HL SEC 2012 Solutions
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Paper 1

Section A (Concepts and Skills)

1. Simultaneous equations, rational inequalities
   Topics: Algebraic equations

2. Sets of numbers
   Topics: Number

3. Roots of complex numbers
   Topics: Complex numbers

4. Proof by induction, recurring decimals
   Topics: Proof by induction, sequences and series

5. Intersecting functions
   Topics: Functions, Integration

6. Exponential functions, point of inflection
   Topics: Differentiation

Section B (Contexts and Applications)

7. Cylindrical tank [50 marks]
   Topics: Algebra, Differentiation

8. Conical drinking cup [50 marks]
   Topics: Measurement, Algebra, Differentiation, Trigonometry

9. Atmospheric pressure [50 marks]
   Topics: Algebra, Functions, Sequences and Series

Paper 2

Section A (Concepts and Skills)

1. Properties of a parallelogram
   Topics: Co-ordinate geometry, Geometry

2. Touching circles
   Topics: Co-ordinate geometry

3. Tangents to circles
   Topics: Co-ordinate geometry

4. Bernoulli trials
   Topics: Probability

5. Tolerance levels of batteries
   Topics: Statistics

6. Theorem cut: Incircle
   Topics: Geometry

Section B (Contexts and Applications)

7. Mortgage data [75 marks]
   Topics: Statistics, Probability

8. Robot arm [75 marks]
   Topics: Trigonometry