Advanced · 2h 24m · 18 lessons
Mathematics: Advanced
Functions, calculus, vectors and probability: worked out exactly, for Class 11-12.
What you'll learn
- ✦Perform set operations (union, intersection, difference) and use them to count elements in combined groups
- ✦Decide whether a relation is a function, and classify a function as one-one, onto or bijective
- ✦Simplify a trigonometric expression using standard identities, and solve a trigonometric equation for its general solution
- ✦Perform arithmetic on complex numbers, including finding the modulus and solving a quadratic equation with complex roots
- ✦Find the nth term and sum of a geometric progression. Count arrangements and selections using permutations and combinations, and multiply matrices to solve a pair of linear equations
- ✦Find the equation of a straight line and a conic section. Locate a point and a line using vectors and 3-D coordinates
- ✦Evaluate a limit, and differentiate a function using the standard rules. Then use the derivative to find a maximum, minimum or rate of change
- ✦Integrate a function to find an area under a curve. Then use conditional probability and Bayes' theorem to interpret a real test result
Certification projects
Build 3 projects to earn your certificate
Hands-on work that proves you can apply what you learned — part of the certificate requirements.
Syllabus
Module 1 · 24m
Sets, Relations and Functions Free
What you'll be able to do
- Can use union, intersection and difference to count elements in combined groups
- Can decide whether a given relation is a function
- Can classify a function as one-one, onto or bijective
Module 2 · 24m
Trigonometric Functions and Complex Numbers Locked
What you'll be able to do
- Can simplify a trigonometric expression using a standard identity
- Can write the general solution of a simple trigonometric equation
- Can add, multiply and find the modulus of a complex number
Module 3 · 24m
Sequences, Permutations and Matrices Locked
What you'll be able to do
- Can find the nth term and the sum of a geometric progression
- Can decide whether a counting problem needs a permutation or a combination, and calculate it
- Can multiply two matrices and use a determinant to solve a pair of linear equations
Module 4 · 24m
Coordinate Geometry, Vectors and 3-D Locked
What you'll be able to do
- Can find the equation of a straight line and identify a circle or a parabola from its equation
- Can add two vectors and find a vector's magnitude and direction
- Can find the distance between two points in 3-D and the direction ratios of a line
Module 5 · 24m
Limits, Derivatives and Applications Locked
What you'll be able to do
- Can evaluate the limit of a simple algebraic function as x approaches a value
- Can differentiate a function using the sum, product and quotient rules
- Can use a derivative to find a function's rate of change and its maximum or minimum value
Module 6 · 24m
Integrals and Probability Locked
What you'll be able to do
- Can find the indefinite integral of a simple function
- Can use a definite integral to find the area under a curve
- Can use Bayes' theorem to find the real chance of an event given new evidence