QCE Specialist Mathematics Units 3&4 Notes

These are the 20 revision notes inside the QCE Specialist Mathematics Mastery Pack. Open any note to see what it covers before you buy.

1. De Moivre's theorem and roots of unity3 · Further complex numbers

   De Moivre's theorem

2. Factorising polynomials over the complex field3 · Further complex numbers

   Polynomial factorisation over C

3. Proving trig identities using De Moivre's theorem3 · Further complex numbers

   Trigonometric identities via De Moivre

4. Mathematical induction for sums and divisibility3 · Mathematical induction and trigonometric proofs

   Proof by induction — summation and divisibility

5. Lines and planes in three-dimensional space3 · Vectors in two and three dimensions

   Vector equations of lines and planes

6. Cross product and geometric applications in 3D3 · Vectors in two and three dimensions

   Vectors in 3D

7. Equations of spheres and 3D regions3 · Vectors in two and three dimensions

   Spheres and regions in 3D

8. Calculus of vector-valued functions3 · Vector calculus

   Differentiation and integration of vector functions

9. Projectile motion and uniform circular motion via vectors3 · Vector calculus

   Projectile and circular motion

10. Solving systems of linear equations using Gaussian elimination3 · Further matrices

    Systems of linear equations and Gaussian elimination

11. Integration by parts and partial fraction decomposition4 · Integration techniques

    Integration by parts and partial fractions

12. Inverse trig integrals and integration by substitution4 · Integration techniques

    Inverse trigonometric integrals and substitution

13. Volumes of solids of revolution (disk and shell methods)4 · Applications of integral calculus

    Volumes of solids of revolution

14. Areas between curves and PDF applications4 · Applications of integral calculus

    Areas between curves and probability density functions

15. Separable differential equations and slope field analysis4 · Rates of change and differential equations

    Separable differential equations and slope fields

16. Implicit differentiation and related rates of change4 · Rates of change and differential equations

    Implicit differentiation and related rates

17. Simple harmonic motion via differential equations4 · Modelling motion

    Simple harmonic motion

18. Variable forces and motion with non-constant acceleration4 · Modelling motion

    Variable forces and acceleration as a function of velocity

19. Distribution of sample means and confidence intervals for μ4 · Statistical inference

    Sampling distributions and confidence intervals

20. Interpreting and evaluating statistical inference results4 · Statistical inference

    Interpretation and assumptions of statistical inference