Complete the following questions before our next class.
Exercise 5E questions 1, 3–8
9 Extended: Working with the Slope
Complete the questions below before our next class.
- A line contains the point A(1, 3) and has a slope of 3. Find the coordinates of two other points on the same line.
- A line contains the point A(0, 5) and has a slope of \(\displaystyle{-\frac{2}{3}}\). Find the coordinates of two other points on the same line. (Hint: associate the negative sign with the number in numerator before trying to find other points on the line.)
- Consider the point A(1, 1). On a grid, graph a line with a slope of \(\displaystyle{\frac{3}{5}}\) that passes through point A, and a line with a slope of \(\displaystyle{-\frac{5}{3}}\) that also passes through point A. What do you notice about the two lines?
11 SL Combinations of Transformations
For homework before next class, answer the following question.
Does the order in which we apply transformations matter? For example, if I begin with the graph of \(y=f(x)\), and I
- (A) translate by 2 units to the left, and then
- (B) stretch vertically by a factor of 3,
will I always get the same result as I would if I had begun with the graph of \(y=f(x)\), and I
- (B) stretch vertically by a factor of 3, and then
- (A) translate by 2 units to the left?
What if, instead of stretching vertically by a factor of 3, I stretch horizontally by a factor of 3? Does order matter in that case?
Consideration of the function \(f(x)=x^3-2x^2\) may help here.
9 Extended Slope/Gradient
Complete the following exercises before our next class.
Exercise 9C.1 question 1 (pick any two points to calculate the gradient of a line segment)
Exercise 9C.2 questions 1, 2, 3ab
11 SL Transformations
We’ve now covered two types of transformations
- (vertical and horizontal) translations, and
- (vertical and horizontal) stretches.
Complete the following questions before our next class.
Exercise 5B questions 1, 2, 4, 5
Exercise 5C questions 2, 4, 5, 6, 8
Exercise 5D questions 1acde, 2, 4, 5
9 Extended Finding Midpoints
Read the material in Section 9B of our textbook (which introduces a method you can use to find the midpoint of two points), then complete the following questions before our next class.
Exercise 9B questions 1, 2abcd, 4, 5
9 Extended Distance Between Points
Complete the following questions before our next class.
Exercise 9A questions 1abcdh, 2, and 3a
12 HL Properties of Expectation and Variance
Complete the following questions before our next class.
Exercise 25E 3, 4, 8, 14
12 HL Expectation
Complete the following questions before our next class.
Exercise 25D questions 1, 2, 4, and 8
Algorithms in the News
Some of you have an interest in computer science, in which case you may be interested in the New York Times article about Donald Knuth linked here.
(Grade 12 HL students will have some familiarity with Knuth already, as he’s the creator of \(\TeX\), the foundation for \(\LaTeX\).)