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OCR A-level Maths formula sheet

For OCR A-level Maths A the formulae are printed on pages 2 and 3 of every question paper, not in a separate booklet. Further Maths A comes with a Formulae Booklet. Below, we list every formula in our notes from a topic on the OCR specification and say whether OCR prints it or says you must know it.

173 formulae · 62 printed · 47 must know · 64 to check.

Where to find it

OCR sets out the Maths A sheet in section 5d of the H240 specification, and the Further Maths A booklet in section 5d of the H245 specification. Any Maths A past paper is a printed copy of the sheet, on pages 2 and 3.

Section 5d of each specification 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. A formula from a Maths A topic is checked against the Maths A sheet; one from a Further Maths A topic only is checked against the Formulae Booklet, which contains the Maths A sheet and more. The line under each formula names which.

The formulae in these notes, by unit

Every formula displayed in a lesson that covers the OCR 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, H240
• a^x ÷ a^y = a^x−yMUST KNOWIndices and surdssection 5d, H240
• (a^x)^y = a^xyMUST KNOWIndices and surdssection 5d, H240
• √xy = √x√yCHECKIndices and surdsOCR neither prints it nor lists it in section 5d
• ax² + bx + c = a(x + b2a)² + (c − b²4a)CHECKQuadratic functionsA working line: completing the square; neither OCR list has it
• x = −b ± √b² − 4ac2aMUST KNOWQuadratic functionssection 5d, H240
• f(a) = 0 ⇔ (x − a) is a factor of f(x)CHECKPolynomials and the factor theoremOCR neither prints it nor lists it in section 5d

COORDINATE GEOMETRY

• y − y₁ = m(x − x₁)MUST KNOWStraight linessection 5d, H240
• m₁ m₂ = −1MUST KNOWStraight linessection 5d, H240
• (x − a)² + (y − b)² = r²CHECKCirclesOCR neither prints it nor lists it in section 5d

SEQUENCES AND SERIES

• ⁿC_r = n!r!(n − r)!PRINTEDThe binomial expansionMaths A sheet
• (a + b)ⁿ = aⁿ + ⁿC₁aⁿ⁻¹b + … + bⁿPRINTEDThe binomial expansionMaths A sheet
• (1 + x)ⁿ = 1 + nx + n(n − 1)2!x² + …PRINTEDThe general binomial expansionMaths A sheet
• (a + bx)ⁿ = aⁿ(1 + bx/a)ⁿCHECKThe general binomial expansionA working line: OCR prints (1 + x)ⁿ, and this step takes aⁿ out to reach it
• u_n = a + (n − 1)dMUST KNOWArithmetic seriessection 5d, H240
• S_n = n2(2a + (n − 1)d) = n2(a + l)PRINTEDArithmetic seriesMaths A sheet
• u_n = arⁿ⁻¹MUST KNOWGeometric seriessection 5d, H240
• S_n = a(1 − rⁿ)1 − rPRINTEDGeometric seriesMaths A sheet
• S_∞ = a1 − rPRINTEDGeometric seriesMaths A sheet

