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Using a Calculator for the SAT Math Level 2 Exam

Instructor: Michael Eckert

Michael has a Bachelor's in Environmental Chemistry and Integrative Science. He has extensive experience in working with college academic support services as an instructor of mathematics, physics, chemistry and biology.

One should use a scientific calculator with a graphing feature on the SAT Math Level 2 Exam because it can help a student solve many complex math problems quickly and with one hundred percent accuracy. In addition, a plethora of other values and approximations can be obtained with use of this tool. Some examples are given.

Introduction to the TI-84 and the SAT Level 2 Math Exam

The Texas Instruments TI-84 serves a great advantage on the SAT Level 2 Math Exam as it can perform a variety of functions both quickly and accurately. It aides in obtaining graphs of a wide variety of functions (linear, non-linear e.g. quadratic, trigonometric, parametric, etc.) for qualitative analysis. Note that many rough estimates or approximations can be made in seconds, as opposed to minutes, from graphs on the TI-84. This is of tremendous value on multiple choice exams, where deductive reasoning i key. This is of great value on the SAT, where time is often of the essence. For answers in more quantitatively-based questions, like the position of points on a function i.e. x-values vs. y-values and calculation of slope for instance, there are specific commands and programs as well. Through illustration of finding the roots of a quadratic equation, we will unveil quite a bit about the TI-84's capabilities specifically on a standardized exam. In being able to calculate roots of a function by these means, we must cover several of the calculator's operations. These functions will serve us well on a large portion of the SAT Level 2 Math Exam. We should note however that the test is not constrained to concepts in algebra, trigonometry and pre-calculus. The test can also cover operations in math involving data operations or statistics. It should be stressed again that we are only showing finding the roots of a quadratic function as a primary example, because it illustrates this calculator's usefulness over a variety of functions or commands. However, it is capable of much more with regards to the SAT.

Using a Calculator for the SAT Math Level 2 Exam, Approximating Roots of a Quadratic Equation

A student having a scientific calculator with a graphing feature has a tremendous advantage on the SAT Math Level 2 exam over a student who does not. The scientific graphing calculator allows for a variety of math problems to be solved for quickly and with one hundred percent accuracy. Even if this calculator serves no other purpose then to check work done by hand, it is of tremendous value nonetheless. In this lesson, we will be using the Texas Instruments TI-84 graphing calculator to solve for the roots of a function.

Many times, approximating the roots of a quadratic function by hand will require the use of the quadratic formula. When taking an SAT Math component however time is of the essence; therefore, the roots can be determined via a shortcut implementing the intersection command of the TI-84 graphing calculator.

If given a quadratic equation, say y = -2x2 + x +9 for instance and asked to solve for its roots, we first place y = -2x2 + x +9 into our Y =


ye


Before we make use of the GRAPH command, we must set up our MODE and WINDOW accordingly. First, we set up MODE.


mo


Mode sets our calculator's functioning parameters e.g. whether we are in Normal, Scientific or Engineering mode, whether we are in radians or degrees, dealing with real or imaginary numbers, etc.

Second, we set our WINDOW. For most linear and non-linear functions encountered on standardized exams, our WINDOW will usually have the same settings.


w


WINDOW will dictate the layout or dimensions of our cartesian coordinate system i.e. where Xmin = -10, Xmax = 10, Xscl = 1, Ymin = -10, Ymax = 10, Yscl = 1 and Xres = 1. Xscl and Yscl determine how many tic-marks that we will have along the x and y-axis. Xres is a variable we can just take to be 1.

After setting up MODE and WINDOW, we can press the GRAPH command.


gc


We can see that y = -2x2 + x +9 crosses / intersects the x-axis (or y = 0) at two points. Again, these two points intersect y = 0. They are our roots. We can solve for them by placing y = 0 into Y = with y = -2x2 + x +9 and using an intersection command under CALC. After placing y = 0 into our Y =,


y2


we press GRAPH. Note that we are unable to see y = 0 as it runs along our x -axis.


gc


We are now able to find the value of our roots, where y = -2x2 + x +9 crosses the x-axis (where y = 0). We press 2nd CALC and scroll down to the 5: intersect command. We press ENTER.


ic


We are given a display of a graph coupled with a prompt of 'First curve?' We press ENTER.


fc


We are prompted by 'Second curve?' We press Enter a second time.


sc


We are prompted one last time by 'Guess?', and we press Enter one final time.


g


Our intersection point is displayed as x = -1.886001 and y = 0.


r1


To find the 2nd root, we merely use the 5: intersection command under 2nd CALC again. We will TRACE to the general vicinity of the other intersection point and follow the same prompts given for the 1st point of intersection. We will be given the 2nd root at x = 2.3860009 and y = 0.


sr


In summary, we have approximated the two roots of y = -2x2 + x +9 at (1.886001, 0) and (2.3860009, 0).

Tips for Using the Calculator

A graphing calculator can be useful for many problems on the SAT Math Level 2 exam. It serves a tremendous advantage over anyone without one. We can see this primarily through the solving for roots of a quadratic equation. In addition, here are some tips that can be helpful when solving a variety of other types of problems.

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