Cambridge A-Level · Further Mathematics

Complex Numbers, Matrices, Series and Calculus

22 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 22 questions

  1. What is the derivative of with respect to ?
  2. What is the value of , where is the imaginary unit?
  3. Given , what is the modulus ?
  4. Find .
  5. Find the complex conjugate of .
  6. Solve for complex .
  7. What is the value of ?
  8. What is the inverse of ?
  9. A matrix has . What does this tell you?
  10. Evaluate when .
  11. Find when .
  12. Use proof by induction: for the base case , which statement proves ?
  13. What is the derivative of with respect to ?
  14. Find .
  15. Find .
  16. The Maclaurin series of begins . What is the next term?
  17. Solve the differential equation with when .
  18. What is the 3 x 3 identity matrix's determinant?
  19. A polar form of is . What are and ?
  20. Use De Moivre's theorem: what is ?
  21. What is the sum to infinity of the geometric series ?
  22. The roots of are and . What is ?

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