TRIGONOMETRY

• asin A = bsin B = csin CMUST KNOWTriangles and the sine and cosine rulessection 5d, H240
• a² = b² + c² − 2bc cos AMUST KNOWTriangles and the sine and cosine rulessection 5d, H240
• Area = 12ab sin CMUST KNOWTriangles and the sine and cosine rulessection 5d, H240
• tan θ = sin θcos θCHECKTrigonometric graphs and equationsOCR neither prints it nor lists it in section 5d
• sin ² θ + cos ² θ = 1MUST KNOWTrigonometric graphs and equationssection 5d, H240
• s = rθMUST KNOWRadians, arcs and small anglessection 5d, H240
• A = 12r²θMUST KNOWRadians, arcs and small anglessection 5d, H240
• sin θ ≈ θ, cos θ ≈ 1 − θ²2, tan θ ≈ θPRINTEDRadians, arcs and small anglesMaths A sheet
• sec² θ = 1 + tan² θMUST KNOWReciprocal and inverse trigonometric functionssection 5d, H240
• cosec² θ = 1 + cot² θMUST KNOWReciprocal and inverse trigonometric functionssection 5d, H240
• sin (A ± B) = sin A cos B ± cos A sin BPRINTEDCompound angles and the harmonic formMaths A sheet
• cos (A ± B) = cos A cos B ∓ sin A sin BPRINTEDCompound angles and the harmonic formMaths A sheet
• tan (A ± B) = tan A ± tan B1 ∓ tan A tan BPRINTEDCompound angles and the harmonic formMaths A sheet
• sin 2A = 2 sin A cos AMUST KNOWCompound angles and the harmonic formsection 5d, H240
• cos 2A = cos ²A − sin ²A = 2cos ²A − 1 = 1 − 2sin ²AMUST KNOWCompound angles and the harmonic formsection 5d, H240
• tan 2A = 2tan A1 − tan ²AMUST KNOWCompound angles and the harmonic formsection 5d, H240

EXPONENTIALS AND LOGARITHMS

• gradient of e^kx = ke^kxMUST KNOWExponential functions and esection 5d, H240
• x = aⁿ ⇔ n = log_a xMUST KNOWLogarithms and their lawssection 5d, H240
• log_a x + log_a y = log_a xyMUST KNOWLogarithms and their lawssection 5d, H240
• log_a x − log_a y = log_a xyMUST KNOWLogarithms and their lawssection 5d, H240
• k log_a x = log_a x^kMUST KNOWLogarithms and their lawssection 5d, H240

DIFFERENTIATION

• f′(x) = lim_{h → 0} f(x + h) − f(x)hPRINTEDThe derivative from first principlesMaths A sheet
• y = xⁿ ⇒ dydx = nxⁿ⁻¹MUST KNOWDifferentiating powers of xsection 5d, H240
• sin kx → kcos kx, cos kx → −ksin kxMUST KNOWDifferentiating trig, exponentials and logssection 5d, H240
• e^kx → ke^kx, ln x → 1xMUST KNOWDifferentiating trig, exponentials and logssection 5d, H240
• dydx = dydu × dudxMUST KNOWThe product, quotient and chain rulessection 5d, H240
• (uv)′ = u′v − uv′v²PRINTEDThe product, quotient and chain rulesMaths A sheet
• dydx = 1dx/dy = 1cos yCHECKImplicit and parametric differentiationA working line: differentiating x as a function of y and inverting; neither OCR list has it

INTEGRATION

• ∫ xⁿ dx = xⁿ⁺¹n + 1 + c (n ≠ −1)MUST KNOWIntegration as antidifferentiationsection 5d, H240
• ∫ cos kx dx = 1ksin kx + cMUST KNOWIntegrating standard functionssection 5d, H240
• ∫ sin kx dx = −1kcos kx + cMUST KNOWIntegrating standard functionssection 5d, H240
• ∫ e^kx dx = 1ke^kx + cMUST KNOWIntegrating standard functionssection 5d, H240
• ∫ 1x dx = ln|x| + cMUST KNOWIntegrating standard functionssection 5d, H240
• ∫ f′(x)f(x) dx = ln|f(x)| + cPRINTEDIntegration by substitution and by partsMaths A sheet
• ∫ u dvdx dx = uv − ∫ v dudx dxPRINTEDIntegration by substitution and by partsMaths A sheet
• ∫ 23x + 5 dx = 23ln|3x + 5| + cCHECKIntegrating rational functionsA worked case of ∫f′(x)/f(x) dx = ln|f(x)| + c, which OCR 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 OCR list has it
• ∫ 1g(y) dy = ∫ f(x) dxCHECKSolving differential equationsA working line: separating the variables; neither OCR list has it

NUMERICAL METHODS

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

VECTORS

• AB = b − aCHECKVectors in two dimensionsOCR neither prints it nor lists it in section 5d
• |xi + yj + zk| = √x² + y² + z²MUST KNOWVectors in three dimensionssection 5d, H240

