A 10 foot ladder is leaning against a wall, and its base is sliding away from the wall at a rate of 0.5 feet per second. At what rate will the top of the ladder be sliding down the wall when the base is 6 feet from the wall?
Related rates problems are tricky at first, but easily mastered. This ladder problem is very basic, and I chose it because more complex related rates problems are much easier with the help of a sketch to illustrate the situation. 1. Ladder problems almost always use the Pythagorean Theorem: a^2 + b^2 = c^2 Take the derivative of this with respect to time: 2a(da/dt)+2b(db/dt)=2c(dc/dt) 2. The question gives us 3 things: the length of side A, side C, and the rate that A is sliding away from the wall: A=6 C=10 dA/dT=0.5 3. Because it is a right triangle, we can figure out the length of B: 6^2+B^2=10^2 B^2=100-36 B=8 2(6)(0.5)+2(8)dB/dT=2(10)dC/dT 4. Because the ladder does not change height, dC/dT will equal 0. 6+16(dB/dT)=0 5. Solve for dB/dT dB/dT = -3/8 ft/sec The top of the ladder is falling at a rate of 0.375 ft/min
My teacher keeps scoring my essays low, saying that they are too narrative. What does she mean by that?
I struggled with the same thing at first. When writing essays, almost always, graders want to see you establish a point and back it up with evidence and critical thinking. Especially in IB, they don't want you to "throw up" as many facts as you can recall, but instead structure your essay to prove your point. Many tests that require essays will ask questions such as, "To what extent was the United States responsible for Japan's aggression between 1931 and 1945?" When answering these questions, it is best to plan your essay first. Choose your stance on the question, write out a thesis statement that clearly demonstrates your point, and gather three pieces of evidence. Each paragraph should begin with a topic sentence that expresses your stance on the matter and the rest of the paragraph should cite specific events or policies that back up your opinion. Furthermore, you need to show evidence of critical thinking in order to tie your evidence with your point. Finally, your conclusion will restate your evidence, without providing any new information. In this way, your essays will become much stronger and score higher marks, especially in IB and AP classes.
For the writing portion, what are some tips for scoring high marks?
One thing my English teacher told me was that the graders prefer concise answers. On the test, there will be many questions that give you a passage from a piece of text and ask you to select the best sentence that belongs in a particular place. For example, some options they give you will include sentences like, "The pottery is brightly colored" or "The pottery is brightly colored and iridescent." In this instance, the first option is the correct choice as in the latter, "brightly colored" and "iridescent" mean virtually the same thing. It seems tempting to choose the longest and most wordy answer, but in reality it is better to choose the most concise and straightforward one. I used this advice and scored a perfect 36 on the writing portion.