Module 1FA Review (Version 8)

  1. Define Irrational number and rational number, give an example