A Six Week Cambridge 9709 AS Maths Revision Plan That Actually Finishes the Syllabus

Most Cambridge AS Maths revision plans you can find online either skim the whole syllabus in three weeks and call it done, or list every learning objective and quietly assume you will get to all of them. Neither one finishes the 9709 syllabus in time for the real paper.

This plan does. It is six weeks, built specifically for Cambridge International AS & A Level Mathematics 9709, around the Pure 1 (Paper 1) spine that every AS combination shares, with side weeks for Probability & Statistics 1 (Paper 5), Mechanics (Paper 4), and Pure 2 (Paper 2) layered in. It works whether your AS combination is Paper 1 plus Paper 5, Paper 1 plus Paper 4, Paper 1 plus Paper 2, or the full four components.

It is also built around the only thing that actually moves AS marks: doing maths under time pressure, then fixing the specific things you got wrong. Re-reading notes is not revision. This is.

Before week 1: choose your components and clear two evenings

Spend an hour, before the plan starts, doing two specific things.

1. Confirm which papers you are sitting. Paper 1 (Pure Mathematics 1) is mandatory for every 9709 candidate. The AS combinations Cambridge offers are Paper 1 + Paper 2 (Pure-only, AS only), Paper 1 + Paper 4 (Mechanics), or Paper 1 + Paper 5 (Probability & Statistics 1). Write the paper codes at the top of a sheet of paper. This is your scope.
2. Sit one past paper of Paper 1 from 2025 onwards, untimed, with no help. Mark it against the official mark scheme, slowly. The list of topics where you lost marks is your prioritisation map for the next six weeks. The plan below is the default order. If your map says trigonometry is weaker than expected, swap it earlier.

Week 1: Pure 1 algebra, functions, coordinate geometry, and series

The Pure 1 algebra toolkit underpins everything else, in every component. Lock it down first. The Cambridge 9709 Paper 1 syllabus splits this content across sections 1.1 Quadratics, 1.2 Functions, 1.3 Coordinate geometry, and 1.6 Series.

• Surds and indices: rationalising denominators, manipulating fractional and negative indices fluently.
• Quadratics (1.1): factorising, the formula, completing the square, the discriminant condition for real, equal, or no roots ($b^2 - 4ac$).
• Simultaneous equations with one linear and one quadratic, including geometric interpretation (line meets curve).
• Functions (1.2): domain, range, composite functions $fg(x)$, inverse functions $f^{-1}(x)$, including the graphical reflection in $y = x$.
• Transformations of graphs: $f(x) + a$, $f(x + a)$, $af(x)$, $f(ax)$, and combinations.
• Coordinate geometry (1.3): the equation of a straight line, midpoint and distance, parallel and perpendicular gradients, the equation of a circle $(x - a)^2 + (y - b)^2 = r^2$, and intersection problems (line and curve, two circles).
• Series (1.6): the binomial expansion of $(a + b)^n$ for positive integer $n$ using $^nC_r$, and arithmetic and geometric progressions including the formulas for the $n$th term, the sum to $n$ terms, and the sum to infinity of a convergent geometric series ($|r| < 1$).

End each session by redoing, from blank paper, one question you got wrong the day before. If you cannot, you have not learned it yet.

Week 2: Pure 1 calculus, trigonometry, and circular measure

These three strands appear together in the heavier Paper 1 questions, so train them together. They are syllabus sections 1.4 Circular measure, 1.5 Trigonometry, 1.7 Differentiation, and 1.8 Integration.

• Differentiation (1.7) of polynomials and surds, the chain rule for $(ax + b)^n$, increasing and decreasing functions, stationary points and their nature (second-derivative test), and related rates of change.
• Integration (1.8) of $(ax + b)^n$ for any rational $n$ except $-1$, the constant of integration, definite integrals (including simple improper integrals), area of a region bounded by a curve and lines, area between two curves, and volumes of revolution about either the $x$-axis or the $y$-axis.
• Trigonometry (1.5): exact values for the special angles, the unit-circle approach, the identities $\sin^2\theta + \cos^2\theta = 1$ and $\tan\theta = \frac{\sin\theta}{\cos\theta}$, and equation solving over a given interval.
• Circular measure (1.4): arc length $s = r\theta$, sector area $A = \frac{1}{2}r^2\theta$, and the recognisable composite shapes (segment, washer).

By the end of this week, you should be able to look at any Pure 1 question and name its technique within ten seconds. That recognition matters more than memorised formulas.

Week 3: Probability & Statistics 1 (skip only if you do not sit Paper 5)

Probability & Statistics 1 is the most "learnable in a week" 9709 component because the question styles repeat almost identically year to year. The syllabus splits it into sections 5.1 to 5.5.

