DP 1: Applications and Interpretation HL mathematics

The programme

1. Straight Lines — A comprehensive module on Line Equations, covering Slope (Gradient), the Slope Formula, and the y-Intercept. Explores Slope-Intercept (y=mx+c) and General Forms, graphing techniques, and relationships like Parallel and Perpendicular lines. Includes Perpendicular Bisectors, Intersections, and Angle of Inclination.
2. Sets and Venn Diagrams — A comprehensive introduction to set theory: elements, subsets, cardinality, and operations (union, intersection, complement). Explores Venn diagrams, set-builder notation, and number sets (N, Z, Q, R), plus representing solutions to linear inequalities using interval notation.
3. Surds and Exponents — Master square, cube, and nth roots through geometric intuition and algebraic laws. Covers perfect squares, simplification to simplest radical form, operations with like radicals, and rationalizing monomial and binomial denominators using conjugates. Ideal for advancing algebraic fluency.
4. Equations — Master quadratic equations through factorization, completing the square, and the quadratic formula. Explore the discriminant's role in root nature, Vieta's formulas, and substitution methods. Solve complex quadratic inequalities using sign tables and parabolic properties.
5. Sequences and Series — Explore numerical sequences and series. Learn recursive and explicit rules, arithmetic and geometric progressions, and partial sums. Master sigma notation and the convergence of infinite geometric series with practical modeling exercises and formal proofs.
6. Measurement — Comprehensive guide to volume, capacity, and surface area. Learn formulas for prisms, cones, and spheres, perform metric conversions, and solve density problems. Covers practical applications like liquid capacity, pool volume, and mass calculations using the Pythagorean theorem.
7. Right-Angled Triangle Trigonometry — Master right-triangle trigonometry using SOH-CAH-TOA. Covers side naming, sine, cosine, and tangent ratios, inverse functions, and solving 2D/3D real-world problems involving angles between lines and planes in cuboids, pyramids, and prisms.
8. The Unit Circle and Radian Measure — Explore the unit circle and radian measure. Learn to convert degrees to radians and find exact sine, cosine, and tangent values. Covers fundamental trigonometric identities, including Pythagorean, double-angle, and compound angle formulas through proofs and unit circle analysis.
9. Non-Right-Angled Triangle Trigonometry — Learn trigonometry for non-right-angled triangles. This module covers the triangle area formula, the Law of Sines, and the Law of Cosines. Practice calculating unknown sides and angles, and solve real-world problems involving areas, perimeters, and costs.
10. Points in Space — Locate points in space with three coordinates in a right-handed orthonormal system: plot points in perspective and read the coordinates of the vertices of cuboids and pyramids. Proves the distance formula by applying Pythagoras' theorem twice, derives the coordinates of the midpoint of a segment, and applies both inside solids: space diagonals, the angle between two lines and the angle between a line and a plane.
11. Probability — Master probability from basic outcomes to advanced concepts. Learn sample spaces, Venn diagrams, and addition laws. Deep dive into conditional probability, the law of total probability, and Bayes' Theorem using real-world scenarios like medical testing and forensic logic.
12. Conditional Probability — Master probability from basic outcomes to advanced concepts. Learn sample spaces, Venn diagrams, and addition laws. Deep dive into conditional probability, the law of total probability, and Bayes' Theorem using real-world scenarios like medical testing and forensic logic.
13. Sampling and Data — Comprehensive module on the statistical investigation process. Covers variables, sampling methods (stratified, systematic), bias, and error analysis. Includes central tendency, standard deviation, and box plots with a focus on critical evaluation of claims.
14. Descriptive Statistics — Comprehensive module on the statistical investigation process. Covers variables, sampling methods (stratified, systematic), bias, and error analysis. Includes central tendency, standard deviation, and box plots with a focus on critical evaluation of claims.
15. Quadratic Functions — A comprehensive guide to quadratic functions (f(x)=ax^2+bx+c). Covers parabola features (vertex, axis of symmetry, intercepts), concavity, and the discriminant. Includes exercises on algebraic solving, graphical reading, and modeling real-world projectile motion and profits.
16. Functions — Master the foundations of functions: notation, domain, and range. Explore graphical and algebraic methods for finding images and preimages. Covers bijectivity, operations, composition, and inverse functions through diverse exercises including real-world linear models and mapping diagrams.
17. Transformations of Functions — Master function transformations: learn vertical and horizontal translations, stretches, compressions, and reflections across axes. This module covers applying transformations to parent functions, understanding the order of operations, and determining new equations from geometric sequences.
18. Trigonometric Functions — Explore trigonometric functions (sine, cosine, tangent) and their reciprocal/inverse forms. This module covers properties like period, amplitude, and principal axis. Learn to solve complex equations and model periodic data like temperatures or tidal movements using transformations.
19. Exponentials — Master exponential functions through growth and decay models. This module covers graphical features, horizontal asymptotes, and domain/range. Learn to distinguish linear and exponential relationships using constant differences and common ratios with real-world applications.
20. Logarithms — Explore roots (square, cube, nth) and logarithms (base 10, a, e). Master radical laws, rationalizing denominators, and log properties. Apply these tools to solve complex exponential equations and real-world models including the pH scale, Richter scale, and population growth.
21. Approximations and Error — Master rounding (dp, sf), error formulas (absolute, relative, percentage), and measurement accuracy. Learn to estimate values and calculate upper/lower bounds for operations and geometric dimensions like area and volume. Essential for understanding precision in math and science.
22. Loans and Annuities — A comprehensive guide to financial mathematics covering simple and compound interest, the impact of inflation on real value, and loan amortization. Learn to use TVM solvers for calculating regular repayments and annuity durations for retirement planning through real-world scenarios.
23. Modelling — Master the mathematical modeling cycle using diverse functional models: linear, quadratic, cubic, exponential, variation, sinusoidal, logarithmic, and logistic. Learn to determine parameters from data, interpret intercepts and asymptotes, and evaluate model validity in real-world contexts.
24. Bivariate Statistics — Explore the relationship between two quantitative variables. This module covers scatter plots, correlation (direction, strength, form), and causation. Learn to model data with regression lines, calculate coefficients (r, r²), and perform interpolation and extrapolation.
25. Non-Linear Regression — Éducation Nationale extension: the mean point of a two-variable series, covariance, the least squares line proved by minimising second-degree polynomials, the linear correlation coefficient and its bounds, fits reduced to an affine fit by a change of variable (exponential, logarithmic, power), the study domain and critical extrapolation, and the three explanations of a correlation (causation, third factor, chance), with calculator, spreadsheet and Python.