STATISTICS

• stratum sizepopulation size × sample sizeCHECKSampling and the large data setOCR neither prints it nor lists it in section 5d
• mean: Σ xnMUST KNOWMeasures of location and spreadsection 5d, H240
• σ² = Σ x²n − (Σ xn)²PRINTEDMeasures of location and spreadMaths A sheet
• mean(x) = a + b mean(y),     σ_x = |b|σ_yCHECKMeasures of location and spreadOCR neither prints it nor lists it in section 5d
• frequency density = frequencyclass widthCHECKRepresenting and interpreting dataOCR neither prints it nor lists it in section 5d
• outlier: beyond Q₁ − 1.5 × IQR or Q₃ + 1.5 × IQRCHECKRepresenting and interpreting dataOCR neither prints it nor lists it in section 5d
• P(A ∪ B) = P(A) + P(B) − P(A ∩ B)PRINTEDProbability and Venn diagramsMaths A sheet
• P(A|B) = P(A ∩ B)P(B)PRINTEDConditional probabilityMaths A sheet
• P(X = x) = 1nCHECKThe binomial distributionOCR neither prints it nor lists it in section 5d
• P(X = x) = ⁿC_x p^x (1 − p)^{n − x}PRINTEDThe binomial distributionMaths A sheet
• Z = X − μσMUST KNOWThe normal distributionsection 5d, H240
• X ~ B(n, p) ≈ N(np, np(1 − p))CHECKThe normal distributionOCR neither prints it nor lists it in section 5d
• mean of n observations: N(μ, σ²/n)PRINTEDHypothesis testing: correlation and the normalMaths A sheet

MECHANICS

• v = u + at,     s = (u + v)2tPRINTEDKinematics with constant accelerationMaths A sheet
• s = ut + 12at²,     v² = u² + 2asPRINTEDKinematics with constant accelerationMaths A sheet
• s = vt − 12at²PRINTEDKinematics with constant accelerationMaths A sheet
• v = dxdt,     a = dvdtMUST KNOWKinematics with variable accelerationsection 5d, H240
• F = maMUST KNOWForces and Newton's lawssection 5d, H240
• y = x tan θ − gx²2u²cos ² θCHECKProjectilesA working line: the path of a projectile; neither OCR list has it
• F ≤ μRMUST KNOWFriction and inclined planessection 5d, H240
• |m_Bg−m_Agsin θ|≤ μm_Agcos θCHECKFriction and inclined planesA working line: the lesson's test for equilibrium on a rough plane; neither OCR list has it
• moment = force × perpendicular distanceCHECKMomentsOCR neither prints it nor lists it in section 5d

FURTHER PROOF

• true for n = 1, and true for k + 1 whenever true for kCHECKProof by induction: sums and seriesA working line: the structure of a proof by induction; neither OCR list has it

COMPLEX NUMBERS

• z = r(cos θ + i sin θ)MUST KNOWModulus, argument and locisection 5d, H245
• (cos θ + i sin θ)ⁿ = cos nθ + i sin nθPRINTEDDe Moivre's theorem and trigonometric identitiesFurther Maths A booklet

FURTHER ALGEBRA AND SERIES

• α + β + γ = −ba, αβ + αγ + βγ = ca, αβγ = −daMUST KNOWRoots of polynomialssection 5d, H245
• Σ r = n(n+1)2MUST KNOWSumming series and the method of differencessection 5d, H245
• Σ r² = n(n+1)(2n+1)6, Σ r³ = n²(n+1)²4PRINTEDSumming series and the method of differencesFurther Maths A booklet
• f(x) = f(0) + f′(0)x + f″(0)2!x² + …PRINTEDMaclaurin seriesFurther Maths A booklet
• ln(1 + x) = x − x²2 + x³3 − x⁴4 + … (−1 < x ≤ 1)PRINTEDMaclaurin seriesFurther Maths A booklet

FURTHER VECTORS

• r = a + λbMUST KNOWLines and planes in three dimensionssection 5d, H245
• r · n = a · n = dMUST KNOWLines and planes in three dimensionssection 5d, H245
• distance = |n₁x₀ + n₂y₀ + n₃z₀ − d||n|PRINTEDIntersections, angles and distancesFurther Maths A booklet

