Monday, May 08, 2023

Pacing and Time Management

Maintenance of a steady, productive pace and effective management of limited time are keys to unlocking optimal performance on the SAT/ACT. Getting stuck, spending far too much time on a small number of crazy-hard problems, can destroy test results. So can mindless rushing. These twin evils, once discovered, must be quickly and thoroughly exorcised. 

Fortunately, bad testing habits like these can be uprooted and replaced with better ones.

Getting hung up on annoying, difficult questions for long periods of time makes several things happen, all of which are bad for SAT/ACT math scores. Having wasted valuable minutes, you’re now behind the clock and feel an even greater need to rush. The added time pressure also increases stress. Realizing those sticky questions were too hard, and that you probably answered them all incorrectly despite the extra time and effort spent on them, you’re in a bad mood. All this is quite distracting and makes it hard to be energetic, creative, and attentive. Things spiral downward, and you feel you have no choice but to rush even more and nail every question. Which only makes things worse.

Getting stuck and rushing originate in the false belief that one must answer every SAT/ACT math question correctly to earn a high score (“finish the test” at all costs), and that slowing down when necessary is an unaffordable luxury.

This may well be true for tests in class. But on the SAT/ACT, nothing could be further from the truth. Students taking the SAT/ACT math test can safely make many more mistakes than would ordinarily be the case.

The scoring tool on a recent ACT showed students could make 20 errors out of 60 questions to earn an ACT Math 27 (90th percentile), 15 errors for an ACT Math 29 (95th percentile), 10 errors for ACT Math 32 (97th percentile), or seven errors for an ACT Math 34 (99th percentile). In most classes, a score of 90, 10% wrong answers, is an A-, a very respectable grade. On the ACT, however, an identical “grade” is granted even when answering 33% of the questions incorrectly! The same is roughly true on the SAT.

[Note: Since each question has four answer choices, blind guesses are right 1/4 of the time. Guessing on 20 out of 60 questions on the ACT math test would likely earn 5 extra points, which should cancel out any mistakes made on the other 40 (easier) questions. Impossible as it sounds, a student only needs to work on the 2/3 of the questions on the ACT math section, avoiding all the hardest questions, to earn a 90th percentile score.]

In the end, effective time management on the SAT/ACT boils down to not getting stuck. To avoid falling victim, “skip-guess” any difficult question on your first pass through the test, answer it with a random guess, flag the question for later review, and quickly move on to the next problem.

By skip-guessing all the hard problems and working only on relatively easy ones, you’re sure to reach the end of the test super early. With loads of extra time and energy, you can then evaluate how best to spend your remaining minutes. You can calmly and rationally “choose your battles,” deciding which of the harder, flagged questions to come back to on your second pass and the order in which to work on them, slowing down and spending more time on each question to help avoid careless mistakes and ensure success. Knowing you can safely lose a large number of points and still earn a great score, impossibly difficult “nightmare” questions can be safely ignored during your second pass.

Much more time. Much less stress. Far fewer careless errors. No discouragement, headache, or heartache from trying (and failing) to answer crazy-hard questions in a rush. Do you think your score would likely improve under such circumstances?

By employing these three simple strategies – Skip-Guessing, the Two-Pass Approach, and Choosing Your Battles – students routinely cut errors in half. Virtually overnight, an ACT Math 27 (20 errors, 90th percentile) can turn into an ACT Math 32 (10 errors, 97th percentile). That’s an entirely different college! No new math to learn. No additional practice work. All that’s required is the adoption of a new, more comfortable, vastly improved general approach to the SAT/ACT math test.

Following are two additional pacing strategies offering concrete help in the fight to avoid getting stuck.

The Five-Second Skip

It’s crucial to decide quickly whether to work on a given problem during your first pass through the test or skip-guess the question for possible review later on. This is where getting stuck often happens. The rule is: give yourself only five seconds to decide. When in doubt, skip-guess the problem.

The 15-Second Skip

Getting stuck can also happen in the middle of a difficult question as one bargains with oneself for “just a little more time.” A “little more time” can easily turn into several wasted minutes. This is bad. Here’s the rule: Anytime you stop making progress on a problem for 15 seconds, skip-guess the question.

WARNING: If you find yourself finishing early without skip-guessing a large number of questions, you’re rushing. To improve your score, you must skip-guess a lot more problems, and slow down a bit. As you see your practice test scores dramatically improve, you’ll be convinced and converted to this new approach.

Going too fast can be just as bad as going too slow. Slowing down slightly doesn’t cost you points! It actually helps you move faster and more successfully than before, since you won’t waste loads of time and energy to needless confusion and stress, nor will you lose nearly as many points to carelessness. Don’t go slow as a snail, of course! It’s best to drive in the middle lane of the freeway. Not too fast, not too slow.

Whatever you do ... don’t get stuck! 

Remember that, working carefully to avoid pitfalls, there’s really no need to rush. Let go of false assumptions and unnecessary, uninformed expectations about having to perform perfectly. Your test-taking experience will improve, and so will your SAT/ACT math score.

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

Monday, May 01, 2023

Cracking BlueBook Second Modules

With only six available official digital adaptive SATs and PSATs, it’s critical that students get access to all questions contained in the “second modules” of each section of each test in the BlueBook app. 

There’s no way to do so directly, but an easy workaround gets the job done: 

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1. After completing your practice test, save the answer page.  

2. Retake the same practice test. 

3. To access the harder second module, enter only correct answers when you retake the test; to access the easier module, enter only incorrect answers. 

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Click here to view and download (File > Download) correct answers to first modules from BlueBook SAT Tests 1, 2, 3, and 4.
 
