Category: Mathematics

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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!).

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11 SL Arithmetic Sequences

Complete the following questions before our next class. (We’ve talked about arithmetic and geometric sequences, but for this set of questions you’ll see that the focus is on arithmetic sequences.)

Exercise 6A questions 1ac, 2bc, 3
Exercise 6B questions 1, 2, 3bc, 4bc
Exercise 6C.1 questions 1, 2bc, 3, 4, 6, 7bce, 9a, 10, 11
Exercise 6C.2 questions 1, 2

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9 Extended: Equations of Lines

If we plot all the points that satisfy the equation y = mx + c, we’ll see that we get a line with slope m and y-intercept c. This form of the equation of the line (we’ll see another next class) is called the point-slope form equation of a line.

Now that we’re familiar with this type of equation, we can find the equation of a line with a given slope that passes through a given point.

For example, if I want to find the equation of a line with slope –2 that passes through the point A(1, 2), we know the equation will have the form y = –2x + c, but we still need to find the y-intercept (in other words, we still need to find the value of c). Here we can use the fact that the point A(1, 2) should be on our line. Since A is on our line, we should have \[\begin{align}2&=-2(1)+c\quad \text{ and so}\\ 4&=c\end{align} \]

But this means we’ve just found the “right” value for c! Now we now know that the equation for the line with slope –2, and passing through A(1, 2), is y = –2x + 4. (You can check this using GeoGebra.)

Complete the questions below before our next class.

  1. Find the equation of the line with slope –1, passing through the point (1, 4).
  2. Find the equation of the line with slope –1, passing through the point (2, 0).
  3. Find the equation of the line that passes through (1, 3) and (2, –1).
  4. Find the equation of a line perpendicular to the line you found in question 3, which also passes through the point (1, 3).