Mathematics, grade 11

Topics in this grade

• Permutations and Combinations

  A permutation lines up every one of n distinct items in some order.

  6 exercises

• Statistics

  Statistics is the study of collecting, organizing, and summarizing sets of numbers.

  7 exercises

• Random Variables and Expected Value

  A random variable is simply a number attached to each possible outcome of a random experiment.

  5 exercises

• Cylinders and Cones: Surface Area

  A cylinder is formed by two identical circles connected by a curved side, like a can.

  6 exercises · about 25 min

• Sphere and Ball

  A ball is every point within a fixed distance of one center, like a bowling ball.

  6 exercises · about 20 min

• Volumes of Prisms, Pyramids, Cylinders, Cones, and Spheres

  Prisms and pyramids are polyhedra with flat faces.

  8 exercises · about 25 min

• Logarithms

  A logarithm answers one question: what power turns a fixed base into a given number?

  6 exercises

• Exponential Function

  An exponential function raises a fixed positive number to a variable power, written y = a^x.

  6 exercises

• Logarithmic Function

  A logarithmic function reads y as the logarithm of x, written y equals log base a of x.

  6 exercises

• Limits

  A limit describes the value a function approaches as x gets closer and closer to some number.

  9 exercises

• Derivatives

  A derivative measures how fast a function's value changes as x changes.

  9 exercises

• Using the Derivative: Monotonicity and Extrema

  A function is increasing where its derivative is positive, and decreasing where its derivative is negative.

  9 exercises · about 26 min

• Integrals

  An antiderivative of a function is another function whose derivative gives back the original one.

  6 exercises

• Using the Integral: Area, Volume, and Work

  The area between two curves equals the definite integral of the top function minus the bottom function.

  9 exercises · about 26 min

• Complex Numbers

  A complex number is a number written as a + bi, where a and b are real numbers.

  8 exercises

• Probability: Events and Axioms

  A random experiment is any process whose exact result cannot be predicted ahead of time.

  7 exercises

• Independent Events and Conditional Probability

  Two events are independent when knowing one happened tells you nothing new about the other.

  6 exercises

• Euler's Formula for Polyhedra

  A polyhedron's vertices, edges, and faces are connected by a simple rule.

  6 exercises · about 20 min

• Surface Area of a Prism

  A right prism has two parallel matching bases joined by rectangular side faces standing straight up.

  6 exercises · about 20 min

• Diagonal of a Rectangular Box

  A rectangular box has three edge lengths meeting at each corner: its length, width, and height.

  6 exercises · about 20 min

• Surface Area of a Regular Pyramid

  A regular pyramid has a regular polygon base and identical triangular side faces meeting at one apex.

  6 exercises · about 20 min

• The Five Regular Polyhedra

  A regular polyhedron has faces that are all the same regular polygon.

  6 exercises · about 20 min

• Locating a Pyramid's Height Under Given Conditions

  A pyramid's height drops from its apex straight down to one special point on the base.

  6 exercises · about 20 min

• Volume of a Frustum of a Pyramid or Cone

  A frustum is the piece left when a plane parallel to a base slices off a pyramid or cone top.

  6 exercises · about 20 min

• Volume of a Spherical Segment and Sector

  A spherical segment is the smaller piece a plane cuts off a ball, not through the ball's own center.

  6 exercises · about 20 min

• Spheres Inscribed in and Circumscribed About Polyhedra

  A sphere is inscribed in a polyhedron when every one of the polyhedron's faces just touches that sphere.

  6 exercises · about 20 min

Where this leads

These topics feed DTM (State Testing Center), NMT (National Multi-Subject Test), ZNO (External Independent Evaluation).