Mastering Desmos for the SAT

A special version of the Desmos online graphing calculator is included as part of the BlueBook app students use to take the SAT.

Clever use of Desmos on the SAT math section can give a significant boost to scores, but Desmos is as complicated as it is powerful, and many students are unaware of its most helpful features. 

Which Desmos skills are most important to master for use on the SAT? Narrowing the list is critical.

Click here to read my outline of Desmos essentials.

The calculator is no cure-all, however, and the boundaries of its usefulness on the SAT must be kept firmly in mind. Desmos is helpful in solving the following types of problems: basic calculation, and simple data analysis, solving equations and systems, finding intercepts/zeros/max-min values, graphing equations and functions, and finding points along these curve. During the test, students should keep the calculator open but minimized, expanding it when in use.

Desmos is growing in importance in most high school and college math courses. Facility with the calculator beyond beginning levels confers multiple benefits, and taking the time to upgrade one's Desmos skills is highly encouraged. 

Students can progress to the next stage through independent study using targeted Google searches to learn and practice any underdeveloped skills listed in the linked document above.

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

SAT Interpretation Questions

For many students, SAT problems requiring interpretation of details found in equations or graphs can be some of the most difficult. 

These questions are simply unanswerable without a basic understanding of the particular mathematical models tested on the SAT.

Fortunately, firm grounding in those aspects of linear, quadratic, and exponential functions tested on the SAT isn't hard to obtain.

Following are key facts about linear, quadratic, and exponential models students must understand to answer SAT interpretation questions.

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Linear functions
y = mx+b: y-intercept b is the “initial value” (y value when x = 0).
Slope is the “rate of change” (y compared to x, “y per x”).

Quadratic functions
y = ax^2+bx+c: y-intercept c is the “initial value” (y value when x = 0).
max/min value is the y coordinate at the vertex.

Exponential functions
y = A*B^x.
x is usually time, t.
A is the initial value (y value when x or t = 0).
B is the “multiplier” (number repeatedly multiplied in the problem.
B = 1 ± r, where r is the rate of increase or decrease (respectively)..
For example: If the rate of decrease is 15%, B = 85% = .85.

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For practice, search Google for “SAT interpretation questions worksheets,” 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 question type.

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Contact Chris

borlandeducational.com

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

Exponential Functions – What You Need to Know

Exponential models are useful in a number of real-world scenarios, from predicting declines in population to forecasting growth in asset values. This can all get rather complicated, and both the SAT and ACT require some familiarity with exponential functions. 

Fortunately, only knowledge of bare basics is required. 

Following is a list of things you need to know about exponential functions. 

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Simple definition
Exponential functions have an unknown in the exponent.

Exponential functions – general form
y = A*B^x.
x is usually time, t.

Constants
A is the “initial value” (y when x=0).
B is the “multiplier.”

Growth factor
B = (1±r), where r is rate of growth/decay.
(Time and rate units must match).

Parent Graph
Rising curve through (0,A).
Horizontal asymptote y = 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 material.

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Contact Chris

borlandeducational.com

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

Essential Ti-84 Plus CE Skills

Texas Instrument’s handheld Ti-84 Plus CE graphing calculator is a powerful math computer, the best available calculator for use on the ACT (a different  graphing calculator, Desmos, is featured in the BlueBook app used to take the SAT).

Clever use of the Ti-84 Plus CE can make significantly improve scores on the ACT math test. Unfortunately, the calculator is as complicated as it is powerful, with hundreds of features and functions. Shortening the list is critical.

Which calculator skills are most important?

Click here for my outline of essential Ti-84 Plus CE skills. Students are encouraged to do independent study using targeted Google searches to learn and practice any underdeveloped skills listed in the linked document above.

Graphing calculators like the Ti-84 Plus CE have played an important role in teaching and learning mathematics for decades, and as of this writing, this calculator is still standard technology in high and college mathematics courses.

Mastering the Ti-84 Plus CE beyond beginning levels confers multiple benefits, and is highly recommended.

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Contact Chris

borlandeducational.com

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

Exponent Rules

After addition, subtraction, multiplication, and division, exponentiation serves as the 5th and final arithmetic operation.

Calculations involving exponents are crucial in algebra and are a major feature of SAT/ACT math. Seven basic rules and two additional corollaries govern exponentiation.

It’s important to understand these principles well and master their use through practice and application.

Below are the laws governing exponents you'll need to know and follow.


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Basic Exponent Rules (A ≠ 0, B ≠ 0)

Product of Equal-Base Powers: A^m*A^n = A^(m+n)
c: z^3*z^4 = z^7. 

Quotient of Equal-Base Powers: A^m/A^n = A^(m–n).
For example: x^-3/x^5 = x^-8.

Power of a Power: (A^m)^n = A^(mn)
For example: (y^3)^4 = y^12.

Power of a Product: (A*B)^n = (A^n)(B^n)
For example: (x^2*y)^3 = (x^6)(y^3).

Power of a Quotient: (A/B)^n = [(A)^n]/[(B)^n]
For example: (x^7.5/y^-2)^2 = [x^15]/[ y^-4].

Zero Powers: A^0 = 1 (A ≠ 0)
For example: (2z–1)^0 = 1 (z ≠ 1/2).

Negative Powers: A^-n = 1/(A^n)
For example: x^-3 = 1/(x^3).

Additional Corollaries

Quotient of Negative Powers: A^-m/B^-n = B^n/A^m
For example: y^-1/z^4 = z^-4/y^1.
(Changing positions of the lower and/or upper powers changes the signs on those exponents)

Negative Power of a Quotient: (A/B)^-n = (B/A)^n
For example: (x^-1/y^8)^-4 = (y^8/x^-1)^4.

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For practice, search Google for “exponent rules worksheet,” 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 material.

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Contact Chris

borlandeducational.com

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