skills related to the expectations of this course;

• communicate the findings of a culminating investigation and provide constructive critiques of the investigations of others.

### Outline of Course Content

Unit | Title | Time |

1 | Probability | 12 hours |

2 | Permutations | 14 hours |

3 | Combination | 14 hours |

4 | Probability Distribution for Discrete Variable | 10 hours |

5 | Probability Distribution for Continuous Variable | 13 hours |

6 | Organization Data for Analysis | 15 hours |

7 | Statistics: One Variable Data Analysis | 15 hours |

8 | Statistics: Two Variables Data Analysis | 10 hours |

9 | Culminating Task | 5 hours |

Final Examination | 2 hours | |

Total | 110 hours |

### Course Details

Course Code | MHF4U |

Course Type | University Preperation |

Format | Online School Course |

Prerequisite | MCR3U or MCT4C |

Tuition Fee | 650 – 1300 |

Department | Mathematics |

Course Title | Advanced Functions |

Grade | Grade 12 |

Credit Value | 1.0 |

### Overall Curriculum Expectations

**Exponential and logarithmic functions **

By the end of this course, students will:

- Demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions.
- Identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically.
- Solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.

**Trigonometric Functions**

By the end of this course, students will:

- Demonstrate an understanding of the meaning and application of radian measure.
- Make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals and use these connections to solve problems.
- Solve problems involving trigonometric equations and prove trigonometric identities.

**Polynomial and Rational Functions**

By the end of this course, students will:

- Identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions.
- Identify and describe some key features of the graphs of rational functions and represent rational functions graphically.
- Solve problems involving polynomial and simple rational equations graphically and algebraically.

Demonstrate an understanding of solving polynomial and simple rational inequalities.

**Characteristics of Functions**

By the end of this course, students will:

- Demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point.
- Determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems.
- Compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.

### Outline of Course Content

Unit | Title | Time |

1 | Polynomial Functions | 15 hours |

2 | Polynomial Equations and Inequalities | 15 hours |

3 | Rational Functions | 13 hours |

4 | Trigonometry | 13 hours |

5 | Trigonometric Functions | 13 hours |

6 | Exponential and Logarithmic Functions | 13 hours |

7 | Tools and Strategies for Solving Exponential and Logarithmic Equations | 13 hours |

8 | Combining Functions | 13 hours |

Final Examination | 2 hours | |

Total | 110 hours |