Analysis & Approaches
Algebra
Contents:
1.1: Scientific notation
1.2: Arithmetic Sequences
Video
Exercises
Solutions
1.3: Geometric Sequences
Video
1.4: Compound Interest
1.5: Exponents & Logs
Video
Exercises
Solutions
1.6: Simple proofs
1.7: More logarithms
Videos
Exercises
Solutions
1.8: Infinite Geometric Series
Videos
1.9: Binomial Theorem
Exercises
Solutions
Standard Level content
Additional Higher Level content
1.10: Combinations & Permutations [AHL]
1.11: Partial Fractions [AHL]
1.12: Complex Numbers Intro [AHL]
Videos
Videos
1.13: Polar form & Euler’s form [AHL]
1.14: Complex roots & de Moivre’s thm. [AHL]
1.15: Proof by Induction, Contradiction, etc [AHL]
1.16: Systems of 3 Equations [AHL]
Functions
2.1: Linear functions
Problems:
Find the slope of a line passing through (-1,0) & (3,-8):
Parallel, perpendicular, or neither: y=3x+4 & y=3x+7
Parallel, perpendicular, or neither: y+x/3=2 & y=3x-5
Find eq. of a line that’s parallel to y=0.5x+5 and passes (4,-5)
Find eq. of a line that’s perpendicular to y=2x-3 and passes (-5,3)
2.2: Domain, range, inverses
Problems:
Find the range of f(x)=2ˣ + 1:
Find the domain of g(x)=2x² – 3x + 2:
If f(x)=0.2x – 6, find f⁻¹(x):
If g(x)=e²ˣ + 1, find g⁻¹(x):
2.3/2.4: Graphs
2.5: Composite functions
Video
Problems:
If f(x)=2x & g(x)=3x+5, find (f º g)(x):
If f(x)=2x & g(x)=3x+5, find (g º f)(x):
If f(x)=x²+1 & g(x)=2x-7, find (f º g)(x):
If f(x)=4/x, find (f º f)(x):
If f(x)=4x²+x & g(x)=2x, find (f º g⁻¹)(x):
2.6: Forms of quadratics
2.7: Solving quadratics
Videos
Video
Problems:
Factor x² – 2x – 35:
Factor 2x² + 5x – 3:
Hence, find the roots of y = 2x² + 5x – 3:
Solve 5x² – 27x + 10 = 0:
How many real roots does y = 3x² + 5x + 7 have?
2.8: Reciprocal & rational functions
Video
2.9: Exponential & logarithmic functions
2.10: Solving equations
Video
2.11: Transformations
Standard Level content
Additional Higher Level content
2.12: Polynomials [AHL]
2.13: More rational functions [AHL]
2.14: Odd & even functions, self-inverse [AHL]
2.15: Solving inequalities [AHL]
2.16: Absolute value graphs, and more [AHL]
3.1: 3D Geometry
3.2: SOHCAHTOA & triangle rules
3.3: Trigonometric applications
3.4: Arcs & sectors + radians
3.5: Unit circle and exact values
Problems:
Find sin(150°):
Find cos(3π/4):
Find sin(-60°):
Solve x=cos⁻¹(-0.5), for 0<x<360°:
Solve x=sin⁻¹(√3/2), for –π<x<π:
3.6: Trigonometric identities
3.7: Trigonometric graphs
Video
3.8: Solving trigonometric equations
Video
Exercises
Solutions
Standard Level content
3.9: Reciprocal trigonometric ratios [AHL]
Additional Higher Level content
3.10: Compound angle formula [AHL]
3.11: Other trig properties [AHL]
3.12: Vector basics [AHL]
Problems:
Calculate (2i + 5j) + (4i – 7j):
Calculate (i + 8j) – 2(3i – j):
If v = (12i + 5j), calculate |v|:
If w = (-i + 2j – 2k), calculate |w|:
3.13: Scalar (dot) product & angles [AHL]
Problems:
Calculate (2i + 5j)⋅(4i – 7j):
Calculate (i – 3j – 2k)⋅(5i + 11j – 9k):
Find the angle between (i – 3j – 2k) & (5i + 11j – 9k):
Are (2i + 5j) & (-10i + 4j) parallel, perpendicular or neither?:
3.14: Vector equations of lines [AHL]
3.15: Intersections of lines [AHL]
3.16: Vector product [AHL]
3.17: Planes [AHL]
3.18: Intersections of planes [AHL]
4.1: Basics & concepts
4.2: Presentation of data
Videos
4.3: Averages & dispersion
Videos
Exercise Links: IXL Averages 1, IXL Averages 2,
IXL Standard Deviation, Khan Academy Averages 1
4.4: Regression & correlation
Videos
4.5: Probability basics
4.6: Venn diagrams, probability trees, conditional prob.
Videos
4.7: Discrete random variables
4.8: Binomial distribution
Videos
4.9/4.12: Normal distribution
4.10: x-on-y regression & 4.11: Conditional independence
Standard Level content
Additional Higher Level content
4.13: Bayes’ Theorem [AHL]
Video
4.14: Continuous Random Variables [AHL]
5.1: Limits, slopes of curves
5.2: Increasing & decreasing regions
5.3: Derivatives of polynomials
Problems:
If f(x) = 4x², find f'(x):
If g(x) = 5x³ – 2x, find g'(x):
If f(x) = x⁻ ² + 7, find f’(x):
If y = x + 12 – 2x, find dy/dx:
5.4: Equations of tangents and normals
Exercises
Solutions
5.5: Introduction to integration
Problems:
Find ∫2xdx:
Find ∫(4t³-2)dt:
Find ∫9x²dx:
5.6: Given derivatives
Videos
Exercises
Solutions
5.7: Second derivatives and derivative graphs
5.8: Stationary points & inflection points
Exercises
Solutions
5.9: Kinematics
5.10: Integral rules
5.11: Definite integrals & area
Standard Level content
Additional Higher Level content
5.12: Limits & first principles [AHL]
5.13: L’Hôpitals’s rule [AHL]
5.14: Implicit diff. & related rates [AHL]
5.15: More given derivatives [AHL]
5.16: Int by substitution & parts [AHL]
5.17: Volume of revolution [AHL]
5.18: Differential equations [AHL]
5.19: Maclaurin series [AHL]
IB Past Papers 1995 to 2023
