Mathematics Learning Path
High School (11–12) Mathematics
Explore structured mathematics courses, solved problems, simulations and Python activities.
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Pascal's Triangle and the Binomial Expansion
StemPy LabPascal's triangle and the expansion of (a + b) to the power n for a whole number n. The general term, the middle term or terms, and the term that is free of x.
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Properties and Applications of Binomial Coefficients
The sum of the coefficients, the relations among them, and sums that use them. Then finding remainders, proving divisibility and approximating large powers.
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Slope and Equations of Straight Lines
The slope of a line and the angle it makes with the x-axis, the angle between two lines, parallel and perpendicular lines, and collinear points. Then the equation of a line in point-slope, two-point, slope-intercept and intercept forms.
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General Form, Distances and Families of Lines
The general equation Ax + By + C = 0 and its normal form. The distance from a point to a line and between parallel lines, and which side of a line a point is on. Families of lines through an intersection, and the shift of origin.
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Sequences, Series and Arithmetic Progressions
Sequences given by a formula or a rule, series and sigma notation, then arithmetic progressions in depth: the nth term, the sum, properties, and the arithmetic mean.
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Geometric Progressions and the AM-GM Inequality
Geometric progressions: the nth term, the sum of n terms and the sum to infinity, the geometric mean, and the relation between the arithmetic and geometric means.
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The Fundamental Principle of Counting
Count choices made one after another with the multiplication principle, separate cases with the addition principle, and meet the factorial.
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Permutations
Arrangements when order matters: the formula for nPr, arrangements with repeated objects, and arrangements under conditions such as letters that must stay together.
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Combinations
Selections when order does not matter: the formula for nCr, its properties, and problems that mix selecting and arranging.
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Complex Numbers and Their Algebra
Meet i, write numbers as a + ib, and add, subtract, multiply and divide them. Find powers of i, and the identities that still hold for complex numbers.
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The Argand Plane and Quadratic Equations
Picture complex numbers as points, find their modulus and conjugate and what they mean on the plane, then solve quadratic equations with a negative discriminant and find square roots of complex numbers.
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Sum and Difference Formulae
Prove the formula for the cosine of a sum, and build every other formula from it: sums, differences, double and triple angles, and the change of a sum into a product.
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