LC HL DEB 2025 P1 

Analysis 

Question 1: Algebra &  Logs

Inequalities (solving rational inequalities), Roots of polynomial equations (finding unknown coefficients and other roots), Logarithms (properties of logarithms, change of base formula, evaluating complex logarithmic expressions) 

Question 2: Algebra & Simultaneous Equations

Binomial Expansion (finding specific terms, finding the term independent of x), Simultaneous Equations (solving quadratic and linear equations simultaneously) 

Question 3: Complex Numbers

De Moivre's Theorem (proof by induction), Operations with complex numbers in polar form (multiplication), Converting complex numbers to polar form, Evaluating powers of complex numbers in polar form 

Question 4: Calculus – Differentiation

Differentiation from first principles, Finding the equation of a tangent to a curve (involving logarithmic and trigonometric functions), Analysis of functions (showing increasing/decreasing, finding points of inflection) 

Question 5: Sequences and Series 

Geometric Sequences (finding unknown values, determining terms, sum of n terms), Geometric Series (derivation of sum to infinity formula, expressing recurring decimals as fractions) 

Question 6: Calculus - Integration

Definite Integrals (evaluation), Area under a curve (estimation using Trapezoidal Rule, exact calculation using integration), Percentage Error 

Question 7: Contexts and Applications (Financial Mathematics) 

Depreciation (compound rate calculations), Annual Equivalent Rate (AER), Compound Interest, Loan Repayments (using geometric series concepts) 

Question 8: Contexts and Applications (Calculus/Rates of Change/Optimization) 

Modelling with functions (exponential decay for temperature), Interpreting parameters in a model, Rates of change (differentiation applications), Optimization (minimizing surface area of a cylinder) 

Question 9: Contexts and Applications (Kinematics and Related Rates) 

Kinematics (acceleration, velocity, distance in stages), Related Rates (volume and depth in a cone, rate of change of depth) 

Question 10:  Contexts and Applications (Modelling with Functions) 

Patterns (identifying quadratic patterns), Modelling with quadratic functions, Sum of square numbers (using a given formula)