K310 prints a MATHEMATICAL FORMULAE page at the front of every paper. Everything below is given to you, so no marks go for recalling it. The marks go for knowing what each letter means and when the formula applies.

Compound interest

Total amount

$P{(1+\frac{r}{100})}^n$

Mensuration

Curved surface area of a cone	$\pi rl$
Surface area of a sphere	$4\pi r^2$
Volume of a cone	$\frac{1}{3}\pi r^{2}h$
Volume of a sphere	$\frac{4}{3}\pi r^3$
Area of triangle ABC	$\frac{1}{2}ab\sin C$
Arc length	$r\theta$θ in radians — the degree form is not given
Sector area	$\frac{1}{2}{r}^2\theta$θ in radians — the degree form is not given

Trigonometry

Sine Rule	$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
Cosine Rule	$a^2=b^2+c^2-2bc\cos A$

Statistics

Mean	$\frac{\sum fx}{\sum f}$
Standard deviation	$\sqrt{\frac{\sum f{x}^2}{\sum f}-{\left(\frac{\sum fx}{\sum f}\right)}^2}$

None of this is printed on your paper. Every chapter on this site records which of its formulae the sheet gives and which it does not; this page gathers all of the second kind in one place.

Quadratic equations em-c2

The quadratic formula

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ The single most important formula that is not given to you.

Indices and standard form em-c1

The five Laws of Indices	$a^m\times a^n=a^{m+n}$   $a^m÷a^n=a^{m-n}$   ${(a^m)}^n=a^{mn}$and the two bracket laws, for a product and for a quotient
Zero, negative and rational indices	$a^0=1$   $a^{-n}=\frac{1}{a^n}$   $a^{\frac{m}{n}}=\sqrt[n]{a^m}$
Standard form	$A\times {10}^n$with 1 ≤ A < 10 and n an integer

Coordinate geometry em-c11

Length of a line segment	$\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$
Gradient	$\frac{y_2-y_1}{x_2-x_1}$
Equation of a straight line	$y=mx+c$

Vectors em-c12

Magnitude of a column vector

$\left|\begin{array}{c}x\\ y\end{array}\right|=\sqrt{x^2+y^2}$

Arc, sector and segment — in degrees em-c10

Arc length	$\frac{\theta }{360}\times 2\pi r$
Sector area	$\frac{\theta }{360}\times \pi r^2$
Radians and degrees	$\pi \text{ rad }=180°$
Area of a segment	sector − triangleonly the triangle half (½ab sin C) is given to you

Trigonometry of obtuse angles em-c9

Supplementary angles	$\sin (180°-x)=\sin x$   $\cos (180°-x)=-\cos x$same sine, opposite cosine
Right-angled triangles	SOH · CAH · TOA, and Pythagoras' Theorem

Similar figures and solids em-c7

The ratio chain

length $k$ → area $k^2$ → volume $k^3$ and backwards, by square root and cube root. Congruence tests: SSS, SAS, AAS, RHS — never SSA.

Sets em-c5

Counting a union

n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

Probability em-c14

Mutually exclusive — “or”	P(A or B) = P(A) + P(B)
Independent — “and”	P(A and B) = P(A) × P(B)
Complement	P(not A) = 1 − P(A)the route into every “at least one” question

Statistics — the parts that are not given em-c13

Reading a cumulative frequency curve	median at $\frac{n}{2}$, quartiles at $\frac{n}{4}$ and $\frac{3n}{4}$but for a listed set the median sits at position (n + 1) ÷ 2
Interquartile range	IQR = Q3 − Q1

Matrices em-c6   Inequalities em-c3   Circles em-c8

Multiplying matrices	(m × n)(n × p) → m × pthe inner pair must match; the outer pair gives the order. And AB ≠ BA.
Inequalities	multiplying or dividing by a negative reverses the sign
Circle properties	all nine of them — and the reason phrase for eachin this topic the reason is the working

The two papers (K310 G3 Mathematics)

Paper 1 · 2 h 15 min · 90 marks · 50%	About 26 short-answer questions. Answer all of them.
Paper 2 · 2 h 15 min · 90 marks · 50%	9 to 10 questions of varying marks and lengths. The last question applies mathematics to a real-world scenario. Answer all of them.

Geometrical instruments are needed for both papers.

What the front page of every paper says

These are the rules printed on the paper itself. Quoted from the syllabus; the words in brackets are ours.

Working	“Omission of essential working will result in loss of marks.” (A bare answer earns the answer mark at most; the method marks sit on the lines that lead to it.)
Accuracy	“Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. In questions which explicitly require an answer to be shown to be correct to a specific accuracy, the answer must be first shown to a higher degree of accuracy.” (Round once, at the end. Carry at least 4 s.f. through the working, or keep the value in the calculator.)
π	“Unless the question requires the answer in terms of π, the calculator value for π or π = 3.142 should be used.”
Units and time	SI units are used for mass and measures; compound units use the solidus (5 m/s, 13.6 g/cm3); the 12-hour and 24-hour clock may both be used (3.15 p.m. is 15 15).
Calculators	“An approved calculator may be used in both Paper 1 and Paper 2.” (A question that says without using a calculator or do not use a calculator is marked on the exact working it asks for.)
Formulae	“Relevant mathematical formulae will be provided for candidates.” (Exactly what is provided, and what is not, is the other two tabs of this window.)

What this means when you write