MTEL Math Practice Test: 31-35 | Summary and Q&A

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December 16, 2009
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Khan Academy
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MTEL Math Practice Test: 31-35

TL;DR

Analyze and solve math problems involving race distances, circle properties, volume calculations, and tiling floors.

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Key Insights

  • 🐎 Speed and time are related to distance calculations in the first problem.
  • 🛩ī¸ Dividing a circle into smaller sections can help approximate its area and perimeter as a rectangle.
  • 🔇 Changing the radius of a cylinder greatly affects its volume.

Transcript

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Questions & Answers

Q: How does the assumption of the same average speed affect the solution to the first problem?

The assumption is crucial in determining the time required for each car to finish the race and helps calculate the distance traveled by the blue car.

Q: What does dividing the circle into wedges and approximating it as a rectangle demonstrate?

Dividing the circle into wedges allows us to show that the area of the circle (rectangle) is equal to half the circumference multiplied by the radius.

Q: How does the radius change in the third problem affect the volume of the new container compared to the old one?

Doubling the radius leads to an increase in volume by a factor of eight, as the volume of a cylinder is directly proportional to the square of the radius.

Q: How can we calculate the number of tiles needed to cover the floor?

By dividing the dimensions of the room by the dimensions of the tiles, we can determine the number of tiles required in each direction and then multiply them together to get the total number of tiles.

Summary & Key Takeaways

  • In the first problem, two cars race a distance of 100 miles, with the red car finishing before the blue car. The average speed of both cars is assumed to be the same.

  • The second problem discusses the relationship between the circumference, radius, and area of a circle. By dividing the circle into wedges, it can be approximated as a rectangle.

  • The third problem involves comparing the volume of two cylindrical containers with different dimensions to determine the change in volume.

  • The fourth problem requires calculating the number of carpet tiles needed to cover a room based on its dimensions.

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