Mathematics IB — Revision Checklist
All 10 Maths IB chapters broken into checkable items, prioritised by TGBIE exam weight. Covers everything that appears in SAQ and LAQ sections.
Ch. 3 The Straight Line — High Weight
High- All forms of straight line: slope-intercept, point-slope, two-point, intercept, normal, symmetric — derive and apply each
- Angle between two lines: tanθ = |(m₁−m₂)/(1+m₁m₂)| — condition for perpendicular and parallel
- Perpendicular distance from a point to a line: d = |ax₁+by₁+c|/√(a²+b²)
- Distance between two parallel lines
- Concurrent lines: three lines ax+by+c=0 are concurrent if their determinant is zero
- Foot of perpendicular from a point to a line — formula and application
- Family of lines through intersection of L₁ and L₂: L₁ + λL₂ = 0
Ch. 4 Pair of Straight Lines — High Weight
High- Combined equation ax²+2hxy+by²=0: find slopes, angle between lines, bisectors
- Condition for perpendicular pair: a + b = 0; coincident pair: h² = ab
- Angle bisectors equation: (x²−y²)/(a−b) = xy/h
- Second degree equation represents a pair if Δ = abc+2fgh−af²−bg²−ch² = 0
- Distance between parallel lines if second degree equation represents a pair of parallel lines
Ch. 10 Applications of Derivatives — High Weight (LAQ)
High- Tangent at (x₁,y₁): y−y₁ = (dy/dx)_(x₁,y₁)·(x−x₁); normal is perpendicular to tangent
- Angle between two curves: find slopes m₁, m₂ at intersection, then tanθ = |(m₁−m₂)/(1+m₁m₂)|
- Rolle's theorem: check f(a)=f(b), continuity, differentiability, then find c
- LMVT: verify conditions, then solve f'(c) = (f(b)−f(a))/(b−a) for c
- Maxima/minima: f'(x)=0, classify by second derivative test (f''>0 = min, f''<0 = max)
- Increasing/decreasing: f'(x)>0 → increasing; f'(x)<0 → decreasing on an interval
Ch. 9 Differentiation — High Weight
High- Product rule, quotient rule, chain rule — apply correctly for composite functions
- Parametric differentiation: dy/dx = (dy/dθ)/(dx/dθ)
- Implicit differentiation: differentiate both sides w.r.t. x, collect dy/dx terms
- Logarithmic differentiation: for y = f(x)^g(x), take log both sides then differentiate
- Second order derivative: d²y/dx² = d/dx(dy/dx); sign tells concavity
Ch. 8 Limits and Continuity — Medium Weight
Medium- Standard limits: lim(x→0) sinx/x = 1, lim(x→0) tanx/x = 1, lim(x→0) (eˣ−1)/x = 1
- Continuity: f is continuous at a if lim(x→a) f(x) = f(a)
- Evaluating limits: factorisation, rationalisation, L'Hôpital's rule (not in syllabus — use standard limits)
- One-sided limits: check left-hand limit = right-hand limit for continuity at a point
Ch. 1, 2, 5, 6, 7 Locus, Transformation, 3D — Medium Weight
Medium- Locus: translate the geometric condition into an algebraic equation in x and y
- Transformation: shift origin to (h,k) → X = x−h, Y = y−k
- Section formula in 3D: know internal and external division
- Direction cosines: l²+m²+n²=1; angle between two lines using dot product
- Plane equation: ax+by+cz+d=0; normal vector is (a,b,c)