# A-level Core Mathematics Curriculum

##### Stage: 5 Challenge Level:

A-level mathematics is currently modular giving students a choice in the maths they study for their AS (1 year course) or A level (extending the AS). Modules are Core pure maths (C1-4), Statistics (S1, S2), Mechanics (M1, M2) and Decision (D1, D2 being algorithms and so on). There are higher modules for further mathematics candidates. These Further Pure modules would be very handy for engineers.

## 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

1. Laws of indices
2. Integration and differentiation of $x^n$
3. Integration gives areas under curves
4. Laws of logarithms ($\log(ab) = \log(a) + \log(b)$ etc)
7. Simple use of sin, cos and tan functions and graphs, including
1. $\cos^2(x)+\sin^2(x)=1$
3. Sin rule
8. Expanding brackets and geometric series.
9. Basic ideas of statistics: Mean, standard deviation, variance, outliers
10. Various methods of plotting data and linear regression.
11. 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 $Ax^n$ C3 $\frac{d}{dx}\left(\ln(Ax)\right)$ C3 Diff / int $Ae^{nx}$ C3 Diff / int $\sin(ax)$ C3 Diff / int $\cos(ax)$ C3 Diff / int $\tan(ax)$ C3 $\int \frac{1}{ax+b}$ C3 Product rule C3 Quotient rule C3 Function of a function rule': $\frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}$ Logarithms C2 If $y = n^x$then $\log_n(y) = x$ C2 $\ln(a)+\ln(b) = \ln(ab)\quad \ln(a)- \ln(b) = \ln\left(\frac{a}{b}\right)$ C2 $\ln(x^p) = p \ln (x)$ C3 $e^{\ln(a)} = a$ C3 $\ln(y) = \ln(a) \times \log_a(y)$ Integral change of variable C2 Area enclosed by function, average value C2 $\tan(x) = \frac{\sin(x)}{\cos(x)}$ C2 $\sin^2(x)+\cos^2(x) =1$ C3 $\int y(x)dx = \int y(x(u))\frac{dx}{du} du$ C4 $\sec(x) = \frac{1}{\cos(x)}$ C4 $\mbox{cosec}(x) = \frac{1}{\sin(x)}$ C4 $\cot(x) = \frac{1}{\tan(x)}$