Intersect Prep

How to use Desmos on the AP Calculus AB exam

Updated

The AP Calculus AB exam is given in the Bluebook app, and Desmos is built into Bluebook for the calculator parts of the exam. An approved handheld calculator is also allowed if you prefer one.

The College Board lists four things a calculator on this exam has to do. This guide shows each one in Desmos with an AB example, then covers what has to appear on your paper, because a number on a screen earns nothing by itself.

Where Desmos is available

  • Section I, Part B: 13 multiple-choice questions in 38 minutes, calculator allowed.
  • Section II, Part A: 2 free-response questions in 30 minutes, calculator allowed.
  • Section I, Part A and Section II, Part B: no calculator. These parts hold 29 multiple-choice questions and 4 free-response questions, and they make up about 68% of your score.

Desmos is useful for about a third of the exam, and you still need to do the calculus by hand for the rest. The AP Calculus AB exam format guide has the full breakdown.

The four required skills

A calculator on this exam needs to graph a function in any window, find zeros to solve equations, calculate a derivative at a point, and calculate a definite integral. Desmos does all four.

Skill 1: graph in the window you need

Desmos opens with a view that runs roughly from x=−10x = -10 to x=10x = 10. The question decides what window you need, so zoom or set the axes until the whole interval is on the screen.

Look past the default view

How many solutions does the equation e0.5x=x3e^{0.5x} = x^3 have on the interval 0<x<200 < x < 20?

Graph y=e0.5x−x3y = e^{0.5x} - x^3 and count where it crosses the xx-axis. In the default view you see one crossing near x=1.227x = 1.227, and then the curve falls off the bottom of the screen. It's easy to stop there and answer 11.

Stretch the window to x=20x = 20 and make the yy-axis much taller. The exponential term catches up, and the curve comes back through zero near x=16.999x = 16.999.

5101520-2000-100010002000x ≈ 1.227x ≈ 16.999
y=e0.5x−x3y = e^{0.5x} - x^3At this scale the first crossing sits close to the origin, so check both views.

Answer: 22 solutions

Skill 2: solve equations with zeros and intersections

There are two ways to solve an equation. Graph each side and click the point where the curves cross, or move everything to one side and click where the graph crosses the xx-axis. Click a curve to show its gray points, then click one to see its coordinates.

The value promised by the Mean Value Theorem

Let f(x)=x ln⁡(x+1)f(x) = \sqrt{x}\,\ln(x + 1). Find the value of cc in the interval (1,5)(1, 5) where the instantaneous rate of change of ff equals the average rate of change of ff on [1,5][1, 5].
  1. 1Type f(x)=xln⁡(x+1)f(x) = \sqrt{x}\ln(x + 1) on one line.
  2. 2On the next line, type y=f′(x)y = f'(x).
  3. 3On the next line, type y=f(5)−f(1)5−1y = \frac{f(5) - f(1)}{5 - 1}. Desmos draws a horizontal line at about 0.8280.828.
  4. 4Click the crossing between x=1x = 1 and x=5x = 5. It's at x≈3.158x \approx 3.158.

On your paper, write the equation you solved: f′(c)=f(5)−f(1)5−1f'(c) = \frac{f(5) - f(1)}{5 - 1}, so c=3.158c = 3.158.

Answer: c≈3.158c \approx 3.158

Skill 3: find a derivative at a point

Define the function, then type the derivative at the input you want using prime notation. You can also type "d/dx" to get the derivative operator.

A rate with units

The volume of water in a tank is V(t)=40+6t1.5e−0.1tV(t) = 40 + 6t^{1.5}e^{-0.1t} gallons, where tt is in minutes. Find the rate at which the volume is changing at t=4t = 4. Include units.

Type V(t)=40+6t1.5e−0.1tV(t) = 40 + 6t^{1.5}e^{-0.1t}, then V′(4)V'(4). Desmos shows about 8.848228.84822. The rate is positive, so the volume is increasing at that moment.

On your paper, write V′(4)=8.848V'(4) = 8.848 gallons per minute. The derivative of gallons with respect to minutes has units of gallons per minute.

Answer: 8.8488.848 gallons per minute

Skill 4: calculate a definite integral

Type "int" and Desmos builds the integral sign. Fill in the lower and upper limits, the integrand, and the differential. The value appears at the right of the line.

Average value

Find the average value of g(x)=ln⁡(x2+3)g(x) = \ln(x^2 + 3) on the interval [1,6][1, 6].

The average value is 16−1∫16g(x) dx\frac{1}{6 - 1}\int_1^6 g(x)\,dx. The integral is about 13.2491413.24914, and dividing by 55 gives about 2.649832.64983.

Answer: 2.6502.650

Integrals like this come up throughout area and volume problems and rate in and rate out problems.

What to write on your paper

Free-response answers are written by hand, and the people scoring them can't see your screen. The College Board requires you to write the setup, which means the equation you solved or the derivative or integral you evaluated.

  • Write math, not keystrokes. Write ∫16ln⁡(x2+3) dx\int_1^6 \ln(x^2 + 3)\,dx, not the sequence of keys you pressed.
  • Give three decimal places unless the question tells you otherwise. Keep more digits while you work.
  • Show the setup before the number. A correct value with no setup won't earn full credit.
  • Reuse values by name. Name a function or an integral in Desmos and refer to it by name, so you don't retype a rounded value.

The AP Calculus AB free-response guide has more on how to earn each point.

Keep going

Practice on exam-style questions

Intersect Prep has 400 multiple-choice questions across all 8 units, with a full solution for each one. Create a free account to try a full lesson with the calculator. One payment of $44 unlocks the course for 6 months.

Questions

Is Desmos allowed on the AP Calculus AB exam?
Yes, on the calculator parts only. Bluebook has Desmos built in for Section I Part B and Section II Part A. It isn't available on Section I Part A or Section II Part B.
Can I use my own calculator on the AP Calculus AB exam?
Yes, if it's an approved handheld calculator. Check the College Board's current list before exam day.
How many decimal places do I need?
Three places after the decimal point, unless the question says otherwise. Round only at the end of your work.
Does Desmos give me an antiderivative?
No. Desmos gives the numeric value of a definite integral, not a formula for an antiderivative. You need antiderivatives by hand on the no-calculator parts.

Desmos is a trademark of Desmos Studio PBC.