General Mathematics I

The route

Lessons are in the order that makes each one easier than the last. Each unit ends with a short quiz.

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   Unit 1

   The Real Number System, Proportion and Units

   The real number family, intervals and absolute value, ratio, proportion and percentages, and the unit conversions behind every dosage calculation.
   1. The Real Number SystemFree Every number you have ever used belongs to one big family. Here is who is related to whom. 12 min
   3. Intervals and Absolute Value How far is a number from zero, or from 37 degrees? Absolute value measures distance and ignores direction. 10 min
   4. Ratio, Proportion and Percentages Sharing money, scaling a recipe, reading a discount. The arithmetic of fair comparison. 10 min
   5. Units of Measurement and Dosage Calculations Milligrams, millilitres and drops per minute. Ratio and proportion doing a real job on a ward. 10 min
   6. Unit 1 quiz6 questions on this unit 8 min
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   Unit 2 Full plan

   Indices, Surds and Logarithms

   Laws of indices, exact work with surds, logarithms and their laws, and solving growth and half-life problems.
   1. Laws of Indices One bacterium becomes a billion before breakfast. Indices are the shorthand for repeated multiplying. 10 min
   2. Surds Keep the square root exact, simplify it, and never leave one in a denominator. 10 min
   3. Logarithms Two to the what gives 32? A logarithm is the answer to that question, and its laws are the index laws in disguise. 10 min
   4. Exponential Growth, Decay and Half-Life When will the culture pass a million? When is only a tenth of the tracer left? Logs bring the unknown down from the index. 10 min
   5. Unit 2 quiz6 questions on this unit 8 min
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   Unit 3 Full plan

   Set Theory and Venn Diagrams

   The language of sets, union, intersection and complement, De Morgan's laws, and counting survey results with two and three sets.
   1. Set Notation and Types of Sets A set is just a well-defined collection. The notation is short, precise and used all over mathematics. 12 min
   2. Set Operations and De Morgan's Laws Or, and, not. Three small words that become the operations of set algebra, plus one law that swaps them. 10 min
   3. Venn Diagrams and Counting Problems A survey of 100 students, three breakfast drinks and one golden rule. Always fill the middle first. 14 min
   4. Unit 3 quiz5 questions on this unit 6 min
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   Unit 4 Full plan

   Sequences, Series and the Binomial Theorem

   Arithmetic and geometric progressions, interest and growth, sums to infinity, proof by induction, and the binomial expansion.
   1. Arithmetic Progression Add the same amount every time. Savings plans, staircases and simple interest all follow this one pattern. 13 min
   2. Geometric Progression and Sum to Infinity Multiply by the same number every time. Compound interest, bouncing balls and why 0.999… equals 1. 14 min
   3. Mathematical Induction Knock over the first domino, show each one knocks the next, and infinitely many fall. 10 min
   4. Pascal's Triangle and the Binomial Theorem Expanding (a + b) to the power 6 by hand takes ages. A triangle of numbers does it in seconds. 10 min
   5. The General Term and Binomial Approximation Jump straight to the one term you need, and estimate 1.02 to the power 5 to five decimal places without a calculator. 10 min
   6. Unit 4 quiz6 questions on this unit 8 min
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   Unit 5 Full plan

   Quadratic Equations and Functions

   Three ways to solve a quadratic, the discriminant, sums and products of roots, functions and inverses, and sketching lines and parabolas.
   1. Solution of Quadratic Equations Factorise when you can, complete the square when you must, and the formula works every single time. 10 min
   2. Nature of Roots and Sum and Product of Roots Know what kind of roots you will get before you solve, and build new equations without ever finding the roots. 10 min
   3. Domain, Range, Composite and Inverse Functions A function is a machine with one output for every input. Chain two together, or run one backwards. 14 min
   4. Graphs of Linear and Quadratic Functions Gradient and intercept for a line. Roots, vertex and axis of symmetry for a parabola. Then read answers off the picture. 14 min
   5. Unit 5 quiz6 questions on this unit 8 min
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   Unit 6 Full plan

   Trigonometry and Complex Numbers

   Radians and exact ratios, identities and compound angles, trig equations and triangles, and a first look at complex numbers.
   1. Circular Measure and Trigonometric Ratios Measure angles the way the circle itself does, and know sin, cos and tan of 30, 45 and 60 degrees by heart. 10 min
   2. Trigonometric Identities and Compound Angles One identity from Pythagoras, a handful of addition formulas, and you can find sin 75 degrees exactly. 10 min
   3. Trigonometric Graphs, Equations and the Sine and Cosine Rules Waves that repeat every 360 degrees, equations with more than one answer, and triangles without a right angle. 10 min
   4. Complex Numbers What if negative numbers had square roots? Invent one, call it i, and every quadratic suddenly has two roots. 16 min
   5. Unit 6 quiz5 questions on this unit 6 min

Practise and remember