List of public pages created with Protopage

# Home

## Plain sticky notes

### Sticky note

Simultaneous equations Simultaneous equations are two equations with two unknowns. They are called simultaneous because they must both be solved at the same time. The first step is to try to eliminate one of the unknowns. Example Solve these simultaneous equations and find the values of x and y. Equation 1: 2x + y = 7 Equation 2: 3x - y = 8 Add the two equations to eliminate the ys: 2x + y = 7 3x - y = 8 ------------ 5x = 15 x = 3 Now you can put x = 3 in either of the equations. Substitute x = 3 into the equation 2x + y = 7: 6 + y = 7 y = 1 So the answers are x = 3 and y = 1 Solve the simultaneous equations: Equation 1: y - 2x = 1 Equation 2: 2y - 3x = 5 Rearranging Equation 1, we get y = 1 + 2x We can replace the 'y' in equation 2 by substituting it with 1 + 2x Equation 2 becomes: 2(1 + 2x) - 3x = 5 2 + 4x - 3x = 5 2 + x = 5 x = 3 Substituting x = 3 into Equation 1 gives us y - 6 = 1, so y = 7.

### Sticky note

How to do Pythagoras Pythagoras' Theorem relates the lengths of the sides in a right-angled triangle. A right-angled triangle has one angle of 90°. The side opposite the right angle is always the longest side, and is called the hypotenuse. For example you could have a right angle triangle with sidesof 3cm, 4cm and 5cm. The hypotenuse is the 5cm side because it is opposite the right-angle and it is the longest side. You draw squares on each of the sides of the triangle. We are going to examine the areas of each of the squares. Shorter sides The square on the 3cm side has an area of 3cm × 3cm = 9cm². The square on the 4cm side has an area of 4cm × 4cm = 16cm². Hypotenuse The square on the 5cm side has an area of 5cm × 5cm = 25cm². How they are related If you add together the areas of the squares on the two shorter sides, you get 25cm². This is the same as the area of the square on the hypotenuse.

## Rich sticky notes

### Useful maths websites

Visit these maths websites (copy and paste into web adress) :
www.numberloving.com
www.emaths.co.uk
www.matheminutes.blogspot.com
www.whatsmyanlge.com
www.everythingmath.co.uk