Saturday, March 08, 2025

Y1Y2

Inexpensive handheld math computers like the Ti-84 series of graphing calculators came of age in the early 1980s and revolutionized the teaching and learning of mathematics. The youngest child in the family, the Ti-84 Plus CE, is still a standard classroom tool, and a powerful one.

While Desmos is the only graphing calculator tool allowed for use on the SAT, the Ti-84 Plus CE is the best of many calculator option for the ACT. “Y1Y2” is one the most helpful “cool calculator tricks” the Ti-84 Plus CE can perform, leveraging raw computing power to solve equations by graphing.

To solve any equation on the ACT using the Ti-84 Plus CE:

1. Set Y1 equal to the left side of the given equation to be solved, and Y2 equal to the right side. 

2. Hit the graph button, and make sure both graphs appear in the viewing window. 

3. Note the coordinates of the points of intersection. The x-coordinate(s) will be the given equation's real solution(s).

It can sometimes be hard to finagle the graphs of Y1 and Y2 so that both show up in the same viewing window, however.

In that case, carry out the following steps to make viewing both graphs easier,:

1. Remember that since Y1= Y2, Y1–Y2 = 0. 

2. Set Y3 equal to Y1–Y2, turn off Y1 and Y2, and graph Y3 alone. 

4. Real solutions to the original equation will be zeros of Y3. These solutions should now conveniently appear as x-intercepts (adjustment of window variables Xmin and Xmax may be necessary to show both zeros).

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Saturday, March 01, 2025

How to Read SAT/ACT Math Questions

Success in mathematics is rooted in efficient reading. Most math mistakes on the SAT/ACT are, in fact, reading mistakes! Learning to avoid them is an opportunity to quickly and significantly boost scores without learning any new math.

Four simple strategies help ensure students aren’t misreading math questions or failing to catch important information.

The Middle Lane

The most effective way to prevent reading mistakes is to slow down a little. It’s counter-intuitive, but slowing down can actually help one move more quickly through the test, since doing so leads to better comprehension, less confusion and stress, and far less re-reading. All this contributes to stronger SAT/ACT math scores. A comfortable, moderate reading pace is the goal. The middle lane of the freeway. Not too fast, not too slow. Students should no faster than they can fully understand what they're reading. 

Read Party-By-Part

When reading gets tough, the best thing to do is slow down, read each sentence part by part, and make sure you understand each part before going on to the next. Yes, this will take some time. But what’s the alternative? Not fully comprehending the question is the best way to answer it incorrectly. Taking the extra time to read slowly and carefully enough to fully understand the problem, students actually save more time than the strategy costs, even as it greatly improves the likelihood of choosing correct answers. 

Boil-Down Questions

This is another great way to boost comprehension and improve the odds on difficult SAT/ACT math questions. The acronym “RCU” outlines the steps: 

“R” stands for read the question all the way through. 

“C” means circle the main words in the question (i.e. the last sentence, with the question mark). 

“U” reminds us to underline the clues. 

Taking these notes on scratch paper increases awareness of the meat and bones of the question and leads naturally to higher scores.

Point to Get the Point

“Tracking” is a tried and true method for improving concentration and comprehension. 

All you do is your pencil or index finger under the text as you read, and pay close attention to both the meaning of the text and your pointer. 

While this technique precludes reaching maximum reading speed, who cares? As we’ve already pointed out, comprehension is more important than speed on the SAT/ACT math section. Point to get the point!

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.