Help Solving Hard Math Problems: Strategies and Sample Exercises

How to Solve Hard Math Problems

Take Careful Notes

When you encounter a difficult math problem in your homework, it can be helpful to refer back to examples from your class notes. Even if the examples in your notes aren't exactly like the homework problem, they may help you figure out what to do. As a result, make sure you actively take notes in class, even if you don't think you'll need them later on. If you still can't figure out the problem, make sure you ask about it in math class the next day.

Learn Definitions

One way to take good notes is to clearly write out definitions for any math terms you may need later. You can copy math vocabulary from the blackboard, your textbook or even from the Internet (as long as it's a reputable site). Keep your handwriting neat and try using a different color pen for the words and the definitions. For instance, you might write the terms in red and the definitions in black. This visual trick can make it easier to read through your notes later.

Find Easy Parts

A lot of hard math problems can be broken down into steps. Sometimes these steps will include very basic math, like addition or single-digit multiplication. Algebraic expressions can often be shortened by combining like terms. They can then be solved by performing several simple math problems with addition, subtraction and multiplication. Ask your teacher for help breaking hard math problems down into more manageable parts.

Solving for Variables

One of the first things you'll need to master in order to succeed in upper level math classes is how to solve for a variable. One example of a problem you might see in pre-algebra is 4 + 3x = 2. In this problem, the letter x is the variable. You can solve this problem by isolating the variable, like this:

4 + 3x = 2

First, subtract four from both sides.

4 - 4+ 3x = 2 - 4

3x = -2

Now, divide both sides by three to isolate the variable.

3x ÷ 3 = -2 ÷ 3

x = -2/3

Practice Problems

Here are a few practice problems. Remember that what you do to one side of the equation, you must do to the other side.

1. 5 - x = 2
2. 12 + x = 97
3. x - 14 = 26
4. 7 + x = 12
5. 96 - x = 87

Answers:

1. x = 3
2. x = 85
3. x = 40
4. x = 5
5. x = 9