My NAME is:
Problem: | 1 | 2 | 3 | 4 | Total |
Score: | | | | | |
MAT 301
Foundations of Secondary School Mathematics
Midterm 1
October 23, 2001
Show all your work on these pages! Total score = 100
- (25 points) Write a careful proof of the irrationality of
the square root of 7.
- (25 points)
- Write 1.234523452345..(2345 repeats) as a rational number
in the form p/q, p,q integers.
- Prove or give a counterexample: A real number has a repeating
binary ``decimal'' expansion if and only if it is a rational.
- (25 points)
- Use the geometric interpretation of complex multiplication
to locate i3 in the complex plane.
- Use the geometric interpretation of complex
multiplication to locate the three cube roots of 8i.
- (25 points)
- Calculate the inverse of the matrix
[4 3]
[2 2]
- Use this inverse to solve the system of equations:
4x + 3y = 1
2x + 2y = 2