Category: Mathematics

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12 HL The Normal Distribution

Here’s the question we were looking at in class, complete this question (and the other questions that I’ll include in an email to you) before our next class.

An manufacturing process produces aircraft parts such that the length of each part, X, (in cm) is such that \(X\sim N(\mu,\sigma^2)\).

We know that \(P(X\leq 120)=0.4596\) and \(P(X\leq 132)=0.6491\).

Find \(\mu\) and \(\sigma\).

If a part is rejected if it is more than 1 cm away from the mean, what percentage of parts are rejected?

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9 Extended: Term Test

On Wednesday, February 13th we’ll have a test on all of the topics we’ve covered so far this year. Those topics are listed below.

  • Number Sets (\(\mathbb{N}, \mathbb{R}\), etc.)
  • Number lines (representing 1 ≤ x < 4, etc.)
  • Operations with sets (\(A \cup B\), etc.)
  • Radicals (simplifying, adding, multiplying, rationalizing the denominator, etc.)
  • Trigonometry (finding sides, finding angles, working in 2D or 3D)
  • Coordinate Geometry (finding the slope, finding midpoints, parallel and perpendicular lines, equations of lines)
  • Word problems involving any of the above

In order to prepare for the test, the following questions may be helpful. We’ll discuss answers to these questions on Thursday. (Note that you will probably have done some of these before—make sure you still remember how to do them, and if you are absolutely sure you know how to solve a question, skip it and look for a harder question to try!)

Review Set 2B
Review Set 4A
Review Set 13A
Review Set 9A

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9 Extended: General Form Equation of a Line

If we are given a point on a line, and the slope of that line, we already know how to find the equation of that line in slope-intercept form. How can we find the general form equation of that same line?

In one sense it’s very easy, we can just move the x-term to the same side as the y-term. For example, the line with slope-intercept form \[\begin{align}y&=3x+1 \quad\textrm{can also be written as}\\y-3x&=1\end{align}\]

which is in general form.

There is, however, another easy way to find either the general form equation of a line that you may also want to use. If you want to learn that method, have a look at page 174 in our textbook. You can use any method you like!

Complete the following questions before our next class.

Exercise 9E.1 questions 1–3, 4ef, 5, and 7 (if you want a challenge, try 11 as well!).