- IBDP Maths AI SL- IB Style Practice Questions with Answer-Topic Wise-Paper 1
- IBDP Maths AI SL- IB Style Practice Questions with Answer-Topic Wise-Paper 2
- IB DP Maths AI HL- IB Style Practice Questions with Answer-Topic Wise-Paper 1
- IB DP Maths AI HL- IB Style Practice Questions with Answer-Topic Wise-Paper 2

### Paper 3

__HL__

- Time: 150 minutes (150 marks)
- No marks deducted from incorrect answers
- A graphic display calculator is required for this paper.
- A clean copy of the mathematics HL and further mathematics HL formula booklet is

required for this paper

### **New IBDP Mathematics: applications and interpretation HL Paper 3- Syllabus**

**Topic 1: Number and algebra****– AH**L content

- Topic : AHL 1.9
- Topic : AHL 1.10
- Topic : AHL 1.11
- Topic : AHL 1.12
- Topic : AHL 1.13
- Modulus–argument (polar) form \(z = r\left( {\cos \theta + {\text{i}}\sin \theta } \right) = r{\text{cis}}\theta\)
- Exponential form:
- Conversion between Cartesian, polar and exponential forms, by hand and with technology.
- Calculate products, quotients and integer powers in polar or exponential forms.
- Adding sinusoidal functions with the same frequencies but different phase shift angles.
- Geometric interpretation of complex numbers.

- Topic : AHL 1.14
- Definition of a matrix: the terms element, row, column and order for m×n matrices.
- Algebra of matrices: equality; addition; subtraction; multiplication by a scalar for m×n matrices.
- Multiplication of matrices.
- Identity and zero matrices
- Awareness that a system of linear equations can be written in the form Ax=b.
- Solution of the systems of equations using inverse matrix.

- Topic : AHL 1.15
- Eigenvalues and eigenvectors.
- Characteristic polynomial of 2×2 matrices.
- Diagonalization of 2×2 matrices (restricted to the case where there are distinct real eigenvalues).

- Applications to powers of 2×2 matrices.

- Eigenvalues and eigenvectors.

### Topic 2: Functions**– **AHL content

- Topic: AHL 2.7
- Topic : AHL 2.8
- Topic : AHL 2.9
- In addition to the models covered in the SL content the AHL content extends this to include modelling with the following functions:
- Exponential models to calculate half-life.
- Natural logarithmic models:
- Sinusoidal models:
- Logistic models:
- Piecewise models.

- Topic: AHL 2.10

### Topic 3: Geometry and trigonometry-AHL content

- Topic : AHL 3.7
- Topic : AHL 3.8
- Topic : AHL 3.9
- Topic : AHL 3.10
- Concept of a vector; position vectors; displacement vectors.
- Representation of vectors using directed line segments.
- Unit vectors ; Base vectors i, j, k.
- Components of a vector: \(v = \left( {\begin{array}{*{20}{c}} {{v_1}} \\ {{v_2}} \\ {{v_3}} \end{array}} \right) = {v_1}i + {v_2}j + {v_3}k\) .
- The zero vector
**0**, the vector**-v**. - Position vectors \(\vec{{OA}}=a\)
- Rescaling and normalizing vectors.

- Topic : AHL 3.11
- Topic : AHL 3.12
- Topic : AHL 3.13
- Topic : AHL 3.14
- Topic : AHL 3.15
- Topic : AHL 3.16
- Tree and cycle algorithms with undirected graphs.Walks, trails, paths, circuits, cycles.
- Eulerian trails and circuits.
- Hamiltonian paths and cycles.
- Minimum spanning tree (MST) graph algorithms:

- Chinese postman problem and algorithm for solution, to determine the shortest route around a weighted graph with up to four odd vertices, going along each edge at least once.
- Travelling salesman problem to determine the Hamiltonian cycle of least weight in a weighted complete graph.

- Tree and cycle algorithms with undirected graphs.Walks, trails, paths, circuits, cycles.

**Topic 4 : Statistics and probability-AHL content**

- Topic: AHL 4.12
- Topic: AHL 4.13
- Topic: AHL 4.14
- Topic: AHL 4.15
- Topic: AHL 4.16
- Topic: AHL 4.17
- Topic: AHL 4.18
- Critical values and critical regions. Test for population mean for normal distribution.
- Test for proportion using binomial distribution.
- Test for population mean using Poisson distribution.
- Use of technology to test the hypothesis that the population product moment correlation coefficient (ρ) is 0 for bivariate normal distributions.
- Type I and II errors including calculations of their probabilities.

- Topic: AHL 4.19

### Topic 5: Calculus-AHL content

- Topic: AHL 5.9
- Topic: AHL 5.10
- Topic: AHL 5.11
- Topic: AHL 5.12
- Topic: AHL 5.13
- Topic: AHL 5.14
- Topic: AHL 5.15
- Topic: AHL 5.16
- Topic: AHL 5.17
- Phase portrait for the solutions of coupled differential equations of the form:
- \(\frac{dx}{dt}\)=ax+by
- \(\frac{dy}{dt}\)=cx+dy.
- Qualitative analysis of future paths for distinct, real, complex and imaginary eigenvalues.
- Sketching trajectories and using phase portraits to identify key features such as equilibrium points, stable populations and saddle points.

- Topic: AHL 5.18