IB Mathematics Applications & Interpretation Question Type 7: Determining the Number of Real Roots for a Given Real Quadratic

SL 1.1—Using standard form

SL 1.2—Sequences and Sigma Notation

SL 1.3—Geometric Sequences

SL 1.4—Financial apps – compound interest, annual depreciation

SL 1.5—Exponents and Logarithms

SL 1.6—Approximating and estimating

SL 1.7—Loan repayments and amortization

SL 1.8—Use of technology to solve systems of linear equations and polynomial equations

AHL 1.9—Log laws

AHL 1.10—Expressions with non-integer exponents

AHL 1.11—Sum of infinite geometric sequences

AHL 1.12—Complex numbers introduction

AHL 1.13—Complex numbers continued

AHL 1.14—Introduction to matrices

AHL 1.15—Eigenvalues and eigenvectors

SL 2.1—Equations of a line

SL 2.2—Functions, domains, range, graphs

SL 2.3—Graph of a function

SL 2.4—Features of a graph

SL 2.5—Modelling functions

SL 2.6—Modelling skills

AHL 2.7—Composite functions, finding inverse function incl domain restriction

AHL 2.8—Transformations of graphs, composite transformations

AHL 2.9—HL modelling functions

AHL 2.10—Scaling large numbers, log-log graphs

SL 3.1—3d space, volume, angles, midpoints

SL 3.2—2d and 3d trig

SL 3.3—Angles of elevation and depression

SL 3.4—The circle, arc and area of sector, degrees only

SL 3.5—Intersection of lines, equations of perpendicular bisectors

SL 3.6—Voronoi diagrams

AHL 3.7—Radians

AHL 3.8—Unit circle, Pythag identity, solving trig equations graphically

AHL 3.9—Matrix transformations

AHL 3.10—Vector definitions

AHL 3.11—Vector equation of a line in 2d and 3d

AHL 3.12—Vector applications to kinematics

AHL 3.13—Scalar and vector products

AHL 3.14—Graph theory

AHL 3.15—Adjacency matrices and tables

AHL 3.16—Tree and cycle algorithms, Chinese postman, travelling salesman

SL 4.1—Introduction to Statistics

SL 4.2—Presentation of data

SL 4.3—Mean, median, and mode

SL 4.4—Correlation of Data

SL 4.5—Trial and outcome

SL 4.6—Venn diagrams

SL 4.7—Discrete random variables

SL 4.8—Binomial distribution

SL 4.9—Normal distribution

SL 4.10—Spearman’s rank correlation coefficient

SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test

AHL 4.12—Data collection, reliability and validity tests

AHL 4.13—Non-linear regression

AHL 4.14—Linear transformation of a single RV, E(X) and VAR(X), unbiased estimators

AHL 4.15—Central limit theorem

AHL 4.16—Confidence intervals

AHL 4.17—Poisson distribution

AHL 4.18—T and Z test, type I and II errors

AHL 4.19—Transition matrices – Markov chains

SL 5.1—Introduction to Limits

SL 5.2—Increasing and decreasing functions

SL 5.3—Introduction to derivatives

SL 5.4—Tangents and normals

SL 5.5—Introduction to integration

SL 5.6—Stationary points, local max and min

SL 5.7—Optimisation

SL 5.8—Trapezoid rule

AHL 5.9—Differentiating standard functions and derivative rules

AHL 5.10—Second derivatives, testing for max and min

AHL 5.11—Indefinite integration, reverse chain, by substitution

AHL 5.12—Areas under a curve onto x or y axis. Volumes of revolution about x and y

AHL 5.13—Kinematic problems

AHL 5.14—Setting up a DE, solve by separating variables

AHL 5.15—Slope fields

AHL 5.16—Eulers method for 1st order DEs

AHL 5.17—Phase portrait

AHL 5.18—Eulers method for 2nd order DEs