Probability — Rules, Venn Diagrams and Counting
Apply the addition rule, tell independent from mutually exclusive, read a Venn or tree diagram, and count arrangements without listing them.
Work with the common ratio, find any term or sum, and know exactly when an infinite series converges and when it does not.
By the end, you can
identify a geometric sequence, calculate terms and sums, and apply the condition for convergence.
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Geometric Sequences and Infinite Series
Multiplying, not adding
An arithmetic sequence adds the same amount each time. A geometric sequence multiplies by the same amount each time. 📈
That one difference changes everything: how fast it grows, which formulas apply, and whether adding infinitely many terms can give a finite answer. It can — and that result surprises people the first time they meet it.
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Next on the Mathematics P1 path · step 8 of 11
Optimisation and Rates of Change
14 min · R19
Apply the addition rule, tell independent from mutually exclusive, read a Venn or tree diagram, and count arrangements without listing them.
Solve linear and non-linear systems by substitution, keep your ordered pairs matched, and handle the exponent-law questions that look harder than they are.
Read a hyperbola from its equation — both asymptotes, the shape, the axes of symmetry and its domain and range — and sketch it with confidence.
Work through quadratics, the formula, surd equations and inequalities with a method you can trust under pressure, and learn where marks are usually lost.
Tell arithmetic patterns from quadratic ones using differences, build the general term for each, and read sigma notation without panic.
The whole Mathematics P1 path → All High School MicroQuests → Browse all 134 →
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Geometric Sequences and Infinite Series
R19 · 13 min · certificate