## Excel Fast Track: 50 HSC Exam Tips Maths (2 Unit) |

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This book has really good hints that can be useful to you.

### Contents

BASIC ALGEBRA AND ARITHMETIC TIP 1 Calculator Display | 1 |

Difficult Factorisation | 2 |

Inequalities Involving Absolute Values | 3 |

Calculator Exercises | 4 |

Percentage Discount Increase Problems | 5 |

Recurring Decimals Solved Both Ways | 6 |

REAL FUNCTIONS TIP 7 Sketching Familiar Functions | 7 |

Domain Range | 10 |

Understanding Rates of Change | 52 |

DERIVATIVE OF A FUNCTION TIP 29 Differentiation Tricks | 54 |

INTEGRATION TIP 30 Using the Trapezoidal Simpsons Rule | 56 |

Integration Tricks 5 8 | 58 |

Volumes of Solids of Revolution Formed by Rotating the Area Between Two Curves | 60 |

Finding the Volume Using Simpsons Rule | 63 |

Intergrating Both Sides | 65 |

TRIGONOMETRIC FUNCTIONS TIP 35 Sketching More Difficult Trigonometric Functions | 67 |

Shading Regions Involving Inequalities | 11 |

Functional Notation | 13 |

Adding Functions Together | 15 |

TRIGONOMETRIC RATIOS TIP 12 Harder Trigonometric Problems | 17 |

Bearings | 19 |

THE QUADRATIC POLYNOMIAL THE PARABOLA TIP 14 Quadratic Inequalities | 22 |

The Parabola Completing the Square | 24 |

The Locus of a Parabola Circle Straight Line | 26 |

The Discriminant | 28 |

Quadratic Roots | 30 |

Intersection of a Straight Line with a Parabola | 32 |

SERIES TIP 20 Difficult Arithmetic and Geometric Series | 34 |

PLANE GEOMETRY TIP 21 Geometry Questions 3 6 | 36 |

Tests of a Quadrilateral 3 8 | 38 |

GEOMETRICAL APPLICATIONS OF DIFFERENTIATION TIP 23 Verifying Points of Inflection | 39 |

A Reliable Method for Sketching Curves | 42 |

Maxima and Minima Problems | 46 |

Sketching the Derivative Function of a Given Curve fx | 48 |

Finding the Number of Solutions by Graphical Means | 50 |

When to Use Radians Instead of Degrees | 69 |

LOGARITHMIC AND EXPONENTIAL FUNCTIONS TIP 37 Index Laws | 71 |

Logarithmic Laws | 73 |

Logarithmic and Exponential Equations | 76 |

Discarding Unreasonable Answers | 77 |

Maximum Displacement Velocity Involving Trigonometric Functions | 79 |

Distinction Between Displacement and Distance | 80 |

Graphical Understanding of Motion Questions | 82 |

PROBABILITY TIP 44 ProbabilityGeneral Hints | 86 |

Constant Changing Probabilities | 88 |

Conditional Probabilities | 90 |

SERIES APPLICATIONS TIP 47 Arithmetic Series Applications | 92 |

Geometric Series Applications | 95 |

Loan Repayments and Superannuation Questions Using a Time Line | 97 |

Series Application in Probability Other Topics | 101 |

Further Review Exercises | 103 |

Worked Solutions to Review Exercises | 123 |

### Common terms and phrases

angles appears in exams Applications of Calculus asked axes axis calculator changes sign completing the square decimal places Degree of difficulty derivative diagram domain and range Exponential Functions Express your answer Factorise Find the coordinates Find the number find the probability Find the value focal length formed by rotating FUNCTIONS TIP Geometry Questions given graph Graphical hence horizontal point HSC exam HSC examinations HSC examples index laws Inequalities inflection exists intersection Loan Repayments locus Maxima and Minima maxima/minima maximum displacement metres minimum nautical miles negative Note number of solutions origin P(at least P(both parabola point of inflection problems quadratic equation Quadratic Polynomial Quadrilateral Recurring Decimals seconds shaded region sign in passing Simpson's rule Sketch the curve Solids of Revolution solving stationary point Step straight line Topic trapezoidal rule Trigonometric Functions turning point Typically from Question Typically Question velocity verify vertex x-axis