Sample Lessons and Worksheets

In this grade MINDsprinting's math curriculum covers:

• Comparing graphs
• Analytic geometry
• The circle
• Introduction to trigonometry

Plus any other topics your child needs to work on, as determined by our FREE Assessment Test. You can view a complete list of the topics covered in our curriculum by clicking here.

Below is a free sample worksheet from our 12th grade math curriculum. It is only one of many worksheets that are automatically assigned to students in this grade level based on their Assessment Test results and their progress through our curriculum. Each worksheet is designed to take between 10 and 20 minutes to complete. We recommend students do at least 3 worksheets per week, though you can complete as many as you want using the MINDsprinting system.

The lesson below is a HTML reproduction of our worksheet. All lessons are served in PDF format and are designed to be printed out and completed by hand.

Lesson M97-1 - Understanding Quadratic Equations - 1

The general form of a second order equation is ax2+ bx + c = 0.

We call it a second order equation because the highest exponent on x is 2. The order of an equation is determined by the highest exponent on a variable in the equation. We say a is not equal to 0, because if a = 0 the equation could be simplified to bx + c = 0, which is first order. However, b and c can equal zero.

We call x the variable, and we call a, b, and c coefficients. The coefficients are constant (they don't change).

Example 1: What are the coefficients a, b, and c in the trinomial 6x2- x - 3 = 0?

a = 6
b = -1
c = -3

Notice that c is equal to -3 and not 3. This is because the general form is ax2+ bx +c = 0, so if there is a negative sign in front of the coefficient it has to be accounted for. Also notice that when no number is written, 1 is assumed.

Quite often we must do some work on a second order equation to put it in the general form.

Example 2: Write the equation -x + 5x2- 6 = 20x - x2 in the general form.

-x + 5x2- 6 = 20x - x2
5x2+ x2- x - 20x - 6 = 0
6x2- 21x - 6 = 0
2x2- 7x - 2 = 0                         Divide both sides by the GCF of 3.

What are the values of a, b, and c in the following equations?

 1. x2- 3x + 4 = 0 2. 3x2- 4x + 5 = 0 3. - x2- 3x = 0 4. 5x2+ 2 = 0 5. 3x2+ x + 1 = 0 6. -6x2+ 10 = 0

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What is the order of the following equations?

 7. x2+ 3x - 4 = x 8. 3x5- 4x4- 3x3+ 2x2- 1 = 0 9. 5x7- 3 = 0 10. x2= 1 11. 5x4- 3x2= 0 12. (x + 1)x = 0 13. 3x4- x + 6x9- 2x2= 0 14. x2- 4x5= 2x2+ 6x3

Write the following equations in simplified general form.

 15. 5x2- 3x + 2 = 5 + 3x 16. 6x2- 12x + 4 = 14x2- 3x - 5 + 12x

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