One midterm-style challenge. How ready are you?
Try it on the board, if you like. Write your working and pause: a red pen marks the exact line that lost the point, the way your TA grades, then explains it out loud.
- Marks the exact line
- Explains it out loud
- First practice exam free
Evaluate the integral of 6x sin(x²) dx from 0 to √π.
Nothing you write here is saved.
Stared at that integral a little too long?
That feeling comes back on exam day. Leave it here.
RedPen grades every line of a full practice exam, the way your TA will. You find the step that loses points now, not when it costs you a grade.
How a practice exam will work
Pick an exam. Write it like the real one.
Practice exams will be full calculus midterms and finals, set out like a university paper, with a timer if you want one. Every line written with a finger, mouse or stylus.
Every line gets marked
The red pen strikes the first line that lost a point. The working that follows correctly from it keeps its credit, the way partial credit works on the real exam.
You get a fix list, not just a score
Each slip explained out loud, like a TA in office hours, then similar questions to try until it sticks.
What you will get back
- 1. Limits and continuity4 / 4
- 2. Chain rule2 / 3
- 3. Related rates5 / 8
- 4. Optimization7 / 7
- 5. Riemann sums and the FTC8 / 10
- 6. u-substitution5 / 8
The lines that cost the most
- −3Problem 3: the radius is shrinking, but dr/dt was written as +2.
- −3Problem 6: after u = x², the limits were left as 0 and √π.
Fix these before your exam
- Signs of a shrinking quantity in related rates
- Changing the limits in a u-substitution
- The inside derivative in the chain rule
One missing 2x. Not a zero.
University calculus exams give partial credit for the working, not only the last line. Practice exams will score every problem point by point, so you can see what one slip really costs, and what it does not.
Problem 3 (3 points). y = sin(x²). Find dy/dx at x = √π.
| Point | Result | Why |
|---|---|---|
| Chain rule | 0 / 1 | wrote cos(x²): the 2x from the inside is missing |
| Substitutes x = √π | 1 / 1 | right for the derivative you wrote |
| Final value | 1 / 1 | follows from your line, so the point is carried |
2 of 3 points
A checker that only looks at the last line would give this 0 of 3.
Not another app that works it out for you
| Apps that work it out for you | RedPen |
|---|---|
| Read the question | Reads your working |
| Hand you a finished solution | Finds the first line that lost points |
| No score | Scores it like your exam, partial credit included |
| You copy it | You fix it yourself, then try a similar one |
What it covers
Not just Calculus I. The whole sequence, from your first limit to Stokes' theorem: open any unit to see every topic.
Calculus I
Limits and continuityThe foundation of differential calculus
- Functions and their graphs
- Domain and range
- Piecewise-defined functions
- Average rate of change
- The intuitive meaning of a limit
- Left-hand and right-hand limits
- Limits at a point
- Limits at infinity
- Infinite limits and vertical asymptotes
- Limit laws and algebraic evaluation
- Factoring and rationalizing to evaluate limits
- Trigonometric limits
- The squeeze theorem
- Continuity at a point
- Continuity over an interval
- Removable, jump and infinite discontinuities
- Intermediate Value Theorem
Derivatives and differentiationEvery rule, from first principles up
- Derivative as an instantaneous rate of change
- Derivative as the slope of a tangent line
- The limit definition of the derivative
- Differentiability and continuity
- Power, constant multiple, sum and difference rules
- Product rule
- Quotient rule
- Chain rule
- Exponential and logarithmic functions
- Trigonometric functions
- Inverse trigonometric functions
- Implicit differentiation
- Logarithmic differentiation
- Higher-order derivatives
- Second derivative and acceleration
- Derivatives of inverse functions
- Tangent and normal lines
- Parametrically defined curves
Applications of derivativesWhere most midterm points are won and lost
- Increasing and decreasing functions
- Critical points
- Local maxima and minima
- Absolute extrema on a closed interval
- First derivative test
- Second derivative test
- Concavity and points of inflection
- Curve sketching
- Optimization
- Related rates
- Linear approximation
- Differentials and error estimation
- Newton's method
- Rolle's theorem
- Mean Value Theorem
- L'Hôpital's rule
IntegrationAntiderivatives to the Fundamental Theorem
- Antiderivatives and indefinite integrals
- Basic integration formulas
- Exponential, logarithmic and trigonometric integrals
- Initial-value problems
- Riemann sums
- Left, right and midpoint approximations
- Definite integrals and their properties
- The Fundamental Theorem of Calculus, Parts I and II
- Accumulation functions
- Net change
- Average value of a function
- Trapezoidal and Simpson's rules
- u-substitution
Calculus II
Techniques of integrationThe toolbox every Calc II exam tests
- Integration by parts
- Trigonometric integrals and identities
- Trigonometric substitution
- Partial fractions
- Rational functions
- Improper integrals with infinite limits
- Improper integrals with infinite discontinuities
- Convergence and divergence of improper integrals
