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- Mathematics: Applications of Mathematics: Grade 12

# Yukon Territory - Mathematics: Applications of Mathematics: Grade 12

## Learning Outcomes | Adopted: 2006

### A: : Students identify the types and functions of insurance, the preparation of a personal financial plan, the types of taxes imposed by different levels of government, and the costs associated with foreign purchasing and currency exchange.

A.1: : model and solve problems, including those solved previously, using technology to perform matrix operations, including

A.1.1: : addition

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview

A.6: : analyse an investment portfolio applying such concepts as interest rate, rate of return, and total return

Compound Interest

Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

### B: : Students use patterns to describe the world and to solve problems.

B.1: : describe sinusoidal curves using terms, including

B.1.1: : amplitude

Translating and Scaling Functions

Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview

Translating and Scaling Sine and Cosine Functions

Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview

B.1.2: : period

Translating and Scaling Functions

Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview

Translating and Scaling Sine and Cosine Functions

Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview

B.1.4: : vertical and horizontal shift

Translating and Scaling Functions

Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview

Translating and Scaling Sine and Cosine Functions

Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview

### C: : Students describe and compare everyday phenomena, using either direct or indirect measurement, describe the characteristics of 3-D objects and 2-D shapes, and analyse the relationships among them.

C.1: : use dimensions and unit prices to solve problems involving perimeter, area, and volume

Area of Triangles

Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview

Perimeter and Area of Rectangles

Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview

Prisms and Cylinders

Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview

C.5: : use appropriate terminology to describe

C.5.1: : vectors (i.e., direction, magnitude)

Adding Vectors

Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview

Vectors

Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview

### D: : Students use experimental and theoretical probability to represent and solve problems involving uncertainty.

D.1: : classify events as independent or dependent

Independent and Dependent Events

Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview

Correlation last revised: 9/16/2020

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