Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Advanced Investigations

### Converging Quadrilaterals

### A Rational Search

### Few and Far Between?

### The Best Square

### Chance of That

### A Different Differential Equation

### Trig-trig

### Investigating Twilgo

### Factors and Multiples Graphs

## You may also like

### Real(ly) Numbers

### Converging Product

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Fancy something very substantial? These challenging investigations will take time and you will need to pose your own questions in order to make your own mathematical discoveries.

Age 16 to 18

Challenge Level

Explore the properties of this iterative geometrical procedure

Age 16 to 18

Challenge Level

Investigate constructible images which contain rational areas.

Age 16 to 18

Challenge Level

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

Age 16 to 18

Challenge Level

How would you judge a competition to draw a freehand square?

Age 16 to 18

Challenge Level

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

Age 16 to 18

Challenge Level

Explore the properties of this different sort of differential equation.

Age 16 to 18

Challenge Level

Explore the properties of combinations of trig functions in this open investigation.

Age 16 to 18

Challenge Level

What can you create using 140 characters and our cool Twilgo environment?

Age 16 to 18

Challenge Level

Explore creating 'factors and multiples' graphs such that no lines joining the numbers cross

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?