Domain Two- Algebra And Functions Review Flashcards
Square: perimeter, volume
Perimeter: P= 4a
Volume: A= a^2
Rectangle: perimeter, volume
Perimeter: 2b + 2h = P OR P = 2(b+h)
Volume: A = bh
Parallelogram: perimeter, volume
P= 2a + 2b OR P= 2(a + b)
A= bh
Triangle: perimeter, volume
P = a + b + c
A= bh/2
Rhombus: perimeter, volume
P = 4a
A= ah
Trapezoid: perimeter, volume
P= b1 + b2 + x + y
A= h(b1 + b2)/2
Circle: perimeter, volume
Circumference: C= pi x diameter OR C= 2 x pi x radius
A= pi x radius^2
Cube: surface area, volume
SA= 6a^2
V= a^3
Rectangular Prism: perimeter, volume
SA= 2(lengthxwidth + lengthxheight + widthxheight) OR SA= (perimeter of the base)height + 2(area of the base)
V= length x width x height OR V= (Area of the base) x height
Prisms in general: perimeter, volume
SA= (perimeter of the base)x height + 2(area of the base)
V= (area of the base) x height
Cylinder: perimeter, volume
SA= (circumference of the base)x height + 2(area of the base) OR SA= 2 x pi x radius x height + 2 x pi x radius^2 OR SA= 2 x pi x radius( height + radius)
V= (area of the base) x height OR V= pi x radius^2 x height
Sphere: perimeter, volume
SA= 4 x pi x radius^2
V= 4/3 x pi x radius^3
Pythagorean Theorem
a^2 + b^2 = c^2
The sum of the squares of the legs of a right triangle are equal to the square of the hypotenuse
Equation
The relationship between numbers and/or symbols that says that two expressions have the same value
**When two or more letters, or a number and a letter, are written next to each other, it is understood that these values are being multiplied together
Proportions
Two expressions written in fraction form are equal to one another
** can quickly be solved using cross multiplication
Inequalities
Statement which the relationships are not equal
Greater than, less than, greater than or equal to, less than or equal to
**remember if you multiply or divide both sides by a negative number, you MUST reverse the direction of the inequality symbol
Monomial
Consists of only term
Example: 9x, 4a^2, 3mpxz^2
Polynomial
Two or more terms separated with either addition or subtraction
Example x + y
Adding and Subtracting Monomials
**must be like terms (exactly the same variables with exactly the same exponents on them)
5x & 7x are like terms, 5x & 7x^2 are not
Adding and Subtracting Polynomials
Add or subtract the like terms in the polynomials together
Multiplying Monomials
When an expression has a positive integer exponent, it indicates repeated multiplication
(X^a)(x^b)= x^(a+b) (x^a)^b= x^ab
Multiplying Monomials with Polynomials and Polynomials with Polynomials
Remember to use the distributive property
Factoring
Factor= to find two or more quantities whose product equals the original quantity
Factoring out a common factor
- Find the largest common monomial factor of each term
2. Divide the original polynomial by this factor to obtain the second factor (second factor will be a polynomial)
Factoring the Difference between Two Squares
- Find the square root of the first term and the square root of the second term
- Express your answer as the product of the sum of the quantities from step 1 times the difference of those quantities
Factoring Polynomials that have three terms: Ax^2 + Bx + C
- Check to see if you can monomial factor (factor out common terms). Then if A=1 (that is, the first term is simply x^2), use double parentheses and factor the first term. Place these factors in the left sides of the parentheses.
- Factor the last term, and place the factors in the right sides of the parentheses
To decide on the signs of the numbers do the following:
If the sign of the last term is negative:
- Find two numbers whose product is the last term and whose difference is the coefficient (number in front) of the middle term
- Give the larger of these two numbers the sign of the middle term, and give the opposite sign to the other factor
If the sign of the last term is positive:
- Find two numbers whose product is the last term and whose sum is the coefficient of the middle term
- Give both factors the sign of the middle term
Solving Quadratic Equations
An equation that could be written as Ax^2 + Bx + C = 0
To solve:
- Put all the terms on one side of the equal sign, leaving zero on the other side
- Factor
- Set each factor equal to zero
- Solve each of these equations
- Check by inserting your answer in the original equation
Coordinate Graph
Formed by two perpendicular number lines (coordinate axes)
Horizontal line = x-axis or the abscissa
Vertical line= y-axis or the ordinate
Point where the two lines intersect= origin (0,0)
Coordinates: ordered pair of numbers
Quadrant One: x always positive, y always positive
Quadrant Two: x always negative, y always positive
Quadrant Three: x always negative, y always negative
Quadrant Four: x always positive, y always negative
Linear equation
Y = mx + b
**parallel lines have the same slope, perpendicular lines have opposite reciprocal slopes