FURTHER CALCULUS

• V = π ∫_a^b y² dxMUST KNOWVolumes of revolutionsection 5d, H245
• mean value = 1b − a ∫_a^b f(x) dxPRINTEDMean values and improper integralsFurther Maths A booklet
• ddx(arcsin x) = 1√1 − x²PRINTEDCalculus with inverse trigonometric functionsFurther Maths A booklet
• ddx(arctan x) = 11 + x²PRINTEDCalculus with inverse trigonometric functionsFurther Maths A booklet

HYPERBOLIC FUNCTIONS

• cosh x = e^x + e^−x2, sinh x = e^x − e^−x2MUST KNOWHyperbolic functions and identitiessection 5d, H245
• ∫ 1√x² + a² dx = arsinhxa + cPRINTEDCalculus with hyperbolic functionsFurther Maths A booklet

POLAR COORDINATES

• x = r cos θ, y = r sin θ, r² = x² + y²CHECKPolar curvesOCR neither prints it nor lists it in section 5d
• A = 12 ∫_α^β r² dθPRINTEDAreas with polar coordinatesFurther Maths A booklet

DIFFERENTIAL EQUATIONS

• IF = e^{∫ P dx}CHECKFirst order equations and integrating factorsOCR neither prints it nor lists it in section 5d
• am² + bm + c = 0CHECKSecond order equationsOCR neither prints it nor lists it in section 5d

FURTHER PURE 1

• (fg)⁽ⁿ⁾ = Σ ⁿC_r f^(r) g^(n−r)CHECKLeibniz's theorem and the Weierstrass substitutionOCR neither prints it nor lists it in section 5d
• a × b = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁)PRINTEDThe vector product and the scalar triple productFurther Maths A booklet

FURTHER STATISTICS 1

• E(X) = Σ x P(X = x)PRINTEDDiscrete random variables and expectationFurther Maths A booklet
• Var(X) = Σ x² P(X = x) − μ²PRINTEDDiscrete random variables and expectationFurther Maths A booklet
• E(X) = n + 12,      Var(X) = n² − 112PRINTEDDiscrete random variables and expectationFurther Maths A booklet
• P(X = x) = e^−λ λ^xx!, E(X) = Var(X) = λPRINTEDThe Poisson distributionFurther Maths A booklet
• P(X = x) = p(1 − p)^x−1, μ = 1p, σ² = 1 − pp²PRINTEDGeometric and negative binomial distributionsFurther Maths A booklet
• P(X = x) = ^x−1C_r−1 p^r(1 − p)^x−rCHECKGeometric and negative binomial distributionsOCR prints the geometric distribution but not the negative binomial
• μ = rp, σ² = r(1 − p)p²CHECKGeometric and negative binomial distributionsOCR prints the geometric distribution but not the negative binomial
• sample mean ≈ N(μ, σ²n)PRINTEDThe Central Limit TheoremFurther Maths A booklet
• χ² = Σ (O_i − E_i)²E_iPRINTEDGoodness-of-fit testsFurther Maths A booklet
• E_ij = row total × column totalgrand totalCHECKContingency tablesOCR neither prints it nor lists it in section 5d
• χ² = Σ (O_i − E_i)²E_iPRINTEDContingency tablesFurther Maths A booklet
• χ² = Σ (|O − E| − 0.5)²ECHECKContingency tablesOCR prints Σ(O − E)²/E without the continuity correction

FURTHER PURE 2

• n I_n = (n − 1) I_n−2, I_n = ∫₀^π/2 sin ⁿ x dxCHECKReduction formulaeA working line: a reduction formula worked in the lesson; neither OCR list has it
• s = ∫ √1 + (dydx)² dxPRINTEDArc length and surface areaFurther Maths A booklet
• a^p−1 ≡ 1 (mod p)CHECKModular arithmetic and Fermat's little theoremOCR neither prints it nor lists it in section 5d

