Mathematics Learning Path
High School (9–10) Mathematics
Explore structured mathematics courses, solved problems, simulations and Python activities.
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Special Angles and Trigonometric Identities
StemPy LabThe exact ratios of 0°, 30°, 45°, 60° and 90° from two simple triangles, and the identities that link the ratios, used to simplify and prove.
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Trigonometric Ratios
Name the sides of a right triangle from an angle, define sine, cosine, tangent and their reciprocals, and find all six ratios when one is known.
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Patterns and the nth Term
Spot an arithmetic progression, find its common difference, and write a formula for its nth term. Then use it to find any term, or to find which term has a given value.
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The Sum of an Arithmetic Progression
Add the first n terms of an arithmetic progression with a formula, the way young Gauss did, and use it for savings, seats, steps and stacks.
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Solving Quadratic Equations by Factorising
Spot a quadratic equation, write a word problem as one, and solve it by splitting the middle term. Then check each root, and decide which roots make sense for the problem.
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The Quadratic Formula and the Nature of Roots
Complete the square, and turn it into the quadratic formula that solves every quadratic equation. Then read the discriminant to know, before solving, whether there are two roots, one or none.
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Irrational Numbers and Proofs
Why can the square root of 2 never be a fraction? Learn to prove it, step by step, with a proof by contradiction. Then prove the same for other roots, and find out when a sum or a product of such numbers is irrational.
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Primes, HCF and LCM
Break any number into primes, and see why there is only one way to do it. Then use the primes to find the HCF and the LCM, and solve real problems with them: bells that ring together, the largest tile for a floor, and buses that meet again.
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Distance, Midpoint and Section Formulas
A ship at one point and a port at another: how far apart are they? Where is the point halfway between them? Here we find the distance between two points, the midpoint, the point that divides a line in a ratio, and we use them to study shapes.
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The Cartesian Plane
A seat in a cinema is found by a row and a seat number. A square on a chessboard is found by a letter and a number. In this course we learn how two numbers fix the position of any point on a flat surface, and how to plot, read and reflect points.
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Factorising Polynomials and Identities
Just as 12 is 3 times 4, a polynomial can be a product of smaller polynomials. Here we learn the factor theorem, how to factorise quadratic and cubic polynomials, and the algebraic identities that help us calculate fast.
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Polynomials and Their Zeroes
A polynomial is an expression with powers of x, such as 3x² − 5x + 2. In this course we learn the words for its parts, how to find its value, which numbers make it zero, and what the remainder is when we divide it.
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