Direct Proportion
When comparing two ratios and one unit increases in tandem with another unit, then the ratios are in direct proportion.
As one value increases so does the other.
Inverse Proportion
Two quantities are inversely proportional to each other if when one increases the other decreases.
For example, increasing the number of designers assigned to a single program would decrease the time it takes to finish the program.
Cross Multiply
Multiply the numeration of the first fraction by the denominator of the second fraction, and vice versa.If the cross-products are equal, te fractions are equal.
How do you write the number 30 as a product of prime numbers?
By dividing into whole numbers such as 6 and 5 then factoring those numbers etc.
30 = 5 x 3 x 2
Prime Number
A prime number has exactly two whole number factors - one and itself.
Factor
A factor is a number that divides into another number without incurring any remainder.
How can you use multiplication to check the result of a division problem?
- ) Multiply the quotient by the divider.
2. ) Add the remainder to the product of item 1 above.
When dividing one can find the remainder by…
finding the highest product of the divisor that does not exceed the dividend.
To find the remainder in a division problem one…
- ) Find the highest product of the divisor with some number that is not larger than the dividend.
- ) Subtract the result of item 1 above from the dividend. (This is the remainder)
FOIL
First, Outer, Inner, Last
- FOIL is method for multiplying two binomials. Multiply terms in parentheses in the following order.
Order of Operations
PEMDAS
- ) Parentheses: do calculations within parentheses
- ) Exponents: evaluate squares, square roots and other exponents or radicals.
- ) Multiplication & Division from L to R
- ) Addition & Subtraction from L to R
- ) Zero Factor Property
2. ) Zero Product Property
- ) A zero factor always gives a zero product. (a)0=0; 0(a)=0
- ) The product of two real numbers may be 0 only if one factor is 0.
- If ab = 0, then a = 0, and/or b = 0
- ) Zero Divisor Property
2. ) Zero Dividend Property
1.) Dividing by zero is not defined. a/o and a
x - Axis
The horizontal line on a coordinate plane.
Y - Axis
the vertical line on a coordinate plane.
Origin (Graph)
The point of intersection of the x - axis and y - axis on a coordinate plane. The coordinates of the origin are (0,0).
Quadrant (Graph)
The x - axis and y - axis divide the coordinate plane into four regions called quadrants.
Percent Decrease
(old - new) / (old) x 100 = % decrease
“new” and “old” refer to the final and original amounts respectively.
Percent Increase
(new - old) / (old) x 100 = % increase
“new” and “old” refer to the final and original amounts respectively.
Complete Factoring
- Complete factoring of a polynomial means to find the prime factors.
1. ) Find the greatest common factor if it exists. Examine each factor.
2. ) If one of the factors is a binomial and the difference of two squares, factor it.
3. ) If one of the factors is a trinomial, factor.
4. ) The answer is the product of all of the factors, which must be a prime factor.
What is the correct procedure for simplifying an expression containing powers or roots?
- ) Simplify any expressions contained within parentheses or other similar symbols.
- ) Simplify any powers or roots.
- ) Do all multiplications and divisions, starting from left to right.
- ) Do all additions and subtractions, starting from left to right.
Quadratic Equation
ax2 + bx + c = 0
Quadratic Formula
- Used to solve any quadratic equation by substitution of a, b, and c from the quadratic form ax^2 + bx + c = 0
x = (-b ± (√b^2 - 4ac)) / (2a)
Theorem of Pythagoras
Pythagorean Theorem: “In a right triangle the square of the length of the hypotenuse (the longest side, opposite of the right angle) is equal to the sum of the squares of the lengths of the other sides.”
the formula a^2 + b^2 = c^2 is used; c = length of the hypotenuse