FURTHER STATISTICS 2

• b = S_xyS_xx,     a = mean of y − b × mean of xPRINTEDLeast squares regression and residualsFurther Maths A booklet
• RSS = S_yy − (S_xy)²S_xxCHECKLeast squares regression and residualsOCR prints Sxx, Syy, Sxy and b, but not the residual sum of squares
• P(a < X ≤ b) = ∫_a^b f(x) dxCHECKContinuous random variables: density and distribution functionsOCR prints F(x) = ∫f(t) dt from −∞ to x, from which this follows, but not this
• f(x) = dF(x)dxCHECKContinuous random variables: density and distribution functionsOCR prints F(x) as the integral of f(x); this is the same fact read the other way
• Σ P(X = c) + ∫ f(x) dx = 1CHECKContinuous random variables: density and distribution functionsOCR neither prints it nor lists it in section 5d
• P(X > x) = e^−λx,      F(x) = 1 − e^−λxCHECKContinuous random variables: density and distribution functionsOCR prints the exponential p.d.f., mean and variance, but not F(x)
• f(x) = λe^−λx for x ≥ 0PRINTEDContinuous random variables: density and distribution functionsFurther Maths A booklet
• P(X > s + t | X > s) = P(X > t)CHECKContinuous random variables: density and distribution functionsOCR neither prints it nor lists it in section 5d
• E(X) = ∫ x f(x) dx,      Var(X) = E(X²) − [E(X)]²PRINTEDMean, variance and skewness of continuous variablesFurther Maths A booklet
• E(X) = 1λ,      Var(X) = 1λ²PRINTEDMean, variance and skewness of continuous variablesFurther Maths A booklet
• F(x) = 0 for x < a,      x − ab − a for a ≤ x ≤ b,      1 for x > bCHECKThe continuous uniform distributionOCR prints the continuous uniform p.d.f., mean and variance, but not F(x)
• E(X) = a + b2,      Var(X) = (b − a)²12PRINTEDThe continuous uniform distributionFurther Maths A booklet
• r = S_xy√S_xx S_yyPRINTEDCorrelation coefficients: product moment and SpearmanFurther Maths A booklet
• r_s = 1 − 6 Σ d²n(n² − 1)PRINTEDCorrelation coefficients: product moment and SpearmanFurther Maths A booklet
• aX ± bY is normal, with mean aμ_x ± bμ_yCHECKCombinations of normal random variablesOCR prints the mean and variance of aX + bY + c, but not that the combination is Normal
• Var(aX ± bY) = a²σ_x² + b²σ_y²PRINTEDCombinations of normal random variablesFurther Maths A booklet
• s² = 1n − 1 Σ (x_i − sample mean)²CHECKEstimators, standard error and confidence intervalsOCR prints the unbiased estimate as (n/(n − 1))(Σx²/n − (Σx/n)²); this is the same estimate written as a sum of squared deviations
• s² = 1n − 1(Σ x² − (Σ x)²n)PRINTEDEstimators, standard error and confidence intervalsFurther Maths A booklet
• sample mean ± z × σ√n,     z = 1.96 at 95 per centCHECKEstimators, standard error and confidence intervalsOCR prints X̄ ~ N(μ, σ²/n) and the Normal percentage points, but not the interval itself
• (difference of means) − (μ_x − μ_y)√σ_x²n_x + σ_y²n_y is N(0, 1)CHECKComparing two normal meansOCR prints (X̄ − μ)/(σ/√n) ~ N(0, 1) for one sample, but not this two-sample form
• sample mean − μS√n is t on n − 1 degrees of freedomCHECKConfidence intervals and tests with the t-distributionOCR neither prints it nor lists it in section 5d
• s² = (n₁ − 1)s₁² + (n₂ − 1)s₂²n₁ + n₂ − 2CHECKConfidence intervals and tests with the t-distributionOCR neither prints it nor lists it in section 5d

