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Mathematics Learning Path

High School (11–12) Mathematics

Explore structured mathematics courses, solved problems, simulations and Python activities.

Choose a topic to see its subtopics.
Complex NumbersFreeCh 3 · 1/3

Complex Numbers and Their Algebra

StemPy LabStemPy Lab

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.

3Lessons10Problems2Python Labs1Question Set1Mock Test
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Complex NumbersQuadratic EquationsFreeCh 3 · 2/3

The Argand Plane and Quadratic Equations

StemPy LabStemPy Lab

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.

3Lessons12Problems2Python Labs1Question Set1Mock Test
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Compound and Multiple AnglesTrigonometric IdentitiesFreeCh 2 · 3/4

Sum and Difference Formulae

StemPy LabStemPy Lab

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.

3Lessons11Problems2Python Labs1Question Set1Mock Test
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Trigonometric Functions and GraphsTrigonometric IdentitiesFreeCh 2 · 2/4

Trigonometric Functions and Their Graphs

StemPy LabStemPy Lab

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.

3Lessons11Problems2Python Labs1Question Set1Mock Test
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Angles and Radian MeasureFreeCh 2 · 1/4

Angles and Radian Measure

StemPy LabStemPy Lab

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.

3Lessons11Problems2Python Labs1Question Set1Mock Test
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Composite and Inverse FunctionsFunctions as Models of DataFreeCh 1 · 3/4

Combining and Reversing Functions

StemPy LabStemPy Lab

Convert metres to centimetres, and then centimetres to millimetres: two functions, one after the other. Can the two steps be one? Can we go back? In this course we add, multiply and compose functions, we find when a function can be reversed, and we use functions to model real data with Python.

3Lessons14Problems3Python Labs1Question Set1Mock Test
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Graphs of FunctionsFreeCh 1 · 2/4

Graphs and Special Functions

StemPy LabStemPy Lab

A picture of a function tells you in a moment what a formula hides. In this course we read and draw the graphs of the common functions, we meet the modulus and the greatest integer function, and we learn how to move, stretch and flip a graph. We also learn to see even, odd, increasing and decreasing functions in a picture.

4Lessons16Problems3Python Labs1Question Set1Mock Test
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Relations and FunctionsSets and IntervalsFreeCh 1 · 1/4

Sets, Relations and Functions

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How many students in a class like neither tea nor coffee, when you know how many like each, and how many like both? Sets answer this kind of question. In this course we learn the language of sets, we pair the elements of two sets in relations, and we find the special relation that we call a function, with its domain and its range.

3Lessons11Problems2Python Labs1Question Set1Mock Test
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Learning Journey

1
Complex Numbers and Their Algebra
Explore →
2
The Argand Plane and Quadratic Equations
Explore →
3
Sum and Difference Formulae
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4
Trigonometric Functions and Their Graphs
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5
Angles and Radian Measure
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6
Combining and Reversing Functions
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7
Graphs and Special Functions
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8
Sets, Relations and Functions
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Extra courses with a plan

These are part of our upcoming paid plans.

Complex Numbers: Deep Dive
StandardFirst lesson freeExtra course

Beyond the textbook: the polar form, multiplication as a rotation, the cube roots of unity, and loci on the Argand plane, the parts JEE asks about most, with a full timed paper.

3Lessons11Problems2Python Labs1Question Set1Mock Test
Opens with a Standard planSee what's inside →
Trigonometric Functions: Exam Practice Pack
StandardFirst lesson free

What the exams add to this chapter: solving trigonometric equations, the greatest and least values of an expression, and identities in a triangle, each with worked examples, and a full timed paper.

3Lessons11Problems2Python Labs1Question Set
Functions: Functional Equations, Counting and JEE Advanced Practice
StandardFirst lesson free

Can you find a function when you know only how it behaves? If f(x + y) = f(x) + f(y) for all x and y, what can f be? In this course we read three ideas that the main chapter only touches: equations whose unknown is a function, the number of solutions of an equation read from a graph (with the fixed points of a function), and the counting of onto functions. Then we solve harder problems and take a JEE Advanced style test.

3Lessons12Problems2Python Labs
1Mock Test
Opens with a Standard planSee what's inside →
1
Question Set
1Mock Test
Opens with a Standard planSee what's inside →