All covered topics

IB Math AA HL

Topic 1

Number & Algebra

Topic 1 All

Read All Questions Under  Topic 1. Number & Algebra

Topic 1.1

1.1 Approximation and scientific notation

Topic 1.2

1.2.1 Arithmetic Sequence/series.
1.2.2 Arithmetic Sequence/series-Sigma Notation/Applications/ including approximate difference

Topic 1.3

1.3.1 Geometric Sequence/Series
1.3.2 (Arithmetic and Geometric Sequence/series
1.3.3 Geometric Sequence/series-Applications

Topic 1.4, 1.5 & 1.6

1.4 Compound Interest
1.5 Exponents
1.6 Exponents and logarithms
1.7 Proofs

Topic 1.7 & 1.8

1.7 Proofs
1.8.1 Binomial expansion
1.8.2 Binomial expansion with rational powers.

Topic 1.9 & 1.10

1.9 Counting Principles, Permutation and Combination
1.10 Partial fractions.

Topic 1.11 & 1.12

1.11 Complex numbers-Definition and properties.
1.12 Complex numbers-Polar and Euler form.

Topic 1.13 & 1.14

1.13 Roots of Polynomials with real coefficients.
1.14 Equations involving complex numbers, powers of complex numbers

Topic 1.5 & 1.6

1.15 Proof by Induction/Contradiction/Counterexample.
1.16 Systems of linear equations

Concept Quiz 1
Test 1 SL –No Calculator.
Test 2 SL –Calculator.

Test 3 SL –No Calculator. Test 4 SL –Calculator

Topic 2

Functions

Topic 2 All

Read All Questions Under  Topic 2. Functions

Topic 2.1, 2.3 & 2.3

2.1Concepts of functions.
2.2 Domain and range
2.3 Sketching functions.

Topic 2.4, 2.5 & 2.6

2.4 Composition and inverse functions.
2.5 Transformation of functions (linear transforms)
2.6 Linear functions

Topic 2.7, 2.8 & 2.9

2.7 Quadratic functions.
2.8 Quadratic equations – Discriminants.
2.9 Quadratic inequalities

Topic 2.10, 2.11 & 2.12

2.10 Polynomial functions. Factor and remainder therorems.
2.11 Rational functions.
2.12 Exponential growth and decay functions

Topic 2.13, 2.14 & 2.15

2.13 Logarithmic functions.
2.14 Absolute value functions and piecewise functions
2.15 Transformation of functions (Non-linear transforms)

Topic 2.15 & 2.16

2.16 Odd and even functions.
2.17 Graphical solutions to equations and inequalities.
Concept Quiz 2
Test 1 SL –No Calculator. Test 2 SL –Calculator. Test 3 SL –No Calculator. Test 4 SL –Calculator

Topic 3

Geometry and trigonometry

Topic 3 All

Read All Questions Under  Topic 3. Geometry and trigonometry

Topic 3.1

3.1.1 Coordinate geometry
3.1.2 Volume and surface area of solids.

Topic 3.2

3.2.1 Right angled trigonometry_SOH CAH TOA
Topic 3.2.2 Non-Right angled trigonometry_Sine and Cosine Rule

Topic 3.3 & 3.4

3.3 Applications of Basic Trigonometry. (elevations, bearings and 3D trig)
3.4 Circles: Radian measure of angle, sector, segment and arc-length.

Topic 3.5, 3.6 & 3.7

3.5 The unit circle and exact values.
3.6 Trig Identities/ Double angle identities.
3.7 Multiple Solutions to basic trig equations

Topic 3.8, 3.9 & 3.10

3.8 Solving Trig equations.
3.9 Graphs of trig functions.
3.10 Applications of trig functions and Ferris Wheel.

Topic 3.11, 3.12, & 3.13

3.11 Reciprocal trig functions.
3.12 More on trig identities( compound angles)
3.13 Inverse trig functions.

Topic 3.14, 3.15 & 3.16

3.14 Vectors (2D and 3D).
3.15 Properties of vectors.
3.16 Scalar dot products. Angle between two vectors.

Topic 3.17 & 3.18

3.17 Cross product. Area of a parallelogram.
3.18 Lines.

Topic 3.19 & 3.20

3.19 Planes.
3.20 Applications of vectors to kinematics

Concept Quiz 3
Test 1 SL –No Calculator.
Test 2 SL –Calculator


Test 3 SL –No Calculator.
Test 4 SL –Calculator

Topic 4

Statistics and probability

Topic 4 All

Read All Questions Under  Topic 4. Statistics and probability

Topic 4.1, 4.2 & 4.3

4.1 Data handling.
4.2 Central measures and dispersion
4.3 Graphical display of discrete and continuous data

Topic 4.4, 4.5 & 4.6

4.4 Linear correlation and regression.
4.5 Definition of probability.
4.6 Venn diagram and combined events

Topic 4.7 & 4.8

4.7 Conditional probabilities and tree diagram.
4.8 Bayes theorem.

Topic 4.9 & 4.10

4.9 Probability distribution of a discrete random variable.
4.10 Binomial distribution

Topic 4.11, 4.12 & 4.13

4.11 Normal distribution / Standard normal curve( z-scores)
4.12 Inverse normal distribution
4.13 Continuous random variables and density functions.

Topic 4.14 & 4.15

4.14 Expectations and variances of both discrete and continuous random variables, Mode and Median.
4.15 Algebra on expectations of functions of random variables

Concept Quiz 4
Test 1 SL –No Calculator.
Test 2 SL –Calculator.
Test 3 SL –No Calculator.
Test 4 SL –Calculator

Topic 5

Calculus

Topic 5 All

Read All Questions Under  Topic 5. Calculus

Topic 5.1, 5.2 & 5.3

5.1 Evaluation of slopes and limits.
5.2 Power rule of differentiation.
5.3 Chain Rule: Differentiation of composite functions

Topic 5.4, 5.5 & 5.6

5.4 Product and Quotient Rule.
5.5 Tangent and normal to a curve.
5.6 Second derivatives and higher order derivatives

Topic 5.7, 5.8 & 5.9

5.7 Analytic properties of functions. (Stationarity, Inflexion, Increasing and decreasing etc)
5.8 Optimization 1
5.9 Optimization 2

Topic 5.10, 5.11, 5.12 & 5.13

5.10 Rate of Change and small changes.
5.11 Limit definition of derivative (informal) and L’hopital’s Rule.
5.12 Implicit differentiation.
5.13 Kinematics 1

Topic 5.14, 5.15, 5.16 & 5.17

5.14 Calculating or Estimating areas under curves(Non-Calculus approach)
5.15 Power rule of Integration.
5.16 Techniques of Integration 1
5.17 Techniques of integration 2

Topic 5.18, 5.19, 20 & 5.21

5.18 Definite integral and area under a curve.
5.19 Area between curves and volume of revolution.
5.20 Kinematics 2.
5.21 Differential equations.

Topic 5.22

5.22 Maclaurin’s Expansion.
Concept Quiz 5
Test 1 SL –No Calculator.
Test 2 SL –Calculator
Test 3 SL –No Calculator.
Test 4 SL –Calculator