## DSAT Maths desmos use guide

DESMOS tips and tricks to use effectively in real exam. Desmos is a powerful tool that can significantly enhance your performance on the Digital SAT math section. In this topic, we will try to explain some of sections where Desmos can be useful.

Use of DESMOS calculator use reduce time required to solve problem drastically and hence use time to think on other questions.

## Digital SAT Maths Desmos usage trick

**1)Finding X/Y-Intercepts and Points of Intersection**

- For any question that asks you to find an X or a Y intercept, you can simply type in the equation and the point will appear for you to click on DESMOS
- if you are asked to solve a system of equations, you are really just looking for a point of intersection, so you can simply type in the two equations and click the point where they meet.

**2) Applying Function Shifts**

If you are asked to shift a function up, down, left, or right, simply start by writing the function on the first line. It is important that you write the function as “f(x) =” and not as “y =” if you want this to work.

Then on the second line, simply write one of the following:

f(x) + a (for an upward shift of a units)

f(x) – a (for a downward shift of a units)

f(x + a) (for a leftward shift of a units)

f(x – a) (for a rightward shift of a units)

Once you do this, simply click the colored button at the left of the first equation to turn it off (but DO NOT delete it), and you will be left with your shifted function.

**3) Finding Center/Radius of Circle from the Raw Equation**

When a circle is written in the raw equation [ax^{2} + ay^{2} + bx + cy + d = 0] or technically in any other form, you can simply write out the full equation on one line of DESMOS to see the circle represented in the coordinate plane. DESMOS will allow you to click the TOP and the BOTTOM points of the circle (but notably NOT the left or the right points) and you can take the midpoint of those two points to find the center and the vertical distance between those two points to find the diameter (and if you divide by two, you get the radius).

**4) Solving system of inequalities **

Rather than entering each inequality as a separate entry and having to discern the overlap region that contains solutions to the system, you can plot just the region corresponding with the system of inequalities by entering one inequality and then applying the second inequality as a condition (restriction) on the first inequality:

So for the system

*x* ≤ 2*y* + 7

3*y* > -12*x* + 8

instead of entering those inequalities as separate entries, you could enter

*x* ≤ 2*y* + 7{3*y* > -12*x* + 8}

Note that the boundary of a region that results from a restriction will not be marked with a solid or dashed line to indicate whether the boundary line is part of the solution region, so that needs to be kept in mind when inspecting a point on the boundary line.

**4) Solving Any Algebra Equation**

To solve any algebra equation, just write other the equation and all solutions will be represented by vertical lines. Click the x-intercepts of any of these vertical lines and the x-values will be the solutions to your equation.

**5) Creating a Linear Equation, Exponential Equation, or Quadratic Equation using a Regression**

If you have several points of a linear equation, exponential equation, or quadratic equation and you want to find out what the actual equation is, start by typing the word table in order to open up the table function and input your x values under x1 and your y values under y1. Then, in a separate line, write out the following:

For a Linear Equation: y1 ~ mx1 + b

For an Exponential Equation: y1 ~ ab^(x1)

For a Quadratic Equation: y1 ~ a(x1)^2 + b(x1) + c

If you then look under parameters it will tell you what all of your different coefficients and constants are in your equation.

**6) Finding Mean, Median, and Standard Deviation**

To find the mean or median of a set, simply type the word mean, median, or stdev (or stdevp) and include all items in the set afterwards between two parentheses with commas between each item. Here are examples:

mean(1, 2, 3, 4) = 2.5

median(1, 3, 5, 7) = 4

stdev(1, 2, 3) = 1

In addition, if you want to find what number needs to be added to a set in order to give it a certain mean, call one of the items in the set “x” and set the mean equal to a particular number.

In other words, if you type in mean(1, 2, 3, x) = 2.5, DESMOS will tell you that x needs to be 4 in order for this set to have the proper mean.

**7) Adding Sliders**

To add sliders to your graph to quickly change coefficients and constants, just type in whatever letter you want (other than x, y, or e) and DESMOS should automatically give you an option to add a slider. Click this button and you’re all set.

**8) Typing Shortcuts**

Type in sqrt to create a square root. Type in cbrt to create a cube root. Type in nthroot to create any other kind of root. You can also type in pi to create the pi symbol.

**9) Finding Factors of Polynomials**

Type out your whole polynomial and click on any x-intercepts on the graph. If that x-intercept is “d”, then (x – d) will be one of the linear factors of your polynomial.