Search by Topic

Resources tagged with Quadratic equations similar to Always Two:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 14 results

Broad Topics > Algebra > Quadratic equations

problem icon

Always Two

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

problem icon

Two Cubes

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

problem icon

Pareq Calc

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

problem icon

How Old Am I?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem icon

Interactive Number Patterns

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Xtra

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

problem icon

Darts and Kites

Stage: 4 Challenge Level: Challenge Level:1

A rhombus PQRS has an angle of 72 degrees. OQ = OR = OS = 1 unit. Find all the angles, show that POR is a straight line and that the side of the rhombus is equal to the Golden Ratio.

problem icon

Pentakite

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

problem icon

Golden Thoughts

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

problem icon

Partly Circles

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Pent

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

problem icon

Power Quady

Stage: 4 Challenge Level: Challenge Level:1

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

problem icon

Square Mean

Stage: 4 Challenge Level: Challenge Level:1

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

problem icon

Proof Sorter - Quadratic Equation

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.