A new series of A Level books written by Dr Allen Brown to ensure your success in A Level Maths by using the Casio fx-991EX CLASSWIZ Calculator. This calculator is the one to buy with a huge number of functions. These books will show you how to use the fx991EX to solve really difficult A Level maths problems – they are a must for your learning and getting ahead.
Algebra Contents 1. Manipulating Algebraic Expressions3 1.1 Algebraic Fractions 1.2 Algebraic Division 1.3 Long Division with Remainders1.4 The Factor Theorem 2. Polynomials2.1Polynomials on the fx 991FX Calculator 2.2 Adding Polynomials 2.3 Multiplying Polynomials 2.4 Factorising Polynomials 3. Identities 4. Quadratic4.1FunctionsSimultaneous Quadratic and Linear Equations 4.2 Simultaneous Quadratic Equations 4.3 Simultaneous Quadratic and Cubic Equations 5. Partial Fractions5.1Partial Fraction with a Quadratic Denominator 5.2 Partial Fractions with Repeated Factor 5.3 Improper Partial Fractions 6. Series and Series Expansion 6.1 Converging Series 6.2 Expansion Series 6.3 The Taylor Series 6.4 The Binomial Series 7. Rational7.1FunctionsSketching Graphs 7.2 Sketching Modulus Functions 8. Parametric Equations 8.1 Parametric Trigonometric Equations 9. Numerical9.1MethodsConverging Sequence 9.2 The Newton Raphson Algorithm 10. Inequalities10.1Inequalities and Quadratic 10.2FunctionsInequalities and the Casio QR Code 11. Worked Examples
Trigonometry Contents 1 Angles and their Measurement 1.1 Measuring Angles 1.2 Angles in Geometrical 1.3FiguresAnglesSmaller than 1 degree 1.4 Acute, Obtuse and Reflex Angles 2 The Pythagoras Theorem 2.1 The Right Angled Triangle 2.2 The Pythagoras Theorem 2.3 More Definitions 2.4 Special Right Angle Triangles 2.5 Right Angled Triangles with Two Equal Sides 2.6 fx 991EX for TrigonometricperformingCalculations 3 Sine, Cosine and Tangent 3.1 The sine function 3.2 Graph of a Sine Function 3.3 The Cosine Function 3.4 Graph of a Cosine Function 3.5 The tangent function 3.6 Graph of a Tan Function 3.7 Trigonometric Calculations 4 Identities4.1 Sum Difference Identities (compound angles) 4.2 Double Angle Identities 4.3 Half Angles 4.4 Sum and Difference of Sine and Cosine 4.5 Problems Involving Identities 5 Triangle5.1CalculationsTrigonometry of an Irregular Triangle 5.2 The Cosine Rule 5.3 The Half Angles 5.4 The Tan Identities for any Triangle 5.5 Obtuse and Reflex Angles 6 Secant, Cosecant and Cotangent 6.1 sec, cosec and cot 6.2 Graphs of Secant, Cosecant and Cotangent Functions 6.3 Identities 6.4 fx 991EX calculator and the reciprocal functions 6.5 Applications 6.6 Proving Expressions 7 Inverse Functions7.1sin1Function7.2cos1Function7.3tan1Function7.4ApplicationtoIrregularTriangles7.5CircularMeasure 8 Hyperbolic8.1FunctionsCalculations involving Hyperbolic Functions 8.2 Hyperbolic Identities
8.3 Inverse Hyperbolic Functions 8.4 Calculations involving Inverse Hyperbolic Functions 8.5 Inverse Hyperbolic Identities 9 Graphs of Trigonometric Functions 9.1 Graphs of Inverse Functions 9.2 Polar Plots of Trigonometric Functions 9.3 Radial Plots of Hyperbolic 9.4FunctionsRadialPlots of Inverse Hyperbolic Functions 9.5 The Sine Function and Rotation 10 Algebraic Trigonometry Problems 11 Trigonometry and Differentiation 12 Trigonometry and Integration Calculus Contents 1. A Very Short History of Calculus 1.1 Differentiation and Integration 1.2 Calculus Features on the Casio fx 991EX Calculator 2. Differentiation2.2Introduce a New Variable the Chain Rule 3. Differentiation Rules 3.1 The Product Rule 3.2 The Quotient