Cheat codes / Math
Desmos first
The graphing calculator inside Bluebook can do in ten seconds what takes me two minutes by hand, if I know the exact moves.
How I think about it
The code in steps
- 1Open Desmos and type the equation or equations exactly as they are written.
- 2Use ^ for powers, and zoom out with the minus button if the graph is off the screen.
- 3Tap the dot you need: the crossing, the x-intercept or the top of the curve.
- 4For 'for what value of k', type k in the equation and move the slider.
- 5Read the coordinates, find the matching option, then check the last sentence of the question once.
Learn it
1. What it is
Bluebook has a graphing calculator, called Desmos, built into every Math question. You open it from the Math screen, and you can drag it around. It is the same calculator for the whole test, so you can practise it at home for free.
The code: when a question is about a graph, a system, a parabola or an equation that is hard to solve by hand, type it into Desmos first and read the answer from the picture.
2. The five moves you must know
1. Intersection of two graphs. Type the first equation on line 1, the second on line 2. Tap the dot where the graphs cross. A small box shows the coordinates. This solves systems of equations, including a line and a curve.
2. Solving an equation. Type the left side as y = (left side) and the right side as y = (right side). The x-coordinate of each crossing is a solution. For something like 2x² - 8x - 10 = 0, just type 2x^2-8x-10 and tap where the curve touches the x-axis.
3. Top or bottom of a parabola. Type the function. Tap the highest or lowest point of the curve. You get the vertex, so you know the maximum or minimum.
4. Checking values. Type f(x) = x^2 - 4x + 3 on line 1 and f(5) on line 2. Desmos prints the number (8). This is quick for 'what is f(5)' and for testing answer options. You can also add a table with the plus sign to see many outputs at once.
5. Regression. Press the plus sign, add a table, type the x-values and y-values, then on a new line type y1 ~ m x1 + b. Desmos gives you the best line of fit.
Do not forget the exponent symbol: type ^ for a power. If the picture is off the screen, use the minus button to zoom out until you can see the curve.
3. The sliders trick
If you type an equation that has a letter that is not x or y, such as y = 2x + k, Desmos offers to make a slider for k. Then you can set k to any number and watch the graph change. This is perfect when the question says 'for what value of k', because you can test the options one by one.
4. A tiny drill
Open Desmos. Type y = x^2 - 4x + 3 and tap the two points where the curve crosses the x-axis. You should see (1, 0) and (3, 0). Now type y = x - 1 on line 2 and tap the two places where the line and the curve cross. You should see (1, 0) and (4, 3). If your points do not match, check your typing.
Practise the five moves until each one takes under 15 seconds.
5. How to know when to use it
Use Desmos first when you see: a system with a curve in it, an equation that does not factor easily, 'maximum' or 'minimum' of a parabola, a table of data with a request for the line of best fit, or 'for what value of k' with a graph.
Do not use it for a simple one-step question such as 3x + 7 = 22. Your head is faster there.
Why it works
Digital SAT Math lets you use a built-in graphing calculator on every question, so the test writers know that graphs can be used. Many questions that look hard by hand are very short in Desmos, because the calculator solves in one tap what takes the student five steps of algebra. The calculator also lowers the chance of small arithmetic slips, and every Math question gives you about 95 seconds, so a ten-second picture is a good use of time. It is not cheating. It is a tool the College Board put in the room for you.
Watch out: Desmos is slow if you type slowly, and it can mislead if the answer is not an easy decimal or the graph is hiding off the screen. If the question asks for an exact answer such as 3 + √2 or a fraction, Desmos gives you a decimal, and you must match it to the option. Also, when the algebra is two lines, do it by hand. Practise both so you can choose.
See it work on real questions
Try each question your usual way first. Then open the box to see the code at work.
Nonlinear equations and systems · question 4
Loading the question…
Nonlinear functions · question 5
Loading the question…
Nonlinear equations and systems · question 5
Loading the question…
Two-variable data · question 3
Loading the question…
Linear functions · question 6
Loading the question…
Do not just believe me. Test it.
Choose 6 problems from the Nonlinear, Systems or Linear Functions skills. Solve 3 by hand and 3 with Desmos, and write down the time for each. If you are slow in Desmos, that is normal: it comes from not knowing the moves, so repeat the five moves above until they are quick. After one week, redo the test. Compare time and mistakes.