Practice

Solve problems

Problems unlock one after another, from simple all the way to genius. Every one you solve adds XP.

  • 1,198 problems
  • 9 difficulty levels
  • +5 to +405 XP per problem

Sign in to solve and collect XP. Your progress is saved.

All problems

Showing 1,009–1,056 of 1,198

  • 8.11Calculus

    Locked

    An expansion centred at one

    Difficulty 8 of 9+320 XP
  • 8.12Calculus

    Locked

    A symmetric system at time ln 2

    Difficulty 8 of 9+320 XP
  • 8.13Calculus

    Locked

    A mixed second-order derivative

    Difficulty 8 of 9+320 XP
  • 8.14Calculus

    Locked

    The volume under a surface

    Difficulty 8 of 9+320 XP
  • 8.15Calculus

    Locked

    A domain of convergence with a square

    Difficulty 8 of 9+320 XP
  • 8.16Calculus

    Locked

    An equation with power coefficients

    Difficulty 8 of 9+320 XP
  • 8.17Calculus

    Locked

    A derivative in the direction of a vector

    Difficulty 8 of 9+320 XP
  • 8.18Calculus

    Locked

    A triple integral over a box

    Difficulty 8 of 9+320 XP
  • 8.19Calculus

    Locked

    A series with odd denominators

    Difficulty 8 of 9+320 XP
  • 8.20Calculus

    Locked

    An equation with a y² term

    Difficulty 8 of 9+320 XP
  • 8.21Calculus

    Locked

    An estimate by the total differential

    Difficulty 8 of 9+320 XP
  • 8.22Calculus

    Locked

    An integral along a quarter circle

    Difficulty 8 of 9+320 XP
  • 8.23Calculus

    Locked

    A Fourier sum at two points

    Difficulty 8 of 9+320 XP
  • 8.24Calculus

    Locked

    An equation in differential form

    Difficulty 8 of 9+320 XP
  • 8.25Calculus

    Locked

    A tangent plane to a graph

    Difficulty 8 of 9+320 XP
  • 8.26Calculus

    Locked

    Work along a parabolic arc

    Difficulty 8 of 9+320 XP
  • 8.27Calculus

    Locked

    The cosine of the ratio y/x

    Difficulty 8 of 9+320 XP
  • 8.28Calculus

    Locked

    The chain rule and a gradient

    Difficulty 8 of 9+320 XP
  • 8.29Calculus

    Locked

    An iterated integral with a cube root

    Difficulty 8 of 9+320 XP
  • 8.30Calculus

    Locked

    A Fourier series with period 4

    Difficulty 8 of 9+320 XP
  • 8.31Calculus

    Locked

    A double root and a logarithm

    Difficulty 8 of 9+320 XP
  • 8.32Calculus

    Locked

    A limit of the form 1^∞

    Difficulty 8 of 9+320 XP
  • 8.33Calculus

    Locked

    A sideways parabola

    Difficulty 8 of 9+320 XP
  • 8.34Calculus

    Locked

    Odd squares from the absolute value

    Difficulty 8 of 9+320 XP
  • 8.35Calculus

    Locked

    A linear equation with a variable coefficient

    Difficulty 8 of 9+320 XP
  • 8.36Calculus

    Locked

    The value at a saddle point

    Difficulty 8 of 9+320 XP
  • 8.37Calculus

    Locked

    A disc away from the centre

    Difficulty 8 of 9+320 XP
  • 8.38Calculus

    Locked

    A sine series of the cosine

    Difficulty 8 of 9+320 XP
  • 8.39Algebra

    Locked

    An entry of a matrix exponential

    Difficulty 8 of 9+320 XP
  • 8.40Calculus

    Locked

    A constrained extremum on an ellipse

    Difficulty 8 of 9+320 XP
  • 8.41Calculus

    Locked

    The centre of mass of a non-uniform lamina

    Difficulty 8 of 9+320 XP
  • 8.42Calculus

    Locked

    The sum function of a series with a product below

    Difficulty 8 of 9+320 XP
  • 8.43Calculus

    Locked

    Resonance at frequency 3

    Difficulty 8 of 9+320 XP
  • 8.44Calculus

    Locked

    A Taylor polynomial of x to the y

    Difficulty 8 of 9+320 XP
  • 8.45Calculus

    Locked

    An integral over a tetrahedron

    Difficulty 8 of 9+320 XP
  • 8.46Calculus

    Locked

    A rational function expanded around one

    Difficulty 8 of 9+320 XP
  • 8.47Calculus

    Locked

    Steady oscillations of a damped spring

    Difficulty 8 of 9+320 XP
  • 8.48Calculus

    Locked

    The intercepts of a tangent plane to an ellipsoid

    Difficulty 8 of 9+320 XP
  • 8.49Calculus

    Locked

    An integral along an unfriendly curve

    Difficulty 8 of 9+320 XP
  • 8.50Calculus

    Locked

    Where a series with a quotient converges

    Difficulty 8 of 9+320 XP
  • 8.51Calculus

    Locked

    A third-order equation

    Difficulty 8 of 9+320 XP
  • 8.52Calculus

    Locked

    An improper integral with a half-integer power

    Difficulty 8 of 9+320 XP
  • 8.53Calculus

    Locked

    A tetrahedron under a tangent plane

    Difficulty 8 of 9+320 XP
  • 8.54Calculus

    Locked

    Between two paraboloids

    Difficulty 8 of 9+320 XP
  • 8.55Calculus

    Locked

    A difference of powers over a logarithm

    Difficulty 8 of 9+320 XP
  • 8.56Calculus

    Locked

    Salt in a filling tank

    Difficulty 8 of 9+320 XP
  • 8.57Calculus

    Locked

    The cheapest box with a lid

    Difficulty 8 of 9+320 XP
  • 8.58Calculus

    Locked

    A tilted rectangle

    Difficulty 8 of 9+320 XP