Introduction to IB Mathematics Studies SL
Duration: 2 years
 Year 1 (Junior Year) – IB Math Analysis
 Year 2 (Senior Year) – IB Statistics & Intro to Differential Calculus
IB Jargon:
 General IB
o TOK: Theory of Knowledge
 Required Class
 All subjects have TOK problems/scenarios embedded in their curriculum
 Adds points to final diploma result score
o CAS: Creativity, Action, & Service
 Project in the last two years (Community service orientated)
 Required, but does not add points to the final diploma result score
o EE: Extended Essay
 Required essay for all
 Based on research
 Adds points to final diploma result score
o SL: Standard Level
o HL: Higher Level (must take 3 or 4 classes in the HL)
o Diploma Score: candidate for the IB Diploma must obtain at least 24 points
 Each subject exam/external assessment can earn a student up to 7 points
 Mathematical Studies SL Specific:
o Paper/External Assessment: the final exam after Year 2 (like an AP Exam)
 Paper 1 – 15 short response questions (Calculator Required)
 Paper 2 – 6 extended response questions (Calculator Required)
o Project/Internal Assessment: individual piece of work involving research and analyzing data
o GDC: the graphic display calculator
Topics Covered:
 Year 1
o Numbers and Algebra
 Number Sets
 Approximation, Percentage Errors, & Estimation
 Scientific Notation
 SI and Basic Units of Measurement
 Currency Conversions
 Solving Linear Systems and Quadratic Equations with a GDC
 Arithmetic Sequences and Series
 Geometric Sequences and Series
 Compound Interest and Annual Depreciation
o Descriptive Statistics
 Discrete or Continuous Data
 Frequency Tables
 Mid-Interval Values, Upper and Lower Boundaries, Histograms
 Cumulative Frequency Curves, Median, Quartiles, Box and Whisker Diagrams
 Central Tendency: Mean, Median, Mode; Estimate of Mean, Modal Class
 Dispersion: Range, Interquartile Range, Standard Deviation
o Geometry and Trigonometry


Linear Equations: Forms, Gradient, Intercepts, Points of Intersection, Parallel, &
Perpendicular
 Sin, Cos and Tan in Right Triangles; Angles of Elevation, Depression
 Sine Rule, Cosine Rule, Area of a Triangle
 3-D Solids, Distance Between Two Points, Size of an Angle
 Volume and Surface Area of 3-D Solids
o Mathematical Models
 Functions: Domain, Range, & Graphing
 Linear Models
 Quadratic Models, Properties of Parabolas
 Exponential Models, Horizontal Asymptotes
 Polynomial and Rational Functions, Vertical Asymptotes
 Drawing Accurate Graphs, Graphing Literacy
 Graphing With the GDC
Year 2
o Logic, Sets and Probability
 Basic knowledge of symbolic logic: definitions and notations
 Compound statements: implication, ⇒; equivalence, ⇔; negation,¬; conjunction, ∧;
disjunction, ∨; exclusive disjunction, ∨ ; Translation between symbolic form and verbal
statements
 Truth tables: logical contradiction and tautology
 Converse, inverse, and contrapositive; Logical equivalence; Testing the validity of an
argument through the use of a truth table
 Basic concepts of set theory: elements 𝑥 ∈ 𝐴, subsets 𝐴 ⊂ 𝐵; intersection 𝐴 ∩ 𝐵; union
𝐴 ∪ 𝐵; complement𝐴′; Venn diagrams
 Sample space; Probability of an event 𝐴; Probability of a complementary event 𝐴′
Expected value
 Probability of combined events, mutually exclusive events, and independent events; Use
of tree diagrams, Venn diagrams, sample space diagrams, and tables of outcomes;
Probability “with” and “without” replacement; Conditional probability
o Statistical Applications
 The normal distribution; The concept of a random variable; the parameters 𝜇 and 𝜎; the
bell shape; the symmetry about 𝑥 = 𝜇; Diagrammatic representation; Normal probability
calculations; Expected value; Inverse normal calculations
 Bivariate data: the concept of correlation; Scatter diagrams; line of best fit, by eye,
passing through the mean point; Pearson’s product-moment correlation coefficient, r;
Interpretation of positive, zero and negative, strong or weak correlations; The regression
line for y on x; Use of the regression line for prediction purposes; The 𝜒 2 test for
independence: formulation of null and alternative hypotheses; significance levels;
contingency tables; expected frequencies; degrees of freedom; p-values
o Introduction to Differential Calculus
 Concept of derivative as a rate of change; Tangent to a curve; The principle that 𝑓(𝑥) =
𝑎𝑥 𝑛 ⟹ 𝑓 ′ (𝑥) = 𝑎𝑛𝑥 𝑛−1 ; The derivative of functions of the form 𝑓(𝑥) = 𝑎𝑥 𝑛 +
𝑏𝑥 𝑛−1 +…, where all exponents are integers Gradients of curves for given values of x
Values of x where 𝑓′(𝑥) is given; Equations of the tangent at a given point; Equations of
the normal line (perpendicular to the tangent) at a given point
 Increasing and decreasing functions
Graphical interpretation of 𝑓 ′ (𝑥) > 0, 𝑓 ′ (𝑥) = 0 and 𝑓 ′ (𝑥) < 0
 Values of x where the gradient of a curve is zero; Solution of 𝑓 ′ (𝑥) = 0; Stationary
points; Local min/max points
 Optimization problems