- 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 1

__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 1- Syllabus**

**Topic 1: Number and algebra****– **SL content

- Topic : SL 1.1
- Topic : SL 1.2
- Topic : SL 1.3
- Topic : SL 1.4
- Topic : SL 1.5
- Topic : SL 1.6
- Topic : SL 1.7
- Amortization and annuities using technology.

- Topic : SL 1.8

**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

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

- Topic: SL 2.1
- Topic: SL 2.2
- Concept of a function, domain, range and graph. Function notation, for example f(x), v(t), C(n). The concept of a function as a mathematical model.
- Informal concept that an inverse function reverses or undoes the effect of a function. Inverse function as a reflection in the line y = x, and the notation f
^{−1}(x).

- Topic: SL 2.3
- Topic: SL 2.4
- Topic: SL 2.5
- Topic: SL 2.6

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

- Topic: AHL 2.7
- Topic : AHL 2.8
- Topic : AHL 2.9
- Topic: AHL 2.10

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

- Topic : SL 3.1
- The distance between two points in three dimensional space, and their midpoint.
- Volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere and combinations of these solids.
- The size of an angle between two intersecting lines or between a line and a plane.

- Topic SL 3.2
- Topic SL 3.3
- Topic SL 3.4
- Topic SL 3.5
- Topic SL 3.6

### 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.
- 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-SL content**

- Topic: SL 4.1
- Topic: SL 4.2
- Topic: SL 4.3
- Topic: SL 4.4
- Linear correlation of bivariate data. Pearson’s product-moment correlation coefficient, r.
- Scatter diagrams; lines of best fit, by eye, passing through the mean point.
- Equation of the regression line of y on x.
- Use of the equation of the regression line for prediction purposes.
- Interpret the meaning of the parameters, a and b, in a linear regression y = ax + b.

- Topic: SL 4.5
- Topic: SL 4.6
- Use of Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes to calculate probabilities.
- Combined events: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
- Mutually exclusive events: P(A ∩ B) = 0.
- Conditional probability; the definition \(P\left( {\left. A \right|P} \right) = \frac{{P\left( {A\mathop \cap \nolimits B} \right)}}{{P\left( B \right)}}\).
- Independent events; the definition \(P\left( {\left. A \right|B} \right) = P\left( A \right) = P\left( {\left. A \right|B’} \right)\) .

- Topic: SL 4.7
- Topic: SL 4.8
- Topic: SL 4.9
- Topic: SL 4.10
- Spearman’s rank correlation coefficient, r
_{s}. - Awareness of the appropriateness and limitations of Pearson’s product moment correlation coefficient and Spearman’s rank correlation coefficient, and the effect of outliers on each.

- Spearman’s rank correlation coefficient, r
- Topic: SL 4.11

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

- Topic: AHL 4.12
- Design of valid data collection methods, such as surveys and questionnaires.
- Selecting relevant variables from many variables.
- Choosing relevant and appropriate data to analyse.

- Categorizing numerical data in a χ
^{2}table and justifying the choice of categorisation.- Choosing an appropriate number of degrees of freedom when estimating parameters from data when carrying out the χ
^{2}goodness of fit test.

- Choosing an appropriate number of degrees of freedom when estimating parameters from data when carrying out the χ
- Definition of reliability and validity.
- Reliability tests.
- Validity tests.

- Design of valid data collection methods, such as surveys and questionnaires.
- Topic: AHL 4.13
- Non-linear regression.
- Evaluation of least squares regression curves using technology.
- Sum of square residuals (SS
_{res}) as a measure of fit for a model. - The coefficient of determination (R
^{2}).- Evaluation of R
^{2}using technology.

- Evaluation of R

- 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
- Transition matrices. Powers of transition matrices.
- Regular Markov chains.
- Initial state probability matrices.

- Calculation of steady state and long-term probabilities by repeated multiplication of the transition matrix or by solving a system of linear equations.

### Topic 5: Calculus-SL content

- Topic SL 5.1
- Topic SL 5.2
- Topic SL 5.3
- Topic SL 5.4
- Topic: SL 5.5
- Introduction to integration as anti-differentiation of functions of the form f(x) = ax
^{n}+ bx^{n−1}+ …., where n ∈ ℤ, n ≠ − 1. - Anti-differentiation with a boundary condition to determine the constant term.
- Definite integrals using technology.
- Area of a region enclosed by a curve y = f(x) and the x -axis, where f(x) > 0.

- Introduction to integration as anti-differentiation of functions of the form f(x) = ax
- Topic: SL 5.6
- Topic: SL 5.7
- Topic: SL 5.8
- Approximating areas using the trapezoidal rule.

### 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