Solving A Hard SAT Math Problem

One of the more difficult math problems in the Official SAT Study Guide 2nd Edition is on page 527 # 8

The Question:
(x-8)(x-k) = x²-5kx + m
In the question above, k and m are constants. If the equation is true for all values of x, what is the value of m?

The Solution:
Step 1 FOIL the left side so that x² -8x + 8k – kx = x² - 5kx + m
Step 2 add kx to both sides so x² -8x + 8k = x² -4kx + m
Step 3 subtract x² from both sides so -8x + 8K = -4kx + m
Step 4 we know that -8x must equal – 4kx so solve for k as follows:
Divide both sides by x so -8 = -4k; k=2
Step 5 we also know that 8k = m; so 8 (2) = 16; choice B

New SAT Study Guide

The Wall Street Journal is reporting that the Collegeboard will revise its Official SAT Study Guide this summer. The Official SAT Study Guide has remained virtually unchanged since its original publication in 2004 to reflect the new SAT format which began testing in March 2005. The Official SAT Study Guide currently includes 8 simulated SAT tests. The new and revised guide will feature 3 actual SAT tests along with 7 simulated tests for a total of 10 practice tests.

Understanding Compound Percent Problems

Most of my student's parents were sold a bill of goods from their financial advisors who were either ignorant or stupid. I will give them the benefit of the doubt and call them ignorant. After suffering losses of 80% on a stock market investment in 2008, they were told not to sell because their stocks will eventually come back. Everyone with massive losses dreams that their investments will someday come back. Let's fantasize that the same stock which declined by 80% in 2008 increases in value by 100% in 2009. You would then be ahead 20% right? Wrong!!!! Never ever add or subtract percent increases or decreases on the SAT or in life.

The correct way to deal with the above compound percent problem is as follows:

1. Assign a theoretical value for our stock--I like to use $100 when dealing with percent.
2. At the end of 2008 our stock is now worth $20 (an 80% decline)
3. At the end of 2009 our stock is now worth $40 (a 100% increase)

Therefore our two year return is minus 60% not a gain of 20%---So the Rule here is when dealing with compound percent problems start with 100 and work your way up or down step by step. For additional practice try p. 491 problem #13 from the Official SAT Study Guide.

Book Review-- Hack the SAT

I am always on the lookout for new and innovative study aids. For the advanced student who is taking the SAT this coming October for the second or third time, I recommend "Hack The SAT" by Eliot Schrefer. An advanced student who has exhausted all the practice tests in the Official SAT Study Guide and who has already read "Up Your Score", "Hack The SAT" will provide additional insight and valuable problem solving lessons. I have read the book and I have written a review of this book. Please click on the Title of this post to read my complete critique.