How do we determine whether or not an ordered pair is a solution to a given inequality? 

Suppose the inequality is 4x + 3y > 19 and the ordered pair is (2, 6)

Substitute 2 for x and 6 for y in the inequality.

4(2) + 3(6) > 19

8 + 18 > 19

26 > 19.

Since that is true, the ordered pair is a solution. If the statement was false, the ordered pair is not a solution.

If you have a graph of an inequality and want to know what portion of the graph is part of the solution, pick an ordered pair on either side of the line and substitute the value into the equation as done above. If the statement is true, that side of the line is shaded to represent the solution region. If if the statement is false, the other side of the line is shaded to represent the solution region.

Percent increase and decrease

Suppose the cost of a particular item last year was $320 and increased to $360 this year. What is the percent increase?

First, calculate the dollar amount of the increase, which is $40. From here we divide that number by the original amount of $320. Multiply that decimal result by 100 to convert to percent. So the increase is 12.5 %

Suppose a item depreciates in value by 20% every year.  The original value of the item is $1,200. What is the value of the item after two years?

We take 20% of $1,200 which is .20 times 1,200, which is 240. Subtract 240 from the initial 1,200 to get 960.  After the first year the value is $960.

Now take 20% of 960, which is 192. Subtract 192 from 960 to get 768. The value of the item after two years is $768.

Suppose two go-carts are driving around a circular track that is 360 feet in circumference. There is a camera in both cars that are 60 degrees apart. How are apart are the two cars?

The number of degrees around a circle is 360. So if the cameras are at a 60 degree angle from each other, that is 1/6 of the entire circle.

Since the circumference of the circle is 360 feet, we take 360 divided by 6 to get the distance between the cars. Therefore, the cars are 60 feet apart.

This method holds true no matter what the angle is between the cameras.

Here's a good sample SAT math problem.

Suppose a and b are real numbers and (a + b)^2 = 56 and a^2 + b^2 = 18. What is the value of  ab?

The key to the problem is knowing that when you expand (a + b)^2, you will have a^2 + b^2 and ab as part of the expansion, which makes the problem easy.

(a + b)^2 = a^2 + 2ab + b^2

Now substitute and solve for ab.

56 = 18  + 2

38 = 2ab

19 = ab

Suppose W,X,Y,Z are all digits with the following conditions:

X = W + Y + Z
W - 5 = Y
Z = W - 1

What is the 4-digit number XWYZ?

We can approach this by listing all the possible values starting with Y.
Y must be 0, 1, 2, 3, 4 since Y + 5 = W and the largest number that W or any of the numbers could be is 9
Therefore, we know that W has to be 5,6,7,8, or 9.

One we know that, it's easy to see that Z must be either 4,5,6,7, or 8 since it's 1 less than W.
X is the other letters added together. The only possible number X can be is 9, obtained when W = 5, Y =0 and Z = 4. Any other combination of those numbers will make X greater than 9.
The 4-digit number is 9504.

If 2^(abc) = 64, where a, b and c are positive integers, what is the value of a + b + c and what is 2^a = 2^b + 2^c?

The first thing we need to do is figure out what power we raise 2 to get 64.
2^2 = 4
2^3 = 8
2^4 = 16
2^5= 32
2^6 = 64

So we know abc = 6 and we know that a,b, and c are different positive integers. So a, b and c must be 1, 2 and 3 in any order since 1*2*3 = 6.

Therefore a + b + c = 6 as well and 2^a + 2^b + 2^c  = 2^1 + 2^2 + 2^3 = 2 + 4 + 8 = 14.

The problem is simply if one knows the rules for exponents and breaks the problem down into steps.

Here's some good math jokes, as nominated by teachers and Twitter.

Source:

http://news.tes.co.uk/b/news/2013/10/09/the-10-best-maths-jokes-as-nominated-by-teachers-and-twitter.aspx


@MaxineHowells2h
Talking sheepdog gets all the sheep in the pen for his farmer. He comes back and says ‘All 40 accounted for.’ Farmer says, ‘I’ve only got 36!’ Sheepdog replies, ‘I know, but I rounded them up.'

@AnnaMFortune
Two cats called '1,2,3' & 'un,deux,trois' had swim race across channel.
1,2,3 cat won because un, deux, trois cat sank!


Followed by seven brilliant runners-up:

@LocalSchoolsN22h
Hired an odd-job man to do 8 jobs for me. When I got back, he'd only done jobs 1,3,5, and 7

@TheRedshiftAcad3h
Have you heard about the mathematical plant? It has square roots

@ppelk1h
After careful investigation, it was found that aliens' heights were paranormally distributed

@sann06384h
I hit someone with a scientific calculator - I used the cosh button

@Mylosafe4h
What kind of tree could a maths teacher climb? = Geometry

@alexamcgregor4h
What do you get if you cross a maths teacher and a clock? Arithma-ticks!

@Maths_George
Last night I dreamed that I was weightless! I was like, 0mg