The tutor visits another common topic of Math 10. Consider the following question: Without a calculator, place in order, least to greatest, the following list: √48,-100,5√2,7 Solution: We know that -100, the only negative, must be least. Among √48,5√2 and …
Math: ordering radicals least to greatest, no calculator Read more »
The tutor returns to a “favourite” topic of high school math. High school math students may soon be posed a question similar to the following: Estimate to one decimal place, without a calculator, the square root of 55. Note that …
Math: approximating a square root (no calculator) Read more »
The tutor follows the idea of the telescoping sum. In my previous post, I gave an example of a telescoping sum. It implies that 1-x^(n+1)=(1-x)(1+x+x^2+x^3+x^4+…..+x^n) Dividing both sides by 1-x we arrive at (1-x^(n+1))/(1-x)=1+x+x^2+x^3+…..+x^n which is familiar from the sum …
The tutor gives brief coverage of a curiosity with polynomials. Imagine expanding the product (1-x)(1+x+x^2+x^3) by multiplying, in turn, both terms from the first bracket by each one in the second: (1-x)(1+x+x^2+x^3)=1-x+x-x^2+x^2-x^3+x^3-x^4 Note, in the expanded expression, the cancellation between …
The tutor follows up his earlier post about an algorithm for exponentiation. In my Aug 28 post I brought up exponentiation and a straightforward algorithm that uses a loop. However, there is a less straightforward, yet more efficient, algorithm for …
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By way of finding a power of a number the tutor opens a discussion about algorithms. Years ago my computer science professor presented the following definition: An algorithm is a set of steps to solve a problem. Suppose there wasn’t …
The tutor further explores the golden ratio. In my previous posts here and here, I’ve discussed some aspects of the golden ratio. Trying to find other special facets of it, I’ve dreamed up color combinations that express the golden ratio …
The tutor continues about the golden ratio. In yesterday’s post I brought up the golden ratio. Historically, it’s believed to be the ideal shape for a rectangle. The ratio of length to width is (1+5^(1/2)):2 or 1.618:1 Below is a …
Math: radical expressions: the golden ratio, continued Read more »
The tutor introduces the golden ratio. The golden ratio is defined as x/y, where x/y = (x+y)/x, x>y, y>0 Muliplying both sides by xy gives x^2=xy+y^2 which leads to x^2-xy-y^2=0 Using the quadratic formula to solve for x, we imagine …
The tutor focuses on the Staples BD-6120G, which has some convenient features. Overlooking the Staples BD-6120G might be easy: I can’t recall any of my students using it. Yet, I picked one up from Staples’ abundant shelves; someone must use …
Calculator usage: linear regression on the Staples BD-6120G Read more »