# **Desmos: Eight Features to Boost Your SAT Math Score** Mastering the built-in Desmos calculator can raise your SAT Math score hundreds of points! It can solve super challenging problems for you, while also saving time and reducing careless errors. Whether you failed algebra or aced calculus, these eight Desmos skills will transform how you approach the test. Stop wrestling with complex equations and start visualizing your way to a higher score. And once you learn these techniques, practice them with our [free Desmos question bank!](https://resolveprep.com/topic-training/desmos-skills "Desmos Practice") ## #1 Solve Any One-Variable Equation Forget struggling with tricky algebra! Avoid careless errors! Solve in 3 simple steps on Desmos instead. ### Method 1. **Enter Left Side of Equation:** Type $y =$ \[Left Side of Equation] on one line.\* 2. **Enter Right Side of Equation:** Type $y =$ \[Right Side of Equation] on the next line. 3. **Click Where They Cross:** The **x-value(s)** of the intersection point(s) are your solutions. \*Always use $x$ as your variable, even if the given equation uses a different variable. *While other Desmos solving methods exist (like typing the equation directly), they can sometimes miss answers or only give estimates. While we review these methods in our in-depth explanations, this visual method is foolproof.* ### Example SAT problem ![-4x^2=5x-6](https://vocabimages.b-cdn.net/blog-images/ws-problems-4-84.webp "One-Variable Solve") ### Desmos Solution Solution to One Variable Solve

Graph $y = -4x^2$ and $y = 5x - 6$. Click the intersection points: $x = -2$ and $x = 0.75$. The question asks for the negative solution? Bam! It's $-2$ **(Choice A)**. Fast, accurate, and no messy algebra. ## #2 Solve Systems of Two Equations Why sweat through substitution or elimination? Solving systems on Desmos is incredibly fast: ### Method 1. **Type Them In:** Enter each equation exactly as it appears, each on its own line. No need to put them in y= format.\* 2. **Click Where They Cross:** Desmos will graph both equations. Simply click on the point (or points!) where they intersect. The coordinates (*x*, *y*) of the intersection point(s) are the solution(s) to the system! \*Always use $x$ and $y$ as your variables, even if the given equation uses different letters. *For complex cases (3+ unknowns), regressions are valuable but typically unnecessary for simpler systems. We review this technique in our longer training.* ### Example SAT problem ![systems-of-equations-practice](https://vocabimages.b-cdn.net/blog-images/ws-problems-3-87.webp "Systems of Equations Example") ### Desmos Solution Systems of Equations Solutions

Just type $x - y = -17.5$ and $2x + 3y = 12.5$ into Desmos. Click the intersection point: $(-8, 9.5)$. Since the question asks for the value of $y$, the answer is **9.5**. Done! ## #3 Graphing: Maximums, Minimums, Intercepts, and Intersection Points Why wrestle with algebra to find key features of a graph? Whether it's the minimum/maximum, where a graph hits the axes, or where two graphs meet, Desmos has you covered. ### Method 1. **Graph It:** Type your function or equation(s) directly into Desmos. 2. **Click the Dots:** Desmos automatically marks important points (like maximums, minimums, and intercepts) with subtle grey dots. Just click on these dots, and see their exact coordinates! ### Example SAT problem Graphing Features

### Desmos Solution Desmos Solution for Graphing Features

Type $\frac{3}{7}x - \frac{2}{5}y = 6$ into Desmos. Pinch to zoom to focus on the $x$-intercept. See that grey dot where the line crosses the x-axis? Click it! Desmos shows $(14, 0)$. The x-coordinate is **14**. Problem solved! ## #4 Regressions from Points Got points but need the equation? Ditch the algebra! Desmos's regression feature uses points to find the equation of a linear, quadratic, or exponential function with just a few clicks. ### Method 1. **Create a Table:** Click the "+" icon in the upper-left corner of Desmos and choose "Table". 2. **Input Your Points:** Carefully enter your given x-coordinates into the x₁ column and the corresponding y-coordinates into the y₁ column. 3. **Click the Regression Button:** Look directly beside your table in the blue vertical bar. Click this :

4. **Choose Your Model (if needed):** Desmos will likely default to Linear Regression. If you need a different type (like Quadratic or Exponential), select it from the dropdown. Desmos calculates and displays the equation of best fit. Regressions From Points Example

### Desmos Solution: Desmos Solution for Regressions from Points

Add a table. Enter 7 under x₁, 29 under y₁. Enter 12 under x₁, 54 under y₁. Click the regression button in the blue bar. Because the question tells us this is a "linear function," make sure Linear Regression is selected. Desmos instantly gives the equation: $y = 5x - 6$. The answer is **Choice (B)**! Quick and painless! ## #5 Sliders Ever face SAT problems with unknown constants (like $k$, $b$, or $a$) where you need to find the value that makes something happen? Sliders are your secret weapon! ### Method 1. **Enter the Equation with a Variable:** Type the equation containing the unknown constant into Desmos. Use any letter for the constant except $x$, $y$, $e$, or $r$. 2. **Add the Slider:** Desmos will automatically detect the letter and ask if you want to "add slider" for it. Click that button! 3. **Graph Any Other Equations:** Enter any other related equations from the problem on separate lines. 4. **Slide to Solve:** Now, drag the slider for your constant. Watch how the graph changes! Adjust the slider until the graph(s) meet the exact condition described in the problem (such as touching another line at one point, having a specific y-intercept, passing through a certain coordinate). 5. **Read the Answer:** The numeric value displayed on the slider when the condition is met is your answer! ### Example SAT problem Example Problem for Sliders

