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OCR MEI A-level Maths formula sheet

OCR Mathematics B (MEI) prints its formulae on pages 2 and 3 of every question paper rather than in a separate booklet. Below, we list every formula in our notes from a topic on the MEI specification and say whether the sheet prints it or OCR says you must know it.

86 formulae · 23 printed · 39 must know · 24 to check.

Where to find it

OCR sets the sheet out in section 5d of the H640 specification, and any MEI past paper is a printed copy of it, on pages 2 and 3.

The same section 5d starts with the formulae and identities you must be able to use without being given them, before the printed ones.

Must know or printed: the difference

Must know means the formula is on the first list in section 5d. OCR expects you to use it without being given it, so it is not on the sheet and you need to learn it. Printed means the sheet in your paper has it, so the job is knowing where it is and how to use it, not memorising it. The two lists do not cover everything. A formula on neither is marked check: the sheet will not give it to you either, so learn it or know how to derive it.

What the marks mean

Printed: the sheet has it, maybe rearranged, with different letters, or in a form you can read it straight off. Must know: section 5d lists it, in this form or an equivalent one. Check: it is on neither list in this form, and the line under it says why. The MEI sheet is not the Maths A sheet: it gives the sample variance rather than the standard deviation, for one.

The formulae in these notes, by unit

Every formula displayed in a lesson that covers the MEI specification, linked to its unit’s formulae page, where it is written out with its conditions.

ALGEBRA AND FUNCTIONS

• a^x × a^y = a^x+yMUST KNOWIndices and surdssection 5d, H640
• a^x ÷ a^y = a^x−yMUST KNOWIndices and surdssection 5d, H640
• (a^x)^y = a^xyMUST KNOWIndices and surdssection 5d, H640
• √xy = √x√yCHECKIndices and surdsThe MEI sheet does not print it and section 5d does not list it
• ax² + bx + c = a(x + b2a)² + (c − b²4a)CHECKQuadratic functionsA working line: completing the square; neither MEI list has it
• x = −b ± √b² − 4ac2aMUST KNOWQuadratic functionssection 5d, H640
• f(a) = 0 ⇔ (x − a) is a factor of f(x)CHECKPolynomials and the factor theoremThe MEI sheet does not print it and section 5d does not list it

COORDINATE GEOMETRY

• y − y₁ = m(x − x₁)MUST KNOWStraight linessection 5d, H640
• m₁ m₂ = −1MUST KNOWStraight linessection 5d, H640
• (x − a)² + (y − b)² = r²CHECKCirclesThe MEI sheet does not print it and section 5d does not list it

SEQUENCES AND SERIES

• ⁿC_r = n!r!(n − r)!PRINTEDThe binomial expansionMEI sheet
• (a + b)ⁿ = aⁿ + ⁿC₁aⁿ⁻¹b + … + bⁿPRINTEDThe binomial expansionMEI sheet
• (1 + x)ⁿ = 1 + nx + n(n − 1)2!x² + …PRINTEDThe general binomial expansionMEI sheet
• (a + bx)ⁿ = aⁿ(1 + bx/a)ⁿCHECKThe general binomial expansionA working line: the MEI sheet prints (1 + x)ⁿ, and this step takes aⁿ out to reach it
• u_n = a + (n − 1)dMUST KNOWArithmetic seriessection 5d, H640
• S_n = n2(2a + (n − 1)d) = n2(a + l)PRINTEDArithmetic seriesMEI sheet
• u_n = arⁿ⁻¹MUST KNOWGeometric seriessection 5d, H640
• S_n = a(1 − rⁿ)1 − rPRINTEDGeometric seriesMEI sheet
• S_∞ = a1 − rPRINTEDGeometric seriesMEI sheet

