Check out www.skool.com/satprep for targeted practice on these patterns and a whole lot more
Overall Tips
●​ Always use Desmos whenever possible (definitely use it anytime there's an equation)
●​ Always predict with detail how you’re going to solve a question before you actually solve
it. Then you can check to see if you predicted correctly. This adds a feedback loop to
help you learn the patterns quickly. If you can’t see how you’re going to solve it you
should skip that question during the test to come back to later.
Desmos Overview (11.61%)
Make sure you know all of these…
●​ Graphing an equation
○​ Desmos will usually tell you the intercepts, max and mins (what a vertex is), and
any intersections.
●​ Typing in a point
●​ Table
○​ Zoom fit
○​ Add Regression
●​ Home button
●​ Undo and redo button
●​ Edit list
○​ Duplicate button
○​ Formatting lines
○​ Table button
○​ Delete all button
●​ Turning on and off equations
●​ Fraction button
●​ How to add sliders (x, y, e and r)
●​ Useful functions
○​ Mean, median, standard deviation, gcd
●​ *, ^, %of, how to get multiple terms in the numerator and exponent, ≥≤, sqrt, cbrt,
nthroot, pi
●​ Functions
●​ Changing from radians to degrees in settings
●​ {}
Single Variable Equation (8.09%)
Any time you see an equation with only one variable…
1.​ Replace the variable with x
2.​ Plug the whole thing into desmos
3.​ The vertical lines will be the values of the variable (they are the solutions)
Systems of Equation (5.05%)
Plug in the 2 equations and the intersections are the solutions.
Number of Solution (6.06%)
ID: Anytime it asks for the number of solutions or asks you to find a value of a constant so that
there are a certain number of solutions
If it’s one equation, plug the left and right side of the equal sign on 2 different lines in
desmos with a “y=” in front.
Move the slider until conditions are met:
●​ No solution = never touching
●​ Infinite solutions = on top of each other
●​ One solution = touching once
●​ Two solutions = touching twice
Equivalent Expressions (3.54%)
(Put “y=” in front of all the lines in desmos just in case)
Plug in the top expression, and the answer choices, the only answer choice that is the same
line/curve as the top expression is the answer.
Functions (2.27%)
As long as the functions are defined, you can just type in f(#) and desmos will tell you the
answer. Desmos will also graph any transformations such as g(x-2)
f(x-2) = shift right 2
f(x+2) = shift left 2
f(x)-2 = shift down 2
f(x)+2= shift up 2
Inequalities (1.77%)
The shaded region is the solution.
If the line is dashed then the line itself isn’t a solution
If the line is solid then the line is also part of the solution.
Circle Equation (1.52%)
2
2
2
The equation of a circle: (𝑥 − ℎ) + (𝑦 − 𝑘) = 𝑟
Center: (ℎ, 𝑘)
Radius: 𝑟
●​ 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒((2, 3), (6, 7)) finds the distance between 2 points
○​ Make sure you use the max and min to find the diameter of the circle
●​ 𝑚𝑖𝑑𝑝𝑜𝑖𝑛𝑡((2, 3), (6, 7)) finds the middle point between 2 points
○​ Make sure you use the max and min to find the center of the circle
Regression w/ Table (9.85%)
When can you use regression? Anytime the question gives you points.
3 steps
1.​ Type in the points
2.​ Type in the equation
3.​ Change the equation into regression format
a.​ Change the variables to what it says in the first row of the table (usually 𝑥1and 𝑦1)
b.​ Change the “=: sign to “~”
If the equation isn’t given in the problem you can also use the add regression button and select
the right equation using the drop down menu…
or use these:
2
●​ Quadratic/parabola vertex form: 𝑦 = 𝑎(𝑥 − ℎ) + 𝑘
𝑥
●​ Exponential: 𝑦 = 𝑎(𝑏) − 𝑐
2
2
2
●​ Circle: (𝑥 − ℎ) + (𝑦 − 𝑘) = 𝑟
Regression w/o Table
●​ Use the tilde (~) to ask Desmos to estimate constants.
●​ Use = to:
○​ Graph expressions
○​ Assign values to variables
●​ Use ~ to:
○​ Estimate unknown constants (e.g., a, b, x1, y1, etc.)
Important Rules
●​ Desmos only estimates constants.
○​ DO NOT use lowercase x, y, or e in regression
○​ Use x1, y1, a, b, etc. instead.
●​ If you already define a constant (a = 3), regression won’t solve for it.
●​ Desmos returns the value with the smallest absolute value if multiple values work.
●​ If you are finding the value of a constant like a or b instead of x or y, you may need to
simulate x being true for many x-values. You can do this by setting 𝑥1 equal to a list like
this 𝑥1 = [1... 10]
○​ Desmos tests all those values and solves for constants like a, b, c.
●​ Use {} to tell desmos constraints like {p>1}
How Desmos Solves
●​ Starts from 0, checks positive and negative values.
●​ Tries integers first before testing decimals.
●​ Will only give one value — not all possible solutions.
Solving Systems of Equations
To solve:
x + y = 10
x² + y² = 58
Write:
2
2
[𝑥1 + 𝑦1, 𝑥1 + 𝑦1 ]~[10, 58]
Brackets = list​
When NOT to Use Regression
Avoid regression if the question asks:
●​ “How many solutions?”
●​ “What is the maximum or minimum solution?”
●​ “What are all possible values of x?”
Desmos only gives one solution, not multiple.
Isolation (1.77%)
You can check to make sure you are correct by…
1.​ Typing the equation in the question in regression format
2.​ Randomly set one of the constants equal to a random number to diversify the value of
the constants
3.​ Type in the answer choices and see which one equals the value of the isolated constant
Factoring (0.76%)
You can check if an expression is a factor of another expression by graphing them both and
checking if they share an x-intercept.