### Desmos Solution: Desmos Solution for Sliders Example Problem

Type $y = 4x² - bx - 2$. Click "add slider" for $b$. Type $-4y = 12$. Drag the slider for $b$. Watch the parabola move. You want the parabola to just touch the line $y = -3$ (intersecting at only one point, meaning the vertex is on the line). This happens when $b = 4$. Since **4** is positive, it fits the condition. That's your answer! ## #6 Equivalent Expressions Stuck trying to manipulate complex expressions to see if they match? Skip the tedious factoring or expanding! Desmos offers a foolproof visual check. ### Method 1. **Graph the Original:** Type the given expression from the question into the first line in Desmos.\* 2. **Graph the Choices:** Type each answer choice expression into another line. 3. **Look for the Perfect Match:** The correct answer will be the expression whose graph perfectly overlaps the graph of the original expression. 4. **Confirm with Toggles (Pro Tip!):** To be absolutely sure which graph matches, click the colored circle icons next to each expression. This turns the graphs on and off. Toggle the original expression and one answer choice at a time. If they disappear and reappear as the exact same curve, you've found your match! \*Always use $x$ as your variable, even if the given equation uses a different variable. ### Example SAT problem Example Problem for Equivalent Expressions

Example Problem for Equivalent Expressions

### Desmos Solution: Desmos Solution for Equivalent Expression Example

Graph $y = x⁴ - 3x² - 10$. Graph each answer choice, e.g., $y = (x² + 1)(x² - 10)$, $y = (x² - 1)(x² + 10)$, etc. Observe the graphs. You'll see one of the answer choice graphs lies exactly on top of the original graph. Use the toggle icons to confirm. When you toggle the original graph and the graph for $y = (x² + 5)(x² - 2)$ **(Choice D)**, you'll see they trace the identical path. No complex factoring needed! ## #7 Equivalent Expressions with Missing Constants Facing an equation where two expressions are supposed to be equal, but one side has unknown constants (like $a$, $b$, or $c$)? Don't get bogged down in monster algebra! Desmos regression can magically find those missing pieces for you. ### Method 1. **Set Up the Equation:** Type the given equation into Desmos, but with two key changes: * Replace the = sign with a \~ (tilde, usually found in the upper left part of your keyboard). * Replace every $x$ with $x₁$ (that's 'x' followed by the number 1). * Example: $(5x₁ - 17)(4x₁ - c)$ \~ $ax₁² + bx₁ + 119$ 2. **Provide Test Values:** On the next line, define x₁ as a list of numbers. Use square brackets \[] and separate the numbers with commas. You need at least as many numbers as there are unknown constants in the equation. Use simple integers like \[1, 2, 3] or \[2, 3, 4]. * Example: $x₁ = \[2, 3, 4]$ (since we have 3 unknowns: $a$, $b$, $c$) 3. **Read the Results:** Desmos instantly works its magic! Look for the "REGRESSION PARAMETERS" section. It will list the values for your unknown constants ($a$, $b$, $c$, etc.). ### Example SAT problem Example Problem Equivalent Expressions Missing Constants

Example Problem Equivalent Expressions Missing Constants

### Desmos Solution: Desmos Solution Example of Equivalent Expressions Missing Constant

Type: $(5x₁ - 17)(4x₁ - c)$ \~ $ax₁² + bx₁ + 119$ Type: $x₁ = \[2, 3, 4]$ (We need at least 3 numbers in the list because there are three constants: $a$, $b$, $c$). Desmos shows the Regression Parameters: $c = 7$, $a = 20$, and $b = -103$. The question asks for $b$, so the answer is **$-103$**. Solved without expanding a single bracket! ## #8 Statistics Forget manually calculating means, medians, or standard deviations – especially under time pressure. Whether an easy question like the one below or a much more challenging question with many moving parts, Desmos tackles statistical analysis instantly. ### Method 1. **Create Your Data List:** Type a variable (like L or any letter you choose), followed by =, then list your data points inside square brackets \[], separated by commas. * Example: $L = \[25.321, 25.305, 25.340, 25.298, 25.314]$ 2. **Choose the Function:** On the next line, type the name of the statistical function you need, followed by your list variable in parentheses (). * mean(L): Calculates the average. * median(L): Finds the middle value. * stdev(L): Calculates the standard deviation. * boxplot(L): Displays the box plot. 3. **Get Your Answer:** Desmos immediately displays the calculated value. ### Example SAT problem Example Problem Statistics

### Desmos Solution: Desmos Solution Statistics Example

Create the list: $L = \[25.321, 25.305, 25.340, 25.298, 25.314]$ Type: median(L) (or even faster, stats(L) and look for the median). Desmos instantly shows the median is 25.314. That's **Choice (B)**. ## Need Further Guidance? This guide scratches the surface. Dive deep with Resolve Prep's comprehensive Desmos training module. Then, solidify your mastery with our massive library: **8 full digital SAT practice tests** and **over 1800 extra practice problems** built for Desmos users. **Unlock expert strategies and extensive practice – level up your SAT prep at Resolve Prep!**