TRIGONOMETRY

• asin A = bsin B = csin CMUST KNOWTriangles and the sine and cosine rulessection 5d, H640
• a² = b² + c² − 2bc cos AMUST KNOWTriangles and the sine and cosine rulessection 5d, H640
• Area = 12ab sin CMUST KNOWTriangles and the sine and cosine rulessection 5d, H640
• tan θ = sin θcos θCHECKTrigonometric graphs and equationsThe MEI sheet does not print it and section 5d does not list it
• sin ² θ + cos ² θ = 1MUST KNOWTrigonometric graphs and equationssection 5d, H640
• s = rθMUST KNOWRadians, arcs and small anglessection 5d, H640
• A = 12r²θMUST KNOWRadians, arcs and small anglessection 5d, H640
• sin θ ≈ θ, cos θ ≈ 1 − θ²2, tan θ ≈ θPRINTEDRadians, arcs and small anglesMEI sheet
• sec² θ = 1 + tan² θMUST KNOWReciprocal and inverse trigonometric functionssection 5d, H640
• cosec² θ = 1 + cot² θMUST KNOWReciprocal and inverse trigonometric functionssection 5d, H640
• sin (A ± B) = sin A cos B ± cos A sin BPRINTEDCompound angles and the harmonic formMEI sheet
• cos (A ± B) = cos A cos B ∓ sin A sin BPRINTEDCompound angles and the harmonic formMEI sheet
• tan (A ± B) = tan A ± tan B1 ∓ tan A tan BPRINTEDCompound angles and the harmonic formMEI sheet
• sin 2A = 2 sin A cos AMUST KNOWCompound angles and the harmonic formsection 5d, H640
• cos 2A = cos ²A − sin ²A = 2cos ²A − 1 = 1 − 2sin ²AMUST KNOWCompound angles and the harmonic formsection 5d, H640
• tan 2A = 2tan A1 − tan ²AMUST KNOWCompound angles and the harmonic formsection 5d, H640

EXPONENTIALS AND LOGARITHMS

• gradient of e^kx = ke^kxMUST KNOWExponential functions and esection 5d, H640
• x = aⁿ ⇔ n = log_a xMUST KNOWLogarithms and their lawssection 5d, H640
• log_a x + log_a y = log_a xyMUST KNOWLogarithms and their lawssection 5d, H640
• log_a x − log_a y = log_a xyMUST KNOWLogarithms and their lawssection 5d, H640
• k log_a x = log_a x^kMUST KNOWLogarithms and their lawssection 5d, H640

DIFFERENTIATION

• f′(x) = lim_{h → 0} f(x + h) − f(x)hPRINTEDThe derivative from first principlesMEI sheet
• y = xⁿ ⇒ dydx = nxⁿ⁻¹MUST KNOWDifferentiating powers of xsection 5d, H640
• sin kx → kcos kx, cos kx → −ksin kxMUST KNOWDifferentiating trig, exponentials and logssection 5d, H640
• e^kx → ke^kx, ln x → 1xMUST KNOWDifferentiating trig, exponentials and logssection 5d, H640
• dydx = dydu × dudxMUST KNOWThe product, quotient and chain rulessection 5d, H640
• (uv)′ = u′v − uv′v²PRINTEDThe product, quotient and chain rulesMEI sheet
• dydx = 1dx/dy = 1cos yCHECKImplicit and parametric differentiationA working line: differentiating x as a function of y and inverting; neither MEI list has it

INTEGRATION

• ∫ xⁿ dx = xⁿ⁺¹n + 1 + c (n ≠ −1)MUST KNOWIntegration as antidifferentiationsection 5d, H640
• ∫ cos kx dx = 1ksin kx + cMUST KNOWIntegrating standard functionssection 5d, H640
• ∫ sin kx dx = −1kcos kx + cMUST KNOWIntegrating standard functionssection 5d, H640
• ∫ e^kx dx = 1ke^kx + cMUST KNOWIntegrating standard functionssection 5d, H640
• ∫ 1x dx = ln|x| + cMUST KNOWIntegrating standard functionssection 5d, H640
• ∫ f′(x)f(x) dx = ln|f(x)| + cPRINTEDIntegration by substitution and by partsMEI sheet
• ∫ u dvdx dx = uv − ∫ v dudx dxPRINTEDIntegration by substitution and by partsMEI sheet
• ∫ 23x + 5 dx = 23ln|3x + 5| + cCHECKIntegrating rational functionsA worked case of ∫f′(x)/f(x) dx = ln|f(x)| + c, which the MEI sheet prints
• area = ∫ y dxdt dtCHECKAreas, parametric curves and the limit of a sumNot printed; section 5d lists the area under a curve, ∫y dx, and this is that integral with x = x(t) substituted
• lim_{δx → 0} Σ f(x) δx = ∫_a^b f(x) dxCHECKAreas, parametric curves and the limit of a sumA working line: the definite integral as the limit of a sum; neither MEI list has it
• ∫ 1g(y) dy = ∫ f(x) dxCHECKSolving differential equationsA working line: separating the variables; neither MEI list has it

