Theta Mathematics links

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Chapter 1 - Coordinate geometry

Page 2       Midpoint calculator
Page 11     Point-gradient grapher
Page 11     Two points: distance, gradient, line
Page 11     Point-point equation



Chapter 2 - Further Coordinate geometry

Page 15      Parallel line through a point
Page 17      Perpendicular line through a point
Page 27      Medians concurrent at the centroid
Page 27     
Medians of a triangle


Chapter 3 - Factored polynomials and their graphs

Page 36     Quadratic grapher
Page 37     y = a(xh)2 + k


Chapter 4 - Functions - domain and range

Page 49      Function machine
Page 54      Domain and range from a graph


Chapter 5 - Other mathematical functions and their graphs

Page 74      Winning time for men's marathon


Chapter 6 - Transformation of graphs and the connection with parameters

Page 91      Vertical translations of functions
Page 93      Translations of graphs (1)
Page 93      Translations of graphs (2)
Page 95      Changes of scale (1)
Page 95      Changes of scale (2)
Page 97      Reflection of graphs (1)
Page 97      Reflection of graphs (2)
Page 97      Reflection of graphs (3)
Page 98      Varying a, h and k in the parabola a(xh)2 + k
Page 98      Placing a parabolic mirror
Page 98      Several transformations at once - exponential (1)
Page 98      Several transformations at once - exponential (2)


Chapter 7 - Trigonometric graphs

Page 105    Sine curve applet
Page 105    Generating the sin, cos and tan graphs
Page 110    Trig graphs - the sin graph
Page 110    Trig graph tracer
Page 111    Trig graphs - the cos graph
Page 121    The graph of y = sin(ax)
Page 123    The graph of y = a sin(bx - c) 


Chapter 9 - Triangle trigonometry

Page 146    The Cairo pentagon


Chapter 10 - The sine rule

Page 159    Sine rule (1) (halfway down)
Page 159    Sine rule (2)
Page 160    
Proof of the sine rule


Chapter 11 - The cosine rule

Page 179    Solving triangles (1)
Page 179    Solving triangles (2)


Chapter 12 - Circular measure

Page 188    Degrees-radians conversions (1)
Page 188    Degrees-radians conversions (2) 
Page 188    Degrees-radians conversions (3) 
Page 191    Using the arc length formula
Page 197    Area of a sector
Page 201    Area of a segment
Page 205    The Reuleaux triangle (1)
Page 205    The Reuleaux triangle (2)


Chapter 13 - Basic algebra

Page 212       Expanding cubics


Chapter 15 - Factorising and quadratic expressions

Page 234     The peg puzzle
Page 235     Two-stage factorising
Page 235     Factorising quadratics where the coefficient of x2 is greater than 1

                 (Contributed by Joel Dodd, HOF Mathematics, Coastal Taranaki  School, Okato, NZ)















Chapter 16 - Solving equations and rearranging formulae

Page 241     Filling the bath


Chapter 17 - Quadratic equations

Page 258    Completing the square
Page 259    Proof of the quadratic formula
Page 260    Quadratic equation solver

Page 262    The Golden ratio (1)
Page 262    The Golden ratio (2)
Page 262    The Golden rectangle


Chapter 18 - Exponential expressions

Page 275    Exponent rules (1)
Page 275    Exponent rules (2)
Page 281    Tower of Hanoi gif
Page 282    Tower of Hanoi applet


Chapter 19 - Logarithms

Page 285     Log conversions
Page 290     Moore's Law


Chapter 20 - Introducing differentiation

Page 295    The gradient of the tangent
Page 298    The tangent line problem
Page 304    Derived function graph (1) 
Page 304    Derived function graph (2)
Page 304    Derived function graph (3)
Page 304    Derived function graph (4)


Chapter 23 - Calculus applications

Page 352    Enclosed area under a curve
Page 355    Maximising the volume of a box (1)
Page 355    Maximising the volume of a box (2)
Page 355    Maximising the volume of a box (3)


Chapter 24 - Probability 

Page 360    A monkey can eventually type Shakespeare
Page 374    Venn diagrams (1)
Page 374    Venn diagrams (2)
Page 374    Venn diagrams (3)


Chapter 26 - Normal distribution

Page 405    The normal distribution
Page 405    The normal distribution graph
Page 412    Standard normal probability calculator
Page 419    Calculating any normal probability (1)
Page 419    Calculating any normal probability (2)
Page 425    Witch of Agnesi (1)
Page 425    Witch of Agnesi (2)
Page 425    Witch of Agnesi (3)
Page 430    Inverse normal calculator


Chapter 27 - Simulation methods

Page 438    Forest fire (1)
Page 438    Forest fire (2)
Page 438    Forest fire (3)
Page 438    Bridge control applet
Page 439    Heads or tails simulation
Page 442    The cereal box problem
Page 442    Collecting coupons
Page 449    The Monty Hall problem (1)
Page 449    The Monty Hall problem (2)
Page 449    The Monty Hall problem (3)
Page 449    The Monty Hall problem (4)
Page 454    Predator-prey simulation
(applet at bottom)
Page 454    Predator-prey simulation (rabbits and wolves


Chapter 28 - Simultaneous equations

Page 461     Simultaneous equation solver
Page 462     Multiplying through by suitable numbers


Chapter 29 - Non-linear simultaneous equations

Page 468     Where does a line cut a parabola?
Page 472     Where does a line cut a circle?