Domain Two- Algebra And Functions Review

Question 1

Square: perimeter, volume

Answer 1

Perimeter: P= 4a
Volume: A= a^2

Question 2

Rectangle: perimeter, volume

Answer 2

Perimeter: 2b + 2h = P OR P = 2(b+h)
Volume: A = bh

Question 3

Parallelogram: perimeter, volume

Answer 3

P= 2a + 2b OR P= 2(a + b)

A= bh

Question 4

Triangle: perimeter, volume

Answer 4

P = a + b + c

A= bh/2

Question 5

Rhombus: perimeter, volume

Answer 5

P = 4a

A= ah

Question 6

Trapezoid: perimeter, volume

Answer 6

P= b1 + b2 + x + y

A= h(b1 + b2)/2

Question 7

Circle: perimeter, volume

Answer 7

Circumference: C= pi x diameter OR C= 2 x pi x radius

A= pi x radius^2

Question 8

Cube: surface area, volume

Answer 8

SA= 6a^2

V= a^3

Question 9

Rectangular Prism: perimeter, volume

Answer 9

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

Question 10

Prisms in general: perimeter, volume

Answer 10

SA= (perimeter of the base)x height + 2(area of the base)

V= (area of the base) x height

Question 11

Cylinder: perimeter, volume

Answer 11

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

Question 12

Sphere: perimeter, volume

Answer 12

SA= 4 x pi x radius^2

V= 4/3 x pi x radius^3

Question 13

Pythagorean Theorem

Answer 13

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

Question 14

Equation

Answer 14

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

Question 15

Proportions

Answer 15

Two expressions written in fraction form are equal to one another

** can quickly be solved using cross multiplication

Question 16

Inequalities

Answer 16

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

Question 17

Monomial

Answer 17

Consists of only term

Example: 9x, 4a^2, 3mpxz^2

Question 18

Polynomial

Answer 18

Two or more terms separated with either addition or subtraction

Example x + y

Question 19

Adding and Subtracting Monomials

Answer 19

**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

Question 20

Adding and Subtracting Polynomials

Answer 20

Add or subtract the like terms in the polynomials together

Question 21

Multiplying Monomials

Answer 21

When an expression has a positive integer exponent, it indicates repeated multiplication

(X^a)(x^b)= x^(a+b) (x^a)^b= x^ab

Question 22

Multiplying Monomials with Polynomials and Polynomials with Polynomials

Answer 22

Remember to use the distributive property

Question 23

Factoring

Answer 23

Factor= to find two or more quantities whose product equals the original quantity

Question 24

Factoring out a common factor

Answer 24

1. 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)

Question 25

Factoring the Difference between Two Squares

Answer 25

1. Find the square root of the first term and the square root of the second term 2. Express your answer as the product of the sum of the quantities from step 1 times the difference of those quantities

Question 26

Factoring Polynomials that have three terms: Ax^2 + Bx + C

Answer 26

1. 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. 2. 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: 1. Find two numbers whose product is the last term and whose difference is the coefficient (number in front) of the middle term 2. 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: 1. Find two numbers whose product is the last term and whose sum is the coefficient of the middle term 2. Give both factors the sign of the middle term

Question 27

Solving Quadratic Equations

Answer 27

An equation that could be written as Ax^2 + Bx + C = 0 To solve: 1. Put all the terms on one side of the equal sign, leaving zero on the other side 2. Factor 3. Set each factor equal to zero 4. Solve each of these equations 5. Check by inserting your answer in the original equation

Question 28

Coordinate Graph

Answer 28

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

Question 29

Linear equation

Answer 29

Y = mx + b **parallel lines have the same slope, perpendicular lines have opposite reciprocal slopes