NUMERICAL METHODS

• x_n+1 = (x_n + 1)^1/3CHECKLocating roots and iterationA working line: a worked iteration; neither MEI list has it
• x_n+1 = x_n − f(x_n)f′(x_n)PRINTEDThe Newton-Raphson methodMEI sheet
• T = h2(y₀ + 2(y₁ + … + y_n−1) + y_n)PRINTEDThe trapezium ruleMEI sheet
• L = h(y₀ + … + y_n−1),     R = h(y₁ + … + y_n)CHECKThe trapezium ruleA working line: rectangle sums beside the trapezium rule; neither MEI list has it

VECTORS

• AB = b − aCHECKVectors in two dimensionsThe MEI sheet does not print it and section 5d does not list it
• |xi + yj + zk| = √x² + y² + z²MUST KNOWVectors in three dimensionssection 5d, H640

STATISTICS

• stratum sizepopulation size × sample sizeCHECKSampling and the large data setThe MEI sheet does not print it and section 5d does not list it
• mean: Σ xnMUST KNOWMeasures of location and spreadsection 5d, H640
• σ² = Σ x²n − (Σ xn)²CHECKMeasures of location and spreadThe MEI sheet prints the sample variance s² = Sxx/(n − 1), with divisor n − 1, not this divisor-n form
• mean(x) = a + b mean(y),     σ_x = |b|σ_yCHECKMeasures of location and spreadThe MEI sheet does not print it and section 5d does not list it
• frequency density = frequencyclass widthCHECKRepresenting and interpreting dataThe MEI sheet does not print it and section 5d does not list it
• outlier: beyond Q₁ − 1.5 × IQR or Q₃ + 1.5 × IQRCHECKRepresenting and interpreting dataThe MEI sheet does not print it and section 5d does not list it
• P(A ∪ B) = P(A) + P(B) − P(A ∩ B)PRINTEDProbability and Venn diagramsMEI sheet
• P(A|B) = P(A ∩ B)P(B)PRINTEDConditional probabilityMEI sheet
• P(X = x) = 1nCHECKThe binomial distributionThe MEI sheet does not print it and section 5d does not list it
• P(X = x) = ⁿC_x p^x (1 − p)^{n − x}PRINTEDThe binomial distributionMEI sheet
• Z = X − μσMUST KNOWThe normal distributionsection 5d, H640
• X ~ B(n, p) ≈ N(np, np(1 − p))CHECKThe normal distributionThe MEI sheet does not print it and section 5d does not list it
• mean of n observations: N(μ, σ²/n)PRINTEDHypothesis testing: correlation and the normalMEI sheet

MECHANICS

• v = u + at,     s = (u + v)2tPRINTEDKinematics with constant accelerationMEI sheet
• s = ut + 12at²,     v² = u² + 2asPRINTEDKinematics with constant accelerationMEI sheet
• s = vt − 12at²PRINTEDKinematics with constant accelerationMEI sheet
• v = dxdt,     a = dvdtMUST KNOWKinematics with variable accelerationsection 5d, H640
• F = maMUST KNOWForces and Newton's lawssection 5d, H640
• y = x tan θ − gx²2u²cos ² θCHECKProjectilesA working line: the path of a projectile; neither MEI list has it
• F ≤ μRMUST KNOWFriction and inclined planessection 5d, H640
• |m_Bg−m_Agsin θ|≤ μm_Agcos θCHECKFriction and inclined planesA working line: the lesson's test for equilibrium on a rough plane; neither MEI list has it
• moment = force × perpendicular distanceCHECKMomentsThe MEI sheet does not print it and section 5d does not list it

How this was checked: both lists in section 5d were copied out line by line from OCR’s own PDF, and every formula was matched to them by the mathematics rather than by its name. Each mark is tied to the line it was matched to, and the site will not build if that line leaves its list. If the sheet you are given in the exam ever disagrees with this page, the sheet is right.

Other boards: AQA A-level Maths formula booklet · OCR A-level Maths formula sheet · Pearson Edexcel, on the formulae index