HL SEC 2016 Solutions
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Paper 1

Section A (Concepts and Skills)

1. De Moivre’s theorem, roots of equations
   Topics: Complex numbers

2. Modulus inequality, simultaneous equations
   Topics: Algebraic equations

3. Exponential functions
   Topics: Functions

4. Proving a divisibility by induction; Logs
   Topics: Proof by Induction, Algebraic expressions

5. Pythagoras, injective and inverse functions
   Topics: Algebraic expressions, Functions

6. Differentiate from first principles, product rule, slope of a tangent
   Topics: Differentiation

Section B (Contexts and Applications)

7. Inflating a ball [40 marks]
   Topics: Differentiation, Integration

8. Free shots in basketball, heptathlon [55 marks]
   Topics: Differentiation, Functions

9. Forming a pattern, mating bees [55 marks]
   Topics: Sequences and Series

Paper 2

Section A (Concepts and Skills)

1. Equation of a line, orthocentre of a triangle
   Topics: Coordinate Geometry

2. Equation of a line, tangent to a circle
   Topics: Coordinate Geometry

3. Trig identity proof, trig equation
   Topics: Trigonometry

4. Similar triangles, construction
   Topics: Geometry

5. Probability, independent events
   Topics: Probability

6. Expected value
   Topics: Probability

Section B (Contexts and Applications)

7. Glass roof lantern (3-d triangles) [55 marks]
   Topics: Trigonometry

8. Water levels in a port (Trig graphs) [45 marks]
   Topics: Trigonometry

9. Earning data (Inferential Statistics) [50 marks]
   Topics: Statistics