### There are 14 results

Broad Topics >

Algebra > Quadratic equations

##### Age 14 to 18 Challenge Level:

ABCDE is a regular pentagon of side length one unit. BC produced
meets ED produced at F. Show that triangle CDF is congruent to
triangle EDB. Find the length of BE.

##### Age 14 to 16 Challenge Level:

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
golden ratio.

##### Age 14 to 18 Challenge Level:

The diagram shows a regular pentagon with sides of unit length.
Find all the angles in the diagram. Prove that the quadrilateral
shown in red is a rhombus.

##### Age 14 to 18 Challenge Level:

Find the sides of an equilateral triangle ABC where a trapezium
BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are
2 possible interpretations.

##### Age 14 to 16 Challenge Level:

What is the same and what is different about these circle
questions? What connections can you make?

##### Age 14 to 16 Challenge Level:

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .

##### Age 14 to 16 Challenge Level:

How good are you at finding the formula for a number pattern ?

##### Age 14 to 16 Challenge Level:

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

##### Age 14 to 16 Short Challenge Level:

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?

##### Age 14 to 16 Challenge Level:

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to. . . .

##### Age 14 to 16 Challenge Level:

Is the mean of the squares of two numbers greater than, or less
than, the square of their means?

##### Age 14 to 18 Challenge Level:

Find all the triples of numbers a, b, c such that each one of them
plus the product of the other two is always 2.

##### Age 14 to 16 Challenge Level:

Explore the geometry of these dart and kite shapes!

##### Age 14 to 18 Challenge Level:

This is an interactivity in which you have to sort the steps in the
completion of the square into the correct order to prove the
formula for the solutions of quadratic equations.