Knowledge organisers

Pure Mathematics 2 (P2): Edexcel IAL Maths knowledge organiser

Everything to know about pure mathematics 2 (p2) on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Remainder theorem: When f(x) is divided by (x − a), the remainder is f(a).
Geometric series: The sum of a geometric sequence; when |r| < 1 it has a sum to infinity a/(1 − r).
Logarithm: logₐ b = x means aˣ = b.
Trapezium rule: An estimate of the area under a curve using strips of equal width h.

Key formulas

Formulas marked with a label are given in the exam (we only say so where our formula sheet confirms it). Learn the rest.

Factor & remainder theorems	\(f(a)=0\iff(x-a)\text{ a factor};\) \(\text{remainder }f(a)\)
Circle	\((x-a)^2+(y-b)^2=r^2;\) \(\text{tangent}\perp\text{radius}\)
Arithmetic seriesIn the formula booklet	\(S_n=\tfrac12n(a+l)=\tfrac12n[2a+(n-1)d]\)
\(n\)th termsIn the formula booklet	\(u_n=a+(n-1)d,\) \(u_n=ar^{n-1}\)
Geometric seriesIn the formula booklet	\(S_n=\frac{a(1-r^n)}{1-r},\) \(S_\infty=\frac a{1-r}\ (\|r\|<1)\)
Binomial, \(n\in\mathbb N\)In the formula booklet	\((a+b)^n=a^n+\tbinom n1a^{n-1}b+\cdots+b^n,\) \(\tbinom nr=\frac{n!}{r!(n-r)!}\)
Log laws	\(\log_axy=\log_ax+\log_ay,\) \(\log_a\tfrac xy=\log_ax-\log_ay,\) \(\log_ax^k=k\log_ax\)
Change of baseIn the formula booklet	\(\log_ax=\frac{\log_bx}{\log_ba}\)
Trig	\(\tan\theta=\frac{\sin\theta}{\cos\theta},\) \(\sin^2\theta+\cos^2\theta=1\)
Trapezium rule, \(h=\tfrac{b-a}n\)In the formula booklet	\(\int_a^by\,dx\) \({}\approx\tfrac12h\{(y_0+y_n)+2(y_1+\cdots+y_{n-1})\}\)
Stationary points	\(f'(x)=0;\) \(f''<0\text{ max},\ f''>0\text{ min}\)
Area under a curve	\(\int_a^by\,dx\)

Worked example

Find the remainder when f(x) = 2x³ − 3x² + 4 is divided by (x − 2).

Remainder theorem: remainder = f(2)
f(2) = 16 − 12 + 4

Answer: The remainder is 8

Common mistakes

Logarithms: log laws not shown, and roots not rejected
Trapezium rule: strip width and brackets
F(a) = 0 read as '(x + a) is a factor'
Remainder of f(x) ÷ (2x − 1) found with f(−½) or f(2)

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

Simplify algebraic fractions by factorising, and divide polynomials such as x³ − 3x² + 4 by (x − 2) using algebraic long division.
Use the perpendicular radius–tangent property and chord properties to find equations of tangents and lengths in circle problems.
Expand (a + bx)ⁿ for positive integer n using the binomial expansion, simplifying each coefficient and the powers of x.
Write sums in sigma notation and evaluate them, such as the sum of 2ʳ from r = 1 to 10, using arithmetic and geometric series formulae.
Solve trigonometric equations that are quadratic in sin or cos, such as 2cos²x + 3 sin x = 3, using identities and factorising.
Use the trapezium rule to estimate the area under a curve, and decide whether the estimate is too big or too small from the curve's shape.

The printable sheet

Pure Mathematics 2 (P2) knowledge organiser for Edexcel IAL Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Pure Mathematics 2 (P2) knowledge organiser (Edexcel IAL Maths), A4. Download the PDF.

Revise it next

Other Edexcel IAL Maths topics: Pure Mathematics 1 (P1) · Pure Mathematics 3 (P3) · Pure Mathematics 4 (P4) · Statistics 1 (S1) · Mechanics 1 (M1) · All Edexcel IAL Maths organisers