Libro De Matematica Para Bachillerato

MATEMÁTICAS BI NS

Contents

7

Trigonometry 2
Identities Compound angle (addition) formulae Double angle formulae Using double angle formulae Wave function

Contents
1
1.1 1.2 1.3 1.4 1.5 1.6 1.7

7.1 7.2 7.3 7.4 7.5

159–182 159 163 169 173 176 183–216 184 187 190 193 201 204 209 217–245 218 221 224 229 231 234 238 242 243 246–267 246 253 259 268–304 269 278 287 291 305–336 306315 321 337–372 338 346 353 364 373–402 373 374 377 379 380 382 385 391 395

Trigonometry 1
Circle problems Trigonometric ratios Solving triangles Trigonometric functions and graphs Related angles Trigonometric equations Inverse trigonometric functions

8
1–34 1 7 9 17 24 27 32 35–57 35 39 41 47 51 58–85 58 62 64 67 69 73 76 86–107 87 91 93 95 98 100 103 108–129 109 112 114 117 120 125130–158 131 133 136 138 142 143 146 152 8.1 8.2 8.3 8.4 8.5 8.6 8.7

Differential Calculus 1– Introduction
Differentiation by first principles Differentiation using a rule Gradient of a tangent Stationary points Points of inflexion Curve sketching Sketching the graph of the derived function

2
2.1 2.2 2.3 2.4 2.5

Quadratic Equations, Functions and Inequalities
Introduction to quadraticfunctions Solving quadratic equations Quadratic functions Linear and quadratic inequalities Nature of roots of quadratic equations

9
9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

Differentiation 2 – Further Techniques
Differentiating trigonometric functions Differentiating functions of functions (chain rule) Differentiating exponential and logarithmic functions Product rule Quotient rule Implicitdifferentiation Differentiating inverse trigonometric functions Summary of standard results Further differentiation problems

3
3.1 3.2 3.3 3.4 3.5 3.6 3.7

Functions
Functions Composite functions Inverse functions Graphs of inverse functions Special functions Drawing a graph Transformations of functions

10
10.1 10.2 10.3

Differentiation 3 – Applications
Optimization problems Rates of changeof connected variables Displacement, velocity and acceleration

4
4.1 4.2 4.3 4.4 4.5 4.6 4.7

Polynomials
Polynomial functions Factor and remainder theorems Finding a polynomial’s coefficients Solving polynomial equations Finding a function from its graph Algebraic long division Using a calculator with polynomials

11
11.1 11.2 11.3 11.4

Matrices
Introduction to matrices Determinantsand inverses of matrices Solving simultaneous equations in two unknowns Solving simultaneous equations in three unknowns

12
12.1 12.2 12.3

Vector Techniques
Introduction to vectors A geometric approach to vectors Multiplication of vectors

5
5.1 5.2 5.3 5.4 5.5 5.6

Exponential and Logarithmic Functions
Exponential functions Logarithmic graphs Rules of logarithms Logarithms on acalculator Exponential equations Related graphs

13
13.1 13.2 13.3 13.4

Vectors, Lines and Planes
Equation of a straight line Parallel, intersecting and skew lines Equation of a plane Intersecting lines and planes

6
6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8

Sequences, Series and Binomial Theorem
Arithmetic sequences Sum of the first n terms of an arithmetic sequence Geometric sequences and seriesSum of an infinite series Applications of sequences and series Sigma notation Factorial notation Binomial theorem

14
14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9

Integration 1
Undoing differentiation Constant of integration Initial conditions Basic results Anti-chain rule Definite integration Geometric significance of integration Areas above and below the x-axis Area between two curvesiv

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Contents

15 Integration 2 – Further Techniques
15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 Integration as a process of anti-differentiation – direct reverse Integration of functions to give inverse trigonometric functions Integration of powers of trigonometric functions Selecting the correct technique 1 Integration by substitution Integration by parts Miscellaneous...