Higher Level for the IB Diploma-Oxford
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English
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Entries: 150
Bill Roberts
Sandy MacKenzie
core math
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Higher Level for the IB Diploma-Oxford
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1. Trigonometry 1
Theory
Page 6
1.1 Circle problems
Theory
Page 6
1.2 Trigonometric ratios
Theory
Page 9
1.3 Solving triangles
Theory
Page 10
1.4 Trigonometric functions and graphs
Theory
Page 14
1.5 Related angles
Theory
Page 18
1.6 Trigonometric equations
Theory
Page 19
1.7 Inverse trigonometric functions
Theory
Page 22
2. Quadratic Equations, Functions and Inequalities
Theory
Page 24
2.1 Introduction to quadratic functions
Theory
Page 24
2.2 Solving quadratic equations
Theory
Page 26
2.3 Quadratic functions
Theory
Page 27
2.4 Linear and quadratic inequalities
Theory
Page 30
2.5 Nature of roots of quadratic equations
Theory
Page 32
3. Functions
Theory
Page 36
3.1 Functions
Theory
Page 36
3.2 Composite functions
Theory
Page 39
3.3 Inverse functions
Theory
Page 40
3.4 Graphs of inverse functions
Theory
Page 41
3.5 Special functions
Theory
Page 42
3.6 Drawing a graph
Theory
Page 44
3.7 Transformations of functions
Theory
Page 46
4. Polynomials
Theory
Page 51
4.1 Polynomial functions
Theory
Page 52
4.2 Factor and remainder theorems
Theory
Page 54
4.3 Finding a polynomial’s coefficients
Theory
Page 55
4.4 Solving polynomial equations
Theory
Page 56
4.5 Finding a function from its graph
Theory
Page 58
4.6 Algebraic long division
Theory
Page 59
4.7 Using a calculator with polynomials
Theory
Page 60
5. Exponential and Logarithmic Functions
Theory
Page 63
5.1 Exponential functions
Theory
Page 63
5.2 Logarithmic graphs
Theory
Page 65
5.3 Rules of logarithms
Theory
Page 66
5.4 Logarithms on a calculator
Theory
Page 67
5.5 Exponential equations
Theory
Page 69
5.6 Related graphs
Theory
Page 71
6. Sequences, Series and Binomial Theorem
Theory
Page 74
6.1 Arithmetic sequences
Theory
Page 75
6.2 Sum of the first n terms of an arithmetic sequence
Theory
Page 76
6.3 Geometric sequences and series
Theory
Page 78
6.4 Sum of an infinite series
Theory
Page 79
6.5 Applications of sequences and series
Theory
Page 81
6.6 Sigma notation
Theory
Page 81
6.7 Factorial notation
Theory
Page 83
6.8 Binomial theorem
Theory
Page 86
7. Trigonometry 2
Theory
Page 90
7.1 Identities
Theory
Page 90
7.2 Compound angle formulae
Theory
Page 92
7.3 Double angle formulae
Theory
Page 95
7.4 Using double angle formulae
Theory
Page 97
7.5 Wave function
Theory
Page 99
8. Differential Calculus 1 – Introduction
Theory
Page 103
8.1 Differentiation by first principles
Theory
Page 104
8.2 Differentiation using a rule
Theory
Page 105
8.3 Gradient of a tangent
Theory
Page 107
8.4 Stationary points
Theory
Page 108
8.5 Points of inflexion
Theory
Page 112
8.6 Curve sketching
Theory
Page 114
8.7 Sketching the graph of the derived function
Theory
Page 116
9. Differentiation 2 – Further Techniques
Theory
Page 121
9.1 Differentiating trigonometric functions
Theory
Page 122
9.2 Differentiating functions of functions, chain rule
Theory
Page 123
9.3 Differentiating exponential and logarithmic functions
Theory
Page 125
9.4 Product rule
Theory
Page 127
9.5 Quotient rule
Theory
Page 128
9.6 Implicit differentiation
Theory
Page 130
9.7 Differentiating inverse trigonometric functions
Theory
Page 132
9.8 Summary of standard results
Theory
Page 134
9.9 Further differentiation problems
Problem
Page 134
10. Differentiation 3 – Applications
Theory
Page 136
10.1 Optimization problems
Problem
Page 136
10.2 Rates of change of connected variables
Theory
Page 139
10.3 Displacement, velocity and acceleration
Theory
Page 142
11. Matrices
Theory
Page 147
11.1 Introduction to matrices