Applications of integrationAreas, volumes and physics
- Area under and between curves
- Volumes by cross-sections
- Disk and washer methods
- Cylindrical shells
- Arc length
- Surface area of revolution
- Work
- Fluid pressure and force
- Mass, moments and center of mass
- Probability density functions
Sequences and seriesEvery convergence test, then Taylor series
- Sequences and their limits
- Monotone and bounded sequences
- Partial sums
- Geometric and telescoping series
- Divergence test
- Integral test
- Direct and limit comparison tests
- Alternating series test
- Absolute and conditional convergence
- Ratio and root tests
- Power series
- Radius and interval of convergence
- Taylor and Maclaurin series
- Remainder and approximation error
- Functions as power series
Parametric and polarCurves described a different way
- Parametric curves
- Eliminating the parameter
- First and second derivatives of parametric curves
- Parametric arc length
- Polar coordinates
- Converting between polar and Cartesian
- Graphing polar curves
- Derivatives in polar form
- Areas enclosed by polar curves
Multivariable and Vector Calculus
Vectors and 3D geometryThe language of Calc III
- Vectors in 2D and 3D
- Dot product and angles
- Cross product
- Lines and planes in space
- Distances between points, lines and planes
- Determinants
- Vector-valued curves
- Velocity and acceleration along a curve
Partial derivativesFunctions of several variables
- Functions of two and three variables
- Level curves and level surfaces
- Limits and continuity in several variables
- Partial and mixed partial derivatives
- Tangent planes
- Linear approximation and total differentials
- The multivariable chain rule
- Implicit differentiation in several variables
- Gradients and directional derivatives
- Direction of fastest increase
Multivariable optimizationCritical points, saddles and constraints
- Critical points
- Second derivative test in two variables
- Saddle points
- Extrema on a closed region
- Lagrange multipliers
- Several constraints
Multiple integralsDouble and triple integrals
- Double integrals over rectangles and general regions
- Changing the order of integration
- Polar double integrals
- Triple integrals
- Cylindrical and spherical coordinates
- Jacobians and change of variables
- Areas, volumes and mass
Vector calculusThe big theorems
- Vector fields
- Conservative fields and potential functions
- Line integrals
- Work and path independence
- Flux across a curve
- Green's theorem
- Parametrized surfaces
- Surface integrals and flux
- Divergence and curl
- Divergence theorem
- Stokes' theorem
Intro Differential Equations
First differential equationsOften the last unit of a calculus course
- What a differential equation is
- Order
- Initial-value problems
- Exponential growth and decay
- Separable equations: separating the variables
- Population models
- Newton's law of cooling
Why you can trust the red pen
- In practice exams, a computer algebra system will check every step. A line is marked wrong only when it is proven wrong.
- We will publish how often RedPen agrees with a human calculus grader before anyone pays.
- For practice only. It marks working you wrote, and it will not do graded problem sets for you.
- Your work is never sold or used for advertising.
Before you sign up
Is this against my honor code?
RedPen is for exam practice. It marks working you have already written on practice questions and points to the step that went wrong instead of handing over the result. Do not use it on graded problem sets, and check your course policy if you are unsure.
How is this different from ChatGPT or Photomath?
Those are built to produce a worked solution for a question. RedPen is built to grade: it reads the working you wrote, finds the first line that lost points, scores the problem with partial credit the way your exam will, and explains that one step.
Can it read my handwriting?
Try it on the challenge at the top of this page: that is the same reading the practice exams will use. If it cannot make out a line, it says so and asks you to rewrite it, instead of guessing.
Does it work on my phone or iPad?
Yes. It runs in the browser on a phone, tablet or laptop. A tablet with a stylus feels closest to writing on paper.
Which courses does it cover?
The whole calculus sequence: Calculus I, Calculus II (integration techniques, series, parametric and polar), multivariable and vector calculus, and first differential equations. The full list of topics is in What it covers, above.
My course moves fast. Is this too basic?
The demo questions are the kind a first midterm asks. Practice exams will run up to final-exam level, with longer multi-part problems scored point by point the way a university exam is.
When does it open?
The demo on this page works today. Practice exams are being built now, and we are aiming to open them before fall 2026 finals. People on the list hear first.
What happens to my work?
On this page, nothing you write is stored. When practice exams open, your work will be kept only to show you your results, never sold, and you will be able to delete it at any time.
When's your next exam?
Tell us when it is, and leave your email. When practice exams open, your first marked one is free, and we will time our emails to land before your midterms and finals. Unsubscribe any time.