## GCSE content

Relevant content from GCSE/KS3 is

- Basic number work
- Ratios
- Units
- Arithmetic with fractions, simplest form etc.
- Linear equations and graphs
- Scientific notion
- Areas, volumes, perimeter
- Basic data handling / representation

Students who have only done GCSE are likely to struggle with indices, notation and formal manipulation.

**AS Mathematics**

All AS maths students will do C1 and C2 and one of S1, M1 and D1

For potential biology students, the strong recommendation is to choose the S1 option.

For potential physics or engineering students, the strong recommendation is to choose M1.

You could expect an AS student with statistics to have encountered

- Laws of indices
- Integration and differentiation of xn
- Integration gives areas under curves
- Laws of logarithms (log(ab)=log(a)+log(b) etc)
- Solution of quadratic equations
- Linear and quadratic graphs
- Simple use of sin, cos and tan functions and graphs, including
- cos2(x)+sin2(x)=1
- Radians
- Sin rule

- Expanding brackets and geometric series.
- Basic ideas of statistics: Mean, standard deviation, variance, outliers
- Various methods of plotting data and linear regression.
- The shape of the normal distribution and use of tables

Note: they will not have met e, any other differentiation

**A-level mathematics**

For a full A-level in maths students will have done C1-C4 and two of S1, D1, M1, S2, D2, M2

Where there is a choice, potential biologists would be strongly recommended to choose S1 and S2. Physicists and engineers should choose M1 and M2.

A-level maths candiates will know the graphs of e, ln, trig identities, trig differentiation, product, quotient and chain rule.

If they have taken S2 then they will also know some other distributions, know what a random variable is and know about hypothesis testing in simple contexts.

Specifically, the key module content (full A-level in grey) is

Calculus | |

C2 | Diff / Int Axn |

C3 | ddx(ln(Ax)) |

C3 | Diff / int Aenx |

C3 | Diff / int sin(ax) |

C3 | Diff / int cos(ax) |

C3 | Diff / int tan(ax) |

C3 | ∫1ax+b |

C3 | Product rule |

C3 | Quotient rule |

C3 | Function of a function rule’: dydx=dydududx |

Logarithms | |

C2 | If y=nxthen logn(y)=x |

C2 | ln(a)+ln(b)=ln(ab)ln(a)−ln(b)=ln(ab) |

C2 | ln(xp)=pln(x) |

C3 | eln(a)=a |

C3 | ln(y)=ln(a)×loga(y) |

Integral change of variable | |

C2 | Area enclosed by function, average value |

C2 | tan(x)=sin(x)cos(x) |

C2 | sin2(x)+cos2(x)=1 |

C3 | ∫y(x)dx=∫y(x(u))dxdudu |

C4 | sec(x)=1cos(x) |

C4 | cosec(x)=1sin(x) |

C4 | cot(x)=1tan(x) |