Mathematics is filled with claims that are too often given to students as truths, with no justification. Sometimes this is because the mathematics needed for a justification is not yet understood by the student, or the person handing out the claim does not know the justification themselves.
Can you pass this test...by proving that the these ten common mathematics claims are valid?
Claim 1: For a circle, C = 2(pi)r.
Claim 2: For a fixed perimeter, the circle encloses the maximum area.
Claim 3: If two lines are perpendicular, their slopes are negative reciprocals of each other.
Claim 4: The number e is irrational (and if you want to push further, prove that e is transcendental).
Claim 5: ei(pi)+1 = 0.
Claim 6: The volume V of a cone is (1/3)(base's area)(height).
Claim 7: It is possible for the probability of event E to equal 0, yet occur.
Claim 8: Graph y = 1/x, starting at the x = 1. When that graphed line is rotated around the x-axis, the shape produced (Gabriel's Horn) has a finite volume and an infinite surface area.
Claim 9: All parabolas are similar.
Claim 10: Multiplying a complex number by i involves only a 90° counterclockwise rotation about the origin.
Hint: Feel free to ask others...search on-line...whatever it takes for you to produce an justification.
Solution Commentary: Hope you were successful....now proceeed to search out justifications for any other mathematics claims you confront or use.