Theory
Page 148
11.2 Determinants and inverses of matrices
Theory
Page 153
11.3 Solving simultaneous equations in two unknowns
Theory
Page 157
11.4 Solving simultaneous equations in three unknowns
Theory
Page 159
12. Vector Techniques
Theory
Page 167
12.1 Introduction to vectors
Theory
Page 168
12.2 A geometric approach to vectors
Theory
Page 172
12.3 Multiplication of vectors
Theory
Page 175
13. Vectors, Lines and Planes
Theory
Page 184
13.1 Equation of a straight line
Theory
Page 185
13.2 Parallel, intersecting and skew lines
Theory
Page 189
13.3 Equation of a plane
Theory
Page 192
13.4 Intersecting lines and planes
Theory
Page 197
14. Integration 1
Theory
Page 203
14.1 Undoing differentiation
Theory
Page 203
14.2 Constant of integration
Theory
Page 204
14.3 Initial conditions
Theory
Page 205
14.4 Basic results
Theory
Page 206
14.5 Anti-chain rule
Theory
Page 207
14.6 Definite integration
Theory
Page 208
14.7 Geometric significance of integration
Theory
Page 209
14.8 Areas above and below the x-axis
Theory
Page 212
14.9 Area between two curves
Theory
Page 214
15. Integration 2 – Further Techniques
Theory
Page 219
15.1 Integration as a process of anti-differentiation – direct reverse
Theory
Page 220
15.2 Integration of functions to give inverse trigonometric functions
Theory
Page 223
15.3 Integration of powers of trigonometric functions
Theory
Page 225
15.4 Selecting the correct technique
Theory
Page 228
15.5 Integration by substitution
Theory
Page 229
15.6 Integration by parts
Theory
Page 232
15.7 Miscellaneous techniques
Theory
Page 234
15.8 Further integration practice
Problem
Page 236
15.9 Selecting the correct technique 2
Theory
Page 237
15.10 Finding the area under a curve
Theory
Page 238
16. Integration 3 – Applications
Theory
Page 241
16.1 Differential equations
Theory
Page 241
16.2 Solving differential equations by direct integration
Theory
Page 242
16.3 Solving differential equations by separating variables
Theory
Page 244
16.4 Verifying that a particular solution fits a differential equation
Theory
Page 246
16.5 Displacement, velocity and acceleration
Theory
Page 247
16.6 Volumes of solids of revolution
Theory
Page 249
17. Complex Numbers
Theory
Page 255
17.1 Imaginary numbers
Theory
Page 256
17.2 Complex numbers
Theory
Page 257
17.3 Argand diagrams
Theory
Page 261
17.4 de Moivre’s theorem
Theory
Page 267
18. Mathematical Induction
Theory
Page 274
18.1 Introduction to mathematical induction
Theory
Page 275
18.2 Proving some well-known results
Theory
Page 278
18.3 Forming and proving conjectures
Theory
Page 281
19. Statistics
Theory
Page 284
19.1 Frequency tables
Theory
Page 284
19.2 Frequency diagrams
Theory
Page 288
19.3 Measures of dispersion
Theory
Page 294
19.4 Using a calculator to perform statistical calculations
Theory
Page 297
20. Probability
Theory
Page 301
20.1 Introduction to probability
Theory
Page 301
20.2 Conditional probability
Theory
Page 304
20.3 Independent events
Theory
Page 305
20.4 Bayes’ theorem
Theory
Page 308
20.5 Permutations and combinations
Theory
Page 312
20.6 Probability involving permutations and combinations
Theory
Page 315
21. Discrete Probability Distributions
Theory
Page 319
21.1 Introduction to discrete random variables
Theory
Page 320
21.2 Expectation and variance
Theory
Page 322
21.3 Binomial distribution
Theory
Page 326
21.4 Poisson distribution
Theory
Page 331
22. Continuous Probability Distributions
Theory
Page 339
22.1 Continuous random variables
Theory
Page 340
22.2 Using continuous probability density functions
Theory
Page 342
22.3 Normal distributions
Theory
Page 349
22.4 Problems involving finding μ and σ
Problem
Page 353
22.5 Applications of normal distributions
Theory
Page 354
Answers
Answer
Page 360
Index
Other
Page 366
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