**IBDP Maths- Applications and Interpretation- Syllabus**

### Paper 2

**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
- Laws of exponents with integer exponents.
- Introduction to logarithms with base 10 and e. Numerical evaluation of logarithms using technology.

- Topic : SL 1.6
- Topic : SL 1.7
- Amortization and annuities using technology.

- Topic : SL 1.8

### 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 2.5
- Composite functions.
- (f ∘ g)(x) = f(g(x))

- Identity function.
- Finding the inverse function f
^{−1}(x)- (f ∘ f
^{−1})(x) = (f^{−1}∘ f)(x) = x

- (f ∘ f

- Composite functions.
- Topic: SL 2.6
- Modelling skills:
- Use the modelling process described in the “mathematical modelling” section to create, fit and use the theoretical models in section SL2.5 and their graphs.

- Develop and fit the model:
- Given a context recognize and choose an appropriate model and possible parameters.
- Determine a reasonable domain for a model.

- Find the parameters of a model.
- Test and reflect upon the model:
- Comment on the appropriateness and reasonableness of a model.
- Justify the choice of a particular model, based on the shape of the data, properties of the curve and/or on the context of the situation.
- Use the model:
- Reading, interpreting and making predictions based on the model

- Modelling skills:
- Topic: SL 2.7
- Solution of quadratic equations and inequalities. The quadratic formula.
- The discriminant \(\Delta = {b^2} – 4ac\) and the nature of the roots, that is, two distinct real roots, two equal real roots, no real roots.

- Topic: SL 2.8
- The reciprocal function f(x) = 1 x , x ≠ 0: its graph and self-inverse nature.
- The rational function \(x \mapsto \frac{{ax + b}}{{cx + d}}\) and its graph. Equations of vertical and horizontal asymptotes.

### 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
- length of an arc; area of a sector.

- Topic SL 3.5
- Topic SL 3.6
- Voronoi diagrams: sites, vertices, edges, cells.
- Addition of a site to an existing Voronoi diagram.
- Nearest neighbour interpolation.
- Applications of the “toxic waste dump” problem.

**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
- Concept of discrete random variables and their probability distributions.
- Expected value (mean), for discrete data. Applications.

- Topic: SL 4.8
- Binomial distribution. Mean and variance of the binomial distribution.

- 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 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.