Mathematics, 14–17 years — 20 topics · MyLeoNes™ Kuks
20 mathematics topics written for 14–17 years — not a older text simplified. In teaching order, each a deck of five cards: the idea, why it exists, a worked example, the common trap and where you meet it.
Mathematics · 14–17 years
Arithmetic sequences
How a steady change creates a sequence, and how to find any term without listing all the earlier ones.
Complex numbers
Numbers that extend the number line so equations such as x² = −1 can have a meaningful solution.
Conditional probability
How new information changes the chance of an event.
Counting combinations
How to count possible selections without writing every choice down.
Exponential growth
How repeated percentage change creates curves that rise faster and faster.
Factoring polynomials
Factoring rewrites a complicated polynomial as a product of simpler pieces. That hidden structure can make equations, graphs and calculations much easier to understand.
Geometric sequences
A sequence in which each term is made by multiplying the previous one by the same number.
Linear functions and slope
How a constant rate of change becomes a line on a graph, and how the line helps us predict values.
Logarithms
The reverse operation to powers: finding which exponent produces a given number.
Matrices as transformations
A matrix is a rectangular arrangement of numbers that can act on data, points or shapes in a controlled way.
Quadratic equations and roots
How a squared unknown creates a curved relationship, and how its roots mark where that curve reaches zero.
Right-triangle trigonometry
How an angle links the sides of a right triangle, allowing us to calculate distances and heights we cannot measure directly.
Solving inequalities
Inequalities describe a range of possible answers, not just one number. Learn how to solve them and show the result clearly on a number line.
Standard deviation
The mean gives a centre, but not how tightly data gather around it. Standard deviation measures the typical distance from the mean, helping you compare the spread of different data sets.
Systems of linear equations
How two conditions can meet at one pair of values, and how graphs and algebra find that meeting point.
The cosine rule
How to find a side in a triangle when the triangle is not right-angled.
The definite integral
A way to add up infinitely many tiny contributions, often finding the area under a curve or total accumulated change.
The derivative
A way to measure how fast a quantity changes at one precise moment.
The Pythagorean theorem
A way to connect the three side lengths of a right-angled triangle.
Vectors
A vector describes both a size and a direction. It gives a precise way to combine movements, forces and changes without losing the difference between going north and going south.
In this section
Keep exploring
Other languages
Loading MyLeoNes™…