Quadratic Equations Worksheets - Practice

Quadratic Equations gcse maths worksheets for year 9, year 10 and year 11. Each quadratic equations worksheet is targeted for gcse maths at higher level. Quadratic equations worksheet 1 is more straight-forward, quadratic equations worksheet 2 asks students to solve equations by factorising. Quadratic equations worksheet 3 asks students to solve equations by quadratic formula. Quadratic equations worksheet 5 asks students to solve equations involving the difference of two squares. Quadratic equations worksheet 6 is a more difficult worksheet involving completing the square, aimed at year 11 working at grade 9.

Solving Quadratic Equations

Quadratic equations are solved using four main methods at GCSE: factorising worksheets, completing the square worksheets, quadratic formula worksheets and simultaneous equations worksheets. When Quadratic Equations are mapped on to graphs they form "U" shaped curves called parabolas. The image below shows x² + 10x - 13.  This quadratic equation can be solved using the quadratic formula.

The Quadratic Equations 3

The Quadratic Formula

The quadratic formula is given below. The quadratic formula when ax² + bx + c is [- b ± √(b² - 4ac)]/ 2a. a is the first coefficient before x², b is the second coefficient before x and c is a contact where x has highest power of zero. b and c might take a value of zero.

The Quadratic Formula

What Are Quadratic Equations?

Quadratic Equations take the form ax² + bx + c. The highest power of x is 2, or x². Quadratic Equations is a GCSE Higher topic. We usually learn how to solve quadratic equations after we know how to simplify expressions, and solve linear equations. Once students know how to solve quadratic equations students learn about Quadratic Graphs. When we solve quadratic equations we usually obtain two solutions. However, a quadratic equation can have only one (real) solution or no (real) solutions.

Solve x² + 9x + 18 = 0

Using the quadratic formula to solve x² + 9x + 18 = 0. a takes a value of 1, b takes the value + 9 and c takes the value + 18. In the case of x² - 9x - 18 = 0, b and c would be - 9 and - 18 respectively. The final answer is given below.

The Quadratic Equations 2

Quadratic Equation 2

The quadratic equation below is 3x² + 12x - 3. When 3x² + 12x - 3 = 0, solve it using the quadratic formula. 
The Quadratic Equations 4

Quadratic Equations Worksheets – New & Engaging

For Factorising Quadratics Cazoomy Worksheets try: Factorising Quadratics Worksheets. For Quadratic Graphs Cazoomy Worksheets try: Quadratic Graphs Worksheets. For Completing The Square Cazoomy Worksheets try: Completing The Square Worksheets.