You may also want to screenshot important questions as you practice (hardest problems, any you’ve answered wrongly, etc.) and keep these in a folder for further study.

These few official tests are best used sparingly to assess progress in your prep work or as “dress rehearsals” before test dates.

They're the only ones you’ve got. Don’t waste them!

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

Saturday, April 08, 2023

Quadratic Functions – What You Need to Know

Most intermediate-advanced algebra courses cover second degree polynomial functions, called “quadratic functions,” long before introducing general polynomial functions.
 
Because quadratic functions are simpler versions of general polynomial functions, graph as parabolic curves, and are featured in many real-world situations, this subtopic holds a prominent place in the syllabus.

Following is a list of concepts you should firmly understand before taking the SAT/ACT.

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[Note: “iff” means “if and only if.”]

Definition
Quadratic functions: functions involving one first-degree variable and one second degree variable (typically y^1 and x^2).

Quadratic Function Standard Form
y = ax^2+bx+c.

Parabola
Vertex = (h,k) with h = -b/2a, k = f(h).
Axis: x = h.
y-intercept = c.

Vertex Form
y = a(x–h)^2+k.
Vertex = (h,k).
Radius = r.

Discriminant
D = sqrt(b^2–4ac).
D > 0 iff 2 real solutions.
D = 0 iff 1 real solution.
D < 0 iff no solutions.

Sum and Product Formula
x^2–(sum)x+(prod) = 0.

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For practice, search Google for worksheets covering any or all of the above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this important material.

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

Saturday, April 01, 2023

Factfulness

Despite rumors to the contrary, things aren't so bad. They're probably quite a bit better than you think. That's the thesis of this book by Swedish author and public health expert Hans Rosling.

From the book's description on amazon:

"It turns out that the world, for all its imperfections, is in a much better state than we might think. That doesn’t mean there aren’t real concerns. But when we worry about everything all the time instead of embracing a worldview based on facts, we can lose our ability to focus on the things that threaten us most.

"Inspiring and revelatory, filled with lively anecdotes and moving stories, Factfulness is an urgent and essential book that will change the way you see the world and empower you to respond to the crises and opportunities of the future."

Here's what Bill Gates had to say about Factfulness:

“One of the most important books I’ve ever read―an indispensable guide to thinking clearly about the world.”

And Barack Obama:

"Factfulness by Hans Rosling, an outstanding international public health expert, is a hopeful book about the potential for human progress when we work off facts rather than our inherent biases."

Rosling isn't a Pollyanna who refuses to acknowledge the very real problems and challenges humanity still faces. His point is that, if we actually follow the facts – instead of persistent, unconscious biases – there's much more reason to be proud and hopeful than we might ordinarily believe.

I enjoyed Factfulness, and highly recommend it to all with an interest in the state of the world.

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

Wednesday, March 08, 2023

Winning Focus

Test taking is a competitive activity. 

As is athletics or the performing arts, outstanding achievement on the SAT/ACT depends on maintenance of powerfully sharp, energetic, mindful concentration and “winning focus.” 

In sports, the challenge is the opposing team. In the performing arts, it’s stage fright. In test taking, your adversaries are the test questions. 

Test takers, like athletes and stage performers, need to confront and conquer pressure, stress, fatigue, distractions, and other difficulties with sustained enthusiasm, relentless drive, and total commitment to success. If victory is the object, nothing less will do.

An intense, aggressive, yet controlled state of concentration is critical to performing at one’s best in any competitive activity. “Winning Focus” is so important, in fact, that without it, almost nothing else matters.

By definition, intensity always involves some amount of tension. Undisciplined, raw intensity can lead to varying degrees of frustration, anxiety, and even exhaustion. Athletes, performers, and test takers must learn to thread the needle between two extremes, remaining fully responsive and focused on winning without getting rattled or falling victim to tenseness, tiredness, or negative emotion.

When intelligence is inhibited by inattention, distraction, tiredness, or emotional upset, reduced cognitive bandwidth causes a mental traffic jam, disrupting the efficient flow of ideas.

On the other hand, Winning Focus lights up the brain like a Christmas tree. All kinds of connections, insights, and creative solutions come to mind that would otherwise go unnoticed. Most important of all, careless mistakes are minimized.

Fully half the errors on a typical student's SAT/ACT math test are due to carelessness. If these careless errors were reduced by half, a student scoring 650 on an SAT math section would instead score 720, and one scoring 27 on the ACT would score 31!

These dramatic improvements require neither new math smarts, nor improved testing acumen, nor additional practice – just a 50% cutback in careless mistakes. In fact, math test prep could be restricted entirely to development of Winning Focus, and most students would be well served.

The vast majority of test coaches pay no significant attention to the mental game of test taking. In my work, Winning Focus takes center stage. Using proprietary methods and materials, a natural knack for inspiring and igniting motivation, and a unique ability to train all aspects of effective test prep that only 45+ years in business can bring, I teach my students to track errors, avoid unnecessary mistakes, and generate and sustain powerful, energetic, productive concentration.

The best way to train Winning Focus is to build strength and endurance through gradual exposure to practice tests of increasing length and difficulty, bolstered by professional performance critiquing, feedback, error analysis, and personal support. It boils down to habituating a determined, enthusiastic, mindful concentration on test questions, and training higher levels of focus for longer and longer periods.

Fortunately, most high-performing students already know how to do this. Such students are typically athletes, actors, dancers, and/or musicians, and already know how to generate the state of mind necessary to excel at competitive activities. It’s just a matter of transferring this well-developed ability to the domain of test taking. Although the particulars are more complex, it’s really that simple.

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