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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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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