What you’ll need to know
- Domain, range and notation (1.1-1.3)
- Modulus graphs y = |f(x)| (1.4)
- Inverse functions (1.5, 1.6, 1.8)
- Composite functions (1.7)
Revision notes · Cambridge O Level · 4037
Additional Mathematics 4037 revision notes
Revision notes for Cambridge O Level Additional Mathematics (4037), organised by the official syllabus chapters.
- Notes
- 7
- Chapters covered
- 1 / 14
- ChapterFunctions
- TopicDomain, range and notation (1.1-1.3)Functions
- TopicModulus graphs y = |f(x)| (1.4)Functions
- TopicInverse functions (1.5, 1.6, 1.8)Functions
- TopicComposite functions (1.7)Functions
- ChapterQuadratic functions
- TopicCompleting the square, max/min and range (2.1, 2.2)Quadratic functions
- TopicDiscriminant: roots and line-curve intersection (2.3)Quadratic functions
- TopicQuadratic equations and inequalities (2.4, 2.5)Quadratic functions
- ChapterFactors of polynomials
- TopicRemainder and factor theorems (3.1)Factors of polynomials
- TopicFactorising polynomials and solving cubics (3.2, 3.3)Factors of polynomials
- ChapterEquations, inequalities and graphs
- TopicModulus equations and inequalities (4.1, 4.2)Equations, inequalities and graphs
- TopicEquations reducible to quadratics (4.3)Equations, inequalities and graphs
- TopicCubic graphs, their moduli and cubic inequalities (4.4, 4.5)Equations, inequalities and graphs
- ChapterSimultaneous equations
- TopicLinear and non-linear simultaneous equations (5.1)Simultaneous equations
- ChapterLogarithmic and exponential functions
- TopicExponential and log graphs (6.1)Logarithmic and exponential functions
- TopicLaws of logarithms and change of base (6.2)Logarithmic and exponential functions
- TopicExponential equations a^x = b (6.3)Logarithmic and exponential functions
- ChapterStraight-line graphs
- TopicEquation of a line, parallel and perpendicular (7.1, 7.2)Straight-line graphs
- TopicMidpoint, length and perpendicular bisector (7.3)Straight-line graphs
- TopicTransforming to straight-line form (7.4)Straight-line graphs
- ChapterCoordinate geometry of the circle
- TopicEquation of a circle (8.1)Coordinate geometry of the circle
- TopicCircles and lines: intersection and tangents (8.2, 8.3)Coordinate geometry of the circle
- TopicTwo circles (8.4)Coordinate geometry of the circle
- ChapterCircular measure
- TopicArc length and sector area in radians (9.1)Circular measure
- ChapterTrigonometry
- TopicSix trig functions, amplitude, period and graphs (10.1-10.3)Trigonometry
- TopicTrigonometric equations (10.4, 10.5)Trigonometry
- TopicProving identities (10.6)Trigonometry
- ChapterPermutations and combinations
- TopicPermutations: arrangements (11.1-11.3)Permutations and combinations
- TopicCombinations: selections (11.1-11.3)Permutations and combinations
- ChapterSeries
- TopicBinomial expansion and general term (12.1, 12.2)Series
- TopicArithmetic progressions (12.3, 12.4)Series
- TopicGeometric progressions and sum to infinity (12.3-12.5)Series
- ChapterVectors in two dimensions
- TopicVector notation, position and unit vectors (13.1, 13.2)Vectors in two dimensions
- TopicVector geometry (13.3)Vectors in two dimensions
- TopicVelocity vectors and relative motion (13.4)Vectors in two dimensions
- ChapterCalculus
- TopicDifferentiation: rules (14.1-14.4)Calculus
- TopicTangents, normals and stationary points (14.5, 14.6, 14.9)Calculus
- TopicRates of change, small increments, practical max/min (14.7, 14.8)Calculus
- TopicIntegration and definite integrals (14.10-14.12)Calculus
- TopicAreas by integration (14.13)Calculus
- TopicKinematics (14.14, 14.15)Calculus
- NoteIntegration: powers, 1/x and (ax + b)ⁿCalculus
- NoteIntegrating exponentials and trigCalculus
- NoteDefinite integrals and unknown limitsCalculus
- NoteDifferentiate, then integrate ('hence')Calculus
- NoteFinding a curve from its gradientCalculus
- NoteAreas under curvesCalculus
- NoteAreas between lines and curvesCalculus
Nothing called that in Additional Mathematics notes or the folders inside it.
What you’ll need to know
- Completing the square, max/min and range (2.1, 2.2)
- Discriminant: roots and line-curve intersection (2.3)
- Quadratic equations and inequalities (2.4, 2.5)
What you’ll need to know
- Remainder and factor theorems (3.1)
- Factorising polynomials and solving cubics (3.2, 3.3)
What you’ll need to know
- Modulus equations and inequalities (4.1, 4.2)
- Equations reducible to quadratics (4.3)
- Cubic graphs, their moduli and cubic inequalities (4.4, 4.5)
What you’ll need to know
- Linear and non-linear simultaneous equations (5.1)
What you’ll need to know
- Exponential and log graphs (6.1)
- Laws of logarithms and change of base (6.2)
- Exponential equations a^x = b (6.3)
What you’ll need to know
- Equation of a line, parallel and perpendicular (7.1, 7.2)
- Midpoint, length and perpendicular bisector (7.3)
- Transforming to straight-line form (7.4)
What you’ll need to know
- Equation of a circle (8.1)
- Circles and lines: intersection and tangents (8.2, 8.3)
- Two circles (8.4)
What you’ll need to know
- Arc length and sector area in radians (9.1)
What you’ll need to know
- Six trig functions, amplitude, period and graphs (10.1-10.3)
- Trigonometric equations (10.4, 10.5)
- Proving identities (10.6)
What you’ll need to know
- Permutations: arrangements (11.1-11.3)
- Combinations: selections (11.1-11.3)
What you’ll need to know
- Binomial expansion and general term (12.1, 12.2)
- Arithmetic progressions (12.3, 12.4)
- Geometric progressions and sum to infinity (12.3-12.5)
What you’ll need to know
- Vector notation, position and unit vectors (13.1, 13.2)
- Vector geometry (13.3)
- Velocity vectors and relative motion (13.4)
What you’ll learn · 7 notes
- 1Integration: powers, 1/x and (ax + b)ⁿ7 min
- 2Integrating exponentials and trig6 min
- 3Definite integrals and unknown limits6 min
- 4Differentiate, then integrate ('hence')7 min
- 5Finding a curve from its gradient7 min
- 6Areas under curves8 min
- 7Areas between lines and curves8 min
Not in the notes yet: Differentiation: rules (14.1-14.4), Tangents, normals and stationary points (14.5, 14.6, 14.9), Rates of change, small increments, practical max/min (14.7, 14.8), Kinematics (14.14, 14.15)