Rule 4. Differentiating Trigonometric Functions 4.1 Parametric Graphs of Functions and their Derivatives 4.2 Differentiation of Inverse Functions 5. Higher Order Differentiation 6. Maxima and Minima 6.1 Using the fx Calculator to Determine Stationary Points 7. Differentiation of Power and Logarithmic Functions 7.1 Differentiating Logarithmic Functions 8. Further8.1DifferentiationDifferentiation and Partial Fractions 8.2 Implicit Differentiation 9. Applications of Differentiation 9.1 Understanding Errors 9.2 Solved Problems 10 Elementary Integration 10.1 Definite Integrals 11. Substitution Method 11.1 Substitution on Finite Integrals 12 Integration of Exponential Functions 12.1 Integration of Logarithmic Functions 13. Integration Techniques 13.1 Partial Fractions
13.2 Integrations and Partial 13.3FractionsFiniteIntegrals and Partial Fractions 13.4 Integration and Compound Division 13.5 Finite Integrals and Compound Division 13.6 Finite Exponential and Logarithmic Integrals 14. Integration of Trigonometric Functions 14.1 Integration of Hyperbolic Functions 14.2 Finite Integrals Involving Trigonometric and Hyperbolic Functions 15. Integration by Parts 15.1 Finite Integrals using Integration by Parts 15.2 Reduction Integration Method 16. Applications of Integration 16.1 Calculating the Volume of a Rotated Function 16.2 Calculating the Area between two Functions 17. Harder Integrations Statistics Contents 1 First Look at Probability 1.1 Sample Space 1.2 Independent Events 1.3 Different coloured balls in a bag 1.4 Probability and the Hypergeometric Distribution 2 Sets and2.1ProbabilityCombined Probabilities 2.2 Conditional Probability 2.3 Tree Diagrams and Conditional Probabilities 2.4 Mutually Exclusive Events 2.5 Independent Events 2.6 Dependence 3 First Look at Statistics 3.1 Histogram 3.2 Cumulative Frequency
3.3 The Median 3.4 Average or Mean 3.5 Mean Square 3.6 Variance and Standard 3.7DeviationQuartiles, Percentiles & Interquartile Range 4 Normal Distribution4.1Significance of the Standard Deviation 4.2 Using the Table with Negative Values of z 4.3 Using the Casio fx 991EX for Calculating the Normal Distribution 5 Applying the Normal Distribution 5.1 The Normal Distribution and Real World Applications 5.2 Probability and the Normal Distribution 6 The Poisson Distribution 6.1 Poisson Distribution for P(X < A;Y) 6.2 Poisson Distribution for P(X > A;Y) 6.3 Using Cumulative Poisson Probability Tables 7 The Binomial Distribution 7.1 The Distribution Function 7.2 Using Cumulative Binomial Probability Tables 7.3 Cumulative CalculationsBinomials 8 Continuous Random Variables 8.1 Expectation Values 8.2 Selecting Suitable Functions 8.3 Cumulative Distribution Functions 8.4 Mode, Median and Quartiles of Random Variables 9 Sampling9.1TheorySampling Distributions 9.2 Confidence Limits with a known Standard Deviation 9.3 Student t distribution 9.4 Sampling Distribution of Proportions 10 Hypothesis Testing 10.1 One and Two tailed Tests 10.2 Hypothesis Testing on Population Proportion 10.3 p value 10.4 Difference between Two Means 11 Correlation11.1 Covariance 11.2 Linear Regression 11.3 Spearman’s Rank Correlation Coefficient 11.4 Correlation and Sampling Theory 11.5 Quadratic Regression Mechanics
