Mathematics Learning Path
High School (11–12) Mathematics
Explore structured mathematics courses, solved problems, simulations and Python activities.
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Slope and Equations of Straight Lines
StemPy LabThe 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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Trigonometric Functions and Their Graphs
Define sine and cosine for every angle with the unit circle. Find their signs, values and periods, and draw the graphs of all six functions, with their stretches and shifts.
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Angles and Radian Measure
Turn an angle past 360 degrees, or backwards, and measure it in radians, the natural unit of a circle. Then use radians to find arcs and sectors of wheels, clocks and tracks.
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