Learning Resources
Outcomes
By the end of this lesson you will be able to answer questions like the ones in the pre-test below.
Approach #1
Answer the questions on the pre-test below in your Math 3103 binder. Then refer to the pages of the lesson that contain instruction on the questions you were unable to do, for which you got an incorrect answer, or for which you would like some further explanation.
Approach #2
Proceed directly to the first page of the lesson without attempting the pre-test. To do this simply click on the Lesson button above. You can then return to this pre-test later and use it as a worksheet.
Pre-test
1. The length of a rectangle is x units and its width is y units, as shown in the diagram below.
(a) Express the area, A, as a function of the length and width.
(b) If the length is twice the width, express the area, A, as a function of: (i) the width , (ii) the length.
2. A box has a square base, x metres on a side, and a height of y metres, as shown in the diagram below.
(a) Express the volume, V, as a function of x and y.
(b) If the total surface area of the box is 6 m2 , express the volume as a function of x.
3. In the diagram below, the vertices of the rectangle ABCD are on the x-axis and on the parabola.
(a) Express the area, A, of the rectangle ABCD as a function of x and y.
(b) If the equation of the parabola is y = 12 - x2 , express the area A as a function of x.
Students will be expected to:
- Rearrange formulas to solve for any variable.
- Simplify problem situations involving functions of two or more variables to functions of one variable.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- How to rearrange formulas and solve for any given variable.
- The formulas for the surface area and volume of various geometric solids.
- How to substitute an expression into an equation.