Contents 1. Definitions of Parameters used in Mechanics1.1Energy1.2Momentum and Angular 1.3MomentumForce,Mass, Thrust and Impulse 1.4 Pressure, Stress, Strain and 1.61.5TensionPowerFriction and Reaction 1.7 Velocity, Acceleration and Moments 2. Vectors in 2.1MechanicsRelativePosition and Velocity Vectors 3. Moving3.1ParticlesProcedures for the fx 991EX 3.2calculatorObjectsMoving under Gravity 4. Static Particles4.1Effect of Friction 4.2 Friction on an Inclined Plane 5. Newton’s Second Law of Motion 5.1 Two or more Forces acting on an Object 5.2 Two Weight Pulley System 5.3 Friction 5.4 Pulley System and an Inclined Plane 6. Appreciating Moments 6.1 Beams Suspended by Ropes 7. Projectiles7.1 Projectiles and Vectors 7.2 Projectiles Launched at an Angle 7.3 Equation for a Projectile’s Trajectory 8. Collisions and Impulse 8.1 Inelastic Collisions 9. Work, Energy and Power 9.1 Collisions and Kinetic Energy 9.2 Coalescing Collisions 9.3 Forces at Work 9.4 Work and Potential Energy of Objects on Inclined Planes 9.5 Power 9.6 Variable Resistive Forces 10. Statics and Limited Equilibrium 10.1 Ladders leaning against walls 11. Moment of Inertia 11.1 Moment of Inertia of a Uniform Rod 11.2 Moment of Inertia of a Uniform Disc 11.3 Moment of Inertia of a Solid Sphere 11.4 Moment of Inertia of a Solid Cylinder 11.5 Moment of Inertia of a Hollow Cylinder 11.6 The Additive Rule 12. Rotation12.1 Rotating Flywheel 12.2 Conical Pendulum 12.3 Vertical Rotating Objects 13 Elastic 13.1StringsHorizontal Elastic String with Weight 13.2 Elastic String with Weight on Incline Plane 14. Harmonic14.1MotionASimple Pendulum 14.2 Compound Pendulum 14.3 Weight on a Spring 14.4 Sea Tides 14.5 Damped Harmonic Motion
Matrices and Complex Numbers Contents 1 Vector Revision1.1Vector Notation 1.2 Vector Calculations on the fx-991EX Calculator 1.3 An Application of Vectors 2 First Look at Matrices 2.1 Features of Matrices 2.2 Matrix Algebra Rules 3 Matrix Calculations on the fx 991EX 4 Determinants4.1Sort cut in Calculating a (3×3) Determinant 4.2 Calculating the Area of a Triangle 4.3 Cofactors of a Determinant 4.4 Calculating the Inverse of a Matrix 5 Solving Simultaneous Equations 5.1 Row Echelon Reduction Form 6 Transformations6.1Scaling6.2Rotation6.3Reflexion6.4Shear6.5Stretch6.6Translation6.7LinearTransformations using Matrices 7 Eigenvalues and Eigenvectors 7.1 Eigenvalues Eigenvectorsandonthe fx 991EX 7.2 The Power Method 8 Matrices and Information Encryption 9 Solved Matrix Examples 10 Introduction to Complex Numbers 10.1 Complex CalculationsNumber 11 The fx 991EX and Complex Numbers 12 Trigonometry and Complex Numbers 12.1 De Moivre’s Theorem 12.2 Further fx Calculations991EX 13 Quadratic Equations with Complex 14RootsComplex Numbers Examples
andProgrammingLinearModelling Contents 1 Classification of Linear Programming Graphs 2 Basic Linear Programming 3 Linear Programming with Three Constraints 4 Applying Linear Programming 5 Optimisation 6 Optimising Commercial Performance 7 2D Modelling 8 3D Modelling 9 Other Mathematical Models More Calculus Contents 1 Differentiation Examples 2 Integration Examples 3 Integrals with Rational Functions 4 Integrals with Roots 5 Integrals with Logarithms and Exponentials 6 Integrals with Trigonometric Functions 7 Integrals with Products of Functions 8 Miscellaneous Functions 9 Integrals with Hyperbolic Functions
fx-991EX Practice Examples 1ContentsFeatures of the fx 991EX Calculator 1.1 Number Formats 1.2 Performing Division 1.3 The fx 991EX Memory 1.4 Using the Cursor 1.5 Accessing the Casio Website 2 Fundamental Calculations 2.2 Inequalities 3 Calculations with Indices 4 Calculations with 10x and ex 5 Calculations with Logarithms 6 Calculations with big and small numbers 7 Trigonometry Calculations 8 Ratios 9 Calculations with Physics Equations 9.1 Plank Units 10 Using the Spreadsheet