FURTHER MECHANICS 1

• I = Ft = mv − muCHECKMomentum and impulseOCR neither prints it nor lists it in section 5d
• m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂CHECKMomentum and impulseOCR neither prints it nor lists it in section 5d
• I = mv − muCHECKImpulse and momentum as vectorsOCR neither prints it nor lists it in section 5d
• KE = 12mv²,      GPE = mghCHECKWork, energy and powerOCR neither prints it nor lists it in section 5d
• P = FvCHECKWork, energy and powerOCR neither prints it nor lists it in section 5d
• T = λ xlCHECKHooke's law and elastic stringsOCR neither prints it nor lists it in section 5d
• EPE = λ x²2lCHECKElastic potential energyOCR neither prints it nor lists it in section 5d
• e = speed of separationspeed of approachPRINTEDDirect impact and Newton's law of restitutionFurther Maths A booklet

FURTHER MECHANICS 2

• a = rω² = v²rPRINTEDAngular speed and horizontal circular motionFurther Maths A booklet
• tan θ = v²rgCHECKAngular speed and horizontal circular motionOCR neither prints it nor lists it in section 5d
• T − mgcos θ = mv²rCHECKMotion in a vertical circleA working line: Newton's second law along the radius of a vertical circle; neither OCR list has it
• mean x = Σ m_ix_iΣ m_i,      mean y = Σ m_iy_iΣ m_iCHECKCentre of mass of a discrete distributionOCR neither prints it nor lists it in section 5d
• Triangular lamina: 23 along the median from the vertexPRINTEDCentres of mass of plane figures and frameworksFurther Maths A booklet
• Circular arc, radius r, angle at centre 2α: r sin αα from the centrePRINTEDCentres of mass of plane figures and frameworksFurther Maths A booklet
• Sector of a circle, radius r, angle at centre 2α: 2r sin α3α from the centrePRINTEDCentres of mass of plane figures and frameworksFurther Maths A booklet
• Solid hemisphere, radius r: 38r from the centrePRINTEDCentres of mass of plane figures and frameworksFurther Maths A booklet
• Hemispherical shell, radius r: 12r from the centrePRINTEDCentres of mass of plane figures and frameworksFurther Maths A booklet
• Solid cone or pyramid, height h: 14h above the base, on the line from the centre of the base to the vertexPRINTEDCentres of mass of plane figures and frameworksFurther Maths A booklet
• Conical shell, height h: 13h above the base, on the same linePRINTEDCentres of mass of plane figures and frameworksFurther Maths A booklet
• mean x = ∫ xy dx∫ y dx,      mean y = ∫ 12y² dx∫ y dxCHECKCentres of mass by integrationOCR neither prints it nor lists it in section 5d
• mean x = ∫ x y² dx∫ y² dxCHECKCentres of mass by integrationOCR neither prints it nor lists it in section 5d
• F(x) = mvdvdx,     F(t) = mdvdtCHECKNewton's laws with a variable forceSection 5d lists F = ma and a = dv/dt, which give the dv/dt form; neither list has the v dv/dx form
• d²xdt² = −ω²xMUST KNOWSimple harmonic motionsection 5d, H245
• v² = ω²(a² − x²)CHECKSimple harmonic motionOCR prints x = A cos(ωt) + B sin(ωt) and x = R sin(ωt + φ), from which this follows, but not this
• md²xdt² = −λ xl,     ω² = λmlCHECKOscillations on strings and springsA working line: the equation of motion for an elastic string or spring; neither OCR list has it
• dvdt = f(t) or f(v),     vdvdx = f(v) or f(x)CHECKFurther kinematics: acceleration as a function of x, t or vSection 5d lists v = dr/dt and a = dv/dt, but neither list has the v dv/dx form

DECISION MATHEMATICS 1

• 3x + 2y ≤ 20 becomes 3x + 2y + s₁ = 20CHECKLinear programming: formulation and graphical solutionA working line: a slack variable added to a constraint; neither OCR list has it

How this was checked: both lists in section 5d of each specification were copied out line by line from OCR’s own PDFs, 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 MEI A-level Maths formula sheet · Pearson Edexcel, on the formulae index