Introduction to CBEST Math

If you have a fear of math or think you just can't do it, relax. The CBEST test can be passed with basic skills and logic. You need to realize that math is a part of your daily life, and most of the time you don't think about it. When you tank your car up, you mentally calculate how much gas you need and roughly how much it costs. You do it without thinking. You do it without getting an exact answer. You do it without a calculator. You do it without thinking it's even math. That's how you need to approach the CBEST test. Forget about doing complicated algebra. Forget about worrying how to do long division and fractions. My approach to math problems is radically different than how most people are taught. My approach is the way that "math people" do math. Get yourself thinking like a math person, and you will have the CBEST test licked. Consider the following math problem:

123 x 45 = ?

Answer choices:
a. 5021
b. 5250
c. 5535
d. 5620
e. 5528

While non-math people are busy wasting time calculating the answer, math people know the answer is c. Why? Because 123 ends in a 3, 45 ends in a 5, therefore 123 x 45 ends in a 5 because 3 x 5 = 15. There is only one answer that ends in a 5. Now for you people who would multiply it out, what happens if you made a simple arithmetic error and your answer wasn't there? Like most people, you would panic.

CBEST Math Tip #1: Look for ways of getting the answer without doing a long calculation.

CBEST Math Tip #2: When multiplying 2 numbers together, your answer will end in the number that appears on the end when multiplying the last 2 numbers.

Consider the following problem:

3,456 + 2,345 + 10,567 = ?

Can you pick the answers form the following choices:
a. 16,362
b. 16,368
c. 15,372
d. 16,439
e. 20,324

I hope you picked b rather quickly. The numbers on the end of each number add up : 6 + 5 + 7 = 18, so the answer ends in an 8. The only answer in the choices that ends in 8 is b.

CBEST Math Tip #3: When adding numbers together, the answer will end with the number that appears on the end when adding the end numbers together. Likewise, subtracting 2 numbers will end in the number on the end when you subtract the 2 end numbers. Example: 124 + 54 will end in 8, 178 - 25 will end in 3,etc. Don't worry about borrowing when looking for an end number. Example: 345 - 279. Think of it as 15 - 9.

We will continue with more ways of picking answers. It would be impossible to cite every way of doing things. Your goal is to have an arsenal of weapons to use. You also want to learn to think of ways on your own so that you never read a problem and say, "I can't do it."

Consider the following problem:

12,456 x 5 = ?

Answers:
a. 60,280
b. 70,580
c. 82,490
d. 66,380
e. 62,280

A little tougher. The answer will end in a zero because 6 x 5 = 30. But they all end in zeroes! Okay, we need another clue. You should be able to mentally calculate 12,000 x 5. Just 12 x 5 with 3 zeroes. It is 60,000. That is the lowest possible value. Our answer must be larger than 60,000. But they are all over 60,000. How about getting a maximum value? Do 13,000 x 5 (same as before) to get 65,000. Now we know the answer is between 60,000 and 65,000 AND ends in a zero. The only answer there is e. Again, what happens when you go through the trouble of multiplying something out, and your answer is not there?
Logic: 12,456 x 5 is between 12,000 x 5 and 13,000 x 5.

CBEST Math #4: Calculate low and high values for answer to get boundaries. Eliminate the ones that don't fit.

How about a 2-step problem. Consider the following problem:

(124 x 64) - 25 = ?

Answers:
a. 7911
b. 8021
c. 7903
d. 9011
e. 6911

Okay, you will have to multiply 124 x 64 out. No way around it. But here is one of the biggest tips around.

CBEST Math Tip #5: Do each arithmetic step twice. Do it in  a spot where you cannot look at your first answer. (It might influence you the second time.) Did you get the same answer? Good. Be confident you have the correct answer and move to the next step. Didn't get the same answer? Do it again!

Doing arithmetic is where you are going to make your mistake. This is the number one reason your answer is not there! Catch your mistakes before getting a final answer. If you do not check yourself after each step, you will most likely NOT be able to retrace your steps if you find an error at the end.

Now we move on to the second part of the problem. We now must subtract 25 from the answer from the first part, 7936. But now we can use what we have learned. Let's use logic to eliminate or even choose and answer.  Since we are subtracting, we know the answer will be less than 7936. This eliminates b and d. We also know that the answer will end in a 1 (6 - 5 = 1). This eliminates c. We now have a choice between a and e. But you should logically conclude that e is way to small. Our answer must be a.

CBEST Math Tip #6: Check the answers after each step to eliminate choices.

CBEST Math Tip #7: Do as little arithmetic as possible to avoid errors and actually wasting time.

How about division? Consider the following problem:

156 ÷ 6 = ?

Answers:
a. 35
b. 27
c. 16
d. 26
e. 12

Does long division panic you? Calm down. We can turn this problem into a multiplication problem by trying all the answers. This is also called working backwards. You should realize that 6 times the answer will equal 156. Just do 6 times every answer and see which one works. But, we are looking for a good shortcut. In order to get 156 when a number is multiplied by 6, it MUST end in a 6. Because 6 x 6 is 36, and that is the only possible way to get a 6 on the end. Let's look at each answer individually. Remember what you should now have learned. 35 x 6 ends in a 0, 27 x 6 ends in a 2, 16 times 6 ends in a 6, 26 x 6 ends in a 6, 12 x 6 ends in a 2. The only choices we have are c and d. If you can't tell which one is the answer, multiply them out. But you only need to try one of them. If it's correct, you have found the answer. If it's wrong, the OTHER one MUST be the answer.

CBEST Math Tip #8: Work backwards, trying all answers. Eliminate ones using techniques shown.

CBEST Math Tip #9: When getting a choice between 2 answers, you only need to try one. Either it will turn out correct, avoiding the need to try the second. Or, it will be wrong meaning the second one MUST be right.

CBEST Math Tip #10: Turn division problems into multiplication problems as shown above.