• Representation of data (5.1): histograms with unequal class widths (frequency density is the killer), cumulative frequency curves, finding the median and quartiles from the graph, stem-and-leaf diagrams, box-and-whisker plots, mean, variance and standard deviation (including from grouped data and from $\sum x$ and $\sum x^2$), and the effect of coding $y = ax + b$.
• Permutations and combinations (5.2): $^nP_r$, $^nC_r$, and the arrangement-with-restrictions question types ("must sit together", "must not sit together", "exactly $k$ of these are chosen").
• Probability (5.3): addition and multiplication rules, conditional probability $P(A|B) = \frac{P(A \cap B)}{P(B)}$, independence, mutually exclusive events, and tree diagrams with and without replacement.
• Discrete random variables (5.4): probability distribution tables, expected value $E(X)$, variance $\text{Var}(X)$, and the geometric and binomial distributions.
• The normal distribution (5.5): standardising to $Z = \frac{X - \mu}{\sigma}$, reading the tables, the "find $\mu$ or $\sigma$ given a probability" inverse question, and the normal approximation to the binomial (with continuity correction) when $n$ is large.

If you only have time for one Paper 5 thing, drill the normal distribution. It is on every paper.

Week 4: Mechanics (skip only if you do not sit Paper 4)

Paper 4 Mechanics is unforgiving on diagrams. The students who score well are not the ones with the strongest algebra, they are the ones who draw a clear, fully labelled force diagram before writing a single equation. The syllabus splits Mechanics into sections 4.1 to 4.5.

• Forces and equilibrium (4.1): weight, normal contact, friction (coefficient $\mu$, the limiting condition $F = \mu R$), tension, resolving forces along and perpendicular to a plane, equilibrium of a particle under coplanar forces (including the "three forces in equilibrium" triangle).
• Kinematics of motion in a straight line (4.2): the $suvat$ equations for constant acceleration, displacement-time and velocity-time graphs, and the calculus form $v = \frac{ds}{dt}$, $a = \frac{dv}{dt}$ for non-constant acceleration.
• Momentum (4.3): $\text{impulse} = \text{change in momentum}$, collision in a straight line, and the coalesce or rebound question type, with conservation of momentum.
• Newton's laws of motion (4.4): $F = ma$ on a horizontal surface, on a slope, and connected particles (pulley over a smooth peg, or two particles connected by a light inextensible string).
• Energy, work and power (4.5): work done by a constant force $W = Fd\cos\theta$, kinetic energy $\tfrac{1}{2}mv^2$ and gravitational potential energy $mgh$, the work-energy principle, and power $P = Fv$.

Drill the diagram-first habit. The diagram is the question, the equations are the answer.

Week 5: Pure 2 (skip if your AS combination is Paper 1 + Paper 4 or Paper 1 + Paper 5)

Paper 2 Pure Mathematics 2 sits between Pure 1 and Pure 3 in difficulty, and it is where Pure 1 gaps come back to bite if Week 1 was rushed. Note that the Pure-only AS route (Paper 1 + Paper 2) is available at AS Level only, A Level candidates take Paper 3 instead. The syllabus splits Paper 2 into sections 2.1 to 2.6.

• Algebra (2.1): the modulus function $|f(x)|$ including graph-sketching and equation-solving, the division algorithm for polynomials, the factor theorem and the remainder theorem.
• Logarithmic and exponential functions (2.2): laws of logarithms, solving equations of the form $a^x = b$, the natural exponential $e^x$ and natural logarithm $\ln x$, and the graphs of $y = e^{ax}$ and $y = \ln x$.
• Trigonometry (2.3): extension to $\sec\theta$, $\csc\theta$ (cosec), $\cot\theta$, the identities $1 + \tan^2\theta = \sec^2\theta$ and $1 + \cot^2\theta = \csc^2\theta$, double-angle formulae, and equation-solving using these.
• Differentiation (2.4): of $e^x$, $\ln x$, $\sin x$, $\cos x$, $\tan x$, with the chain rule applied to these (Paper 2 does not require the product or quotient rules — those are Paper 3).
• Integration (2.5): of $e^{ax + b}$, $\frac{1}{ax + b}$, $\sin(ax + b)$, $\cos(ax + b)$, $\sec^2(ax + b)$.
• Numerical solution of equations (2.6): locating a root by sign change, simple iteration $x_{n+1} = g(x_n)$ including the convergence and divergence behaviour and the cobweb/staircase diagram.

If Paper 2 feels harder than expected, the issue is almost always Pure 1 algebra still being slow. Re-do half of Week 1 in parallel rather than slogging through Paper 2 with a wobbly foundation.

Week 6: Mixed past papers, under exam conditions

Stop revising by topic. Sit whole papers to time, in one sitting, with the calculator, formulas booklet, and pen you will use on the day. Mark them honestly against the official mark scheme, and keep an error log: the question, what you did, what the mark scheme wanted, the one sentence that fixes it, and the type of error (method selection, arithmetic, diagram, time management). Re-attempt every logged question 48 hours later from blank paper.

Target: at least three full past papers per Cambridge 9709 component you are sitting, all from 2025 onwards. If you cannot fit three of each, prioritise the most recent series first, since Cambridge tends to repeat question styles closely from one year to the next.

How to know you are actually ready

You are ready when you can open any Cambridge 9709 AS past paper at a random question and know, within fifteen seconds, which technique the question is testing and what step you would write first. That recognition, layered on automatic Pure 1 algebra, is what the AS papers reward.

Inside The Practice Book, every Cambridge 9709 AS subtopic has chapter-mapped questions with step-by-step worked solutions and exam-style timed papers from 2025 onwards, so the fix-every-mistake loop takes minutes rather than an evening of hunting through mark schemes.