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Day 151
Explain what qualifies an expression as a rational expression. Give two examples of rational expressions.
Day 152
Explain the process of simplifying rational expressions. You may want to use the expression 10x + 20x as an example.
Day 153
Describe a situation in which a rational expression is undefined, and explain why this occurs in some cases. Give a specific example of why this happens.
Day 154
How do you know when to rationalize a radical expression.
Day 155
You know that two sides of a right triangle measure 10in. and 8in. Is this enough information to find the length of the third side? Give two different possible values of the third side. Explain how you found your answers.
Day 156
Explain how you can determine whether a triangle is a right triangle if you know the lengths of the three sides.
Day 157
Determine the prime factors of 30 and explain why 30 is in simplest form.
Day 158
Explain how the Pythagorean Right -Triangle theorem and the Distance Formula are related. Graph the coordinates (3,2) (7,2) and (7,5), and use the diagram to support your answer.
Day 159
Write a problem about your commute to and from school that requires the distance formula to solve. Then solve the problem.
Day 160
The measures of the angles of a triangle can be three consecutive integers. They can also be three consecutive even integers. Can the measures of the angles of a triangle be three consecutive odd integers? Explain your reasoning.
Days 161-169
Day 170
You are a chemist designing a new molecule. You want the molecule to have a large surface area for a relatively small volume so that it will dissolve quickly in water. What shape would you choose for your molecule? Explain your choice. You may want to include a diagram.
Day 171
Explore the possibilities of expanding a cylinder. What happens to the volume of a cylinder when you increase the height? What happens to the volume when you increase the radius? Which of these adjustments increases the volume the most? For your exploration, consider the cylinders in the table.
Cylinders
Radius Height 2 2 2 4 4 2 Day 172
Explain how two different rectangular prisms can have the same volume but different surface areas. Find two prisms that this is true. Include diagrams and dimensions of these prisms.
Days 173 - 179
Day 180
Now that you have completed this algebra course, reflect on what you've learned. Write a short essay describing your experiences with algebra in and out of the classroom. You may wish to include the following:
- the most interesting or the most important concepts that you learned
- the most difficult or challenging section of the course
- uses of algebra in other classes or in your daily life
- how your algebraic skills may help you in the future