Mathematics IB — Exam Writing Tips
How to write Maths IB answers for full marks in TGBIE — presentation tips for Straight Lines, Pair of Lines, Limits, Differentiation, and Applications of Derivatives.
Straight Line Problems
- 1Always state which form of line equation you are using (e.g., 'Using slope-point form: y − y₁ = m(x − x₁)').
- 2For perpendicular distance, show the formula first, then substitute values — don't jump to the answer.
- 3For 'find the equation of a line through intersection of L₁ and L₂': write L₁ + λL₂ = 0, find λ from the given condition, then write the final equation.
- 4When proving concurrent lines, set up the 3×3 determinant of coefficients and show it equals zero.
- 5For problems involving intercepts: write the intercept form, identify a and b from given conditions (sum/product), then write the equation.
Pair of Straight Lines
- 1For second degree equations, always check Δ = 0 first before finding equations of individual lines.
- 2When finding angle between pair: apply tanθ = 2√(h²−ab)/(a+b) and state whether the lines are perpendicular (a+b=0) or coincident (h²=ab).
- 3For bisector of angles: write (x²−y²)/(a−b) = xy/h clearly — don't derive from scratch unless asked.
- 4When factorising a combined equation: compare with (y−m₁x)(y−m₂x)=0 and solve for slopes.
Limits and Continuity
- 1For limit problems: always show the substitution step. If 0/0 form, factorise or rationalise before substituting.
- 2For continuity: write 'LHL = ..., RHL = ..., f(a) = ...' and conclude with 'Since LHL = RHL = f(a), f is continuous at x = a.'
- 3For finding k to make a function continuous: set LHL = RHL, solve for k, then state the result.
- 4Standard limit lim(x→0) sinx/x = 1: always convert the argument so it has the same expression above and below.
Differentiation
- 1Show each step of product/quotient/chain rule. Don't skip algebra — marks are awarded for correct steps.
- 2For parametric differentiation: write x = f(t), y = g(t) clearly, find dx/dt and dy/dt, then divide.
- 3For implicit differentiation: differentiate both sides, bring all dy/dx terms to one side, factorise.
- 4For second order derivatives: find dy/dx first, then differentiate again. Express in simplified form.
- 5Logarithmic differentiation: clearly state 'Taking log of both sides: log y = ...' before differentiating.
Applications of Derivatives
- 1For tangent/normal: find slope at given point, then write equation using point-slope form. Normal slope = −1/m.
- 2Rolle's theorem: state all three conditions, verify them, then find c. Conclude with 'By Rolle's theorem, ∃c ∈ (a,b) such that f'(c) = 0.'
- 3LMVT: state conditions, find (f(b)−f(a))/(b−a), then solve f'(c) = this value. Verify c ∈ (a,b).
- 4Maxima/minima: find critical points (f'=0), use second derivative test, state the type (max/min) and the value.
- 5For optimization word problems: define variables, write the expression to optimize, differentiate, set to zero, verify it's max/min.