Week 4 Reading Assignments:
- Precalculus: Ch. 3.2
- Physics: Ch. 3.1, 3.2, 3.4
The Math reading for this week is short but mathematically dense. Take deep breaths, give yourself time, and don’t panic. Carefully mark each line in the reading that you don’t understand or can’t follow so we can have a productive lecture/seminar on Monday. This holds especially for the step-by-step algebraic manipulations – mark each step you don’t understand.
You may find it helpful to spend some time reading algebra tutorials online if your algebra is rusty. Students submitting Week 4 Resource Postings might consider resources related to this reading, and posting them early. All students could consider submitting their individual questions to the Discussion Forum before Monday’s lecture/seminar and responding to each other.
Some specifics reading tips:
- Read the terminology in Ch 3.1 p. 155 and Ch3.1 p. 158 about power functions and polynomials.
- Skip Example 5.
- Example 2 shows a quadratic shifted the the left and down. That should be familiar from Math Lab 3. In our math text that shifting is called a transformation of the simple toolkit quadratic. The example then gives the g(x) formula of the quadratic in what we learned last week as the vertex form. It might help to re-write as g(x) = ½(x – (-2))2 + (-3); then -2 and -3 correspond to the coordinates of the vertex. This example shows one more transformation called a stretch. That will also be familiar to you from Math Lab 3 when you tweaked the A parameter of the parabola to get it to look narrower or wider. Transformations are discussed in at length in Ch 1.5, if you want to skim through that section looking for the bold words and the cute graphs. But don’t get bogged down in Example 2.
- The reading on p. 165 may be challenging, but take it slow and read closely to follow each word and formula, again marking each step that you don’t understand. Keep the general purpose of that part of the reading in mind: to derive a formula for transforming a standard form of any quadratic into the vertex form! The h and the k are the vertex coordinates and the formulas for h and k are given at the top of p. 166 using the standard form parameters a, b, and c (or A, B, C as in Math Lab 3 or in LoggerPro).
The Physics reading for this week extends our study of one-dimensional motion into two dimensions. The two important features for this are The Independence of Perpendicular Motions (p. 87 – 88) and using vectors to represent two-dimensional quantities as well as adding and subtracting vectors to find the magnitude and direction of the resultant vector (Ch. 3.1 and 3.2).
- The reading introduces the Pythagorean Theorem early. For our purposes, the Pythagorean Theorem is important because it relates the lengths of the two perpendicular legs of a right triangle to the length of the third side (called the hypotenuse). If you are unfamiliar or rusty with the Pythagorean Theorem, find some online resources to become familiar/reacquainted with how to use it; if you have time, you may want to read up on the incredible history of this remarkable and powerful mathematical idea. Note that you might run into something called the distance formula; the distance formula is the Pythagorean Theorem.
- Ch. 3.2 describes how to add (and subtract) vectors graphically in order to get the length (magnitude) and the angle (direction) of the resultant vector. We are skipping 3.3 for now (we’ll return to it in a little while), but 3.4 assumes that you’ve read 3.3. Everything in 3.4 that assumes material from 3.3 can be done graphically using the material from 3.2 instead, so don’t panic if you see trigonometric quantities like sin, cos, and tan referred to in 3.4 – we won’t need to use them yet but instead will use graphical methods involving rulers and protractors for now.
- Example 3.5 uses the quadratic formula, which is discussed in this week’s Math reading.