DSE M1 Syllabus: Every Topic, and What Is Not Required

1. Binomial expansion. Not required: trinomials, greatest coefficient or term, numerical approximation.
2. Exponential and logarithmic functions: e, the exponential series, growth and decay, reducing to linear relations.
3. Derivative of a function. Not required: first principles.
4. Differentiation. Not required: implicit, parametric and logarithmic differentiation, inverse functions, trigonometric functions.
5. Second derivative. Not required: third and higher derivatives.
6. Applications of differentiation: tangents, rates of change, maxima and minima.
7. Indefinite integration, including substitution. Not required: integration by parts.
8. Definite integration and area under a curve. Not required: area between a curve and the y-axis, area between two curves, volumes.
9. The trapezoidal rule. Not required: error estimation.

10. Conditional probability and Bayes' theorem.
11. Discrete random variables.
12. Probability distribution, expectation and variance, including E(aX + b) and Var(aX + b).
13. The binomial distribution. Not required: proofs of the mean and variance.
14. The Poisson distribution.
15. Applications of the binomial and Poisson distributions.
16. The normal distribution: definition and properties.
17. Standardisation and the standard normal table.
18. Applications of the normal distribution. Not required: normal approximation to the binomial or Poisson distribution.
19. Sampling distribution and point estimates.
20. Confidence interval for a population mean. Not required: hypothesis testing and the t-distribution.

General calculus and statistics resources, and many AI tools, answer with methods that are not in M1: integrating by parts, differentiating sin x, a continuity correction, or a t-test. The answer may be correct mathematics and still be the wrong method for your paper. Choosing DSE M1 in SketchMath keeps the solution to M1 methods and tells you when a question goes beyond the syllabus.