Evaluate 12 – 22 + 32 – 42 + 52 – 62 + … + 1992.
Pre-Calculus
Minimize Sum of Distances
Given points P (-1,-2) and Q (4,2) in the xy-plane, point R (1,m) is taken so that
- -3/5
- -2/5
- -1/5
- 1/5
- either -1/5 or 1/5
Arithmetic Mean of Logs
Log with Radical Base
Find x if , (note that
is the base of the logarithm).
Log Equation Becomes Quadratic
For what values of x is the following statement true?
log42x2 = 1 – log422x – 1
- -2, 4
- 2, -4
- -1, -3
- 1, 3
- 1,-3
Numerical Log Problem
If a = log8225 and b = log215, then what’s a in terms of b?
- a = b/2
- a = 2b/3
- a = b
- b = a/2
- a = 3b/2
Logs Base x and Base x2
If logx10 + logx2 10 = 10, and if x = 10k, what’s k?
- 1/10
- 1/5
- 3/20
- 2/5
- None of these
Find f(x+1) – f(x)
Hard Functional Equation, f(n) = n
The function f satisfies the functional equation
f(x) + f(y) = f(x + y) – xy – 1
for every pair x, y of real numbers. If f(1) = 1, then the number of positive integers n for which f(n) = n is:
- 0
- 1
- 2
- 3
- infinite
Sequence Formula
Consider the numbers Fn defined by the following formula:
![](/odmp/files/2019/08/2580-61img1.jpg)
where n may be any positive integer. Calculate F1 through F5. Do you notice anything suprising?