Algebra Problems (Quadratics)

Videos, games, activities and worksheets that are suitable for GCSE Maths to help students set up and solve quadratic equations.

Word Problems - Solving Quadratic Equations by Factoring
Examples:

1. The length of a rectangle is 6 cm less than triple the width. The area of the rectangle is 72 cm². Find the dimensions of the rectangle.
   
2. The length of a rectangular yard is 4 ft more than twice the width. Find the dimensions of the yard is the area is 30 ft².
3. A rectangle has dimensions of 6 in. by 20 in. If a uniform border is added on all sides, then the new rectangle has double the area of the original rectangle. Find the new dimensions.

GCSE Maths - Setting up and Solving Equations (Quadratic)
Writing Higher Algebra IGCSE
Examples:

1. The areas of two triangles on the right are equal.
   a) Write down an equation in x and simplify y.
   b) Solve this equation and calculate the area of one of the triangles.
2. Bill enters a 30 km race. He runs the first 20 km at a speed of x km per hour and the last 10 km at (x - 5) kph. His total time for the race was 4 hours.
   a) Write down an equation in terms of x and solve it.
   b) What are his speeds for the two parts of the run?
3. A piece of wire is cut into 2 parts. The first part is bent into the shape of a square. The second part is bent into the shape of a rectangle with one side 4 cm long and the other side twice the length of the square’s side. Let x represent one side of the square.
   a) Write down two expressions in x for the areas of the two shapes.
   b) If the sum of the two areas is 105 cm², show that x² + 8x - 105 = 0.
   c) Calculate the length of the original wire.
4. A small rectangular lawn is twice as long as it is wide. It has a path around it which is 2 m wide. The area of the path is twice the area of the lawn.
   a) If the small side of the lawn is m meters, write down the dimensions of the outside edge of the path.
   b) By writing down the area of the lawn in terms of x and using the answer to part a), form an equation in x.
   c) Simplify this equation so that it can be written as 4(x² - 3x - 4) = 0 and solve it.
   d) Write down the dimensions of the lawn.
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Quadratic equations: setting up and solving areas of triangles
Example:
The area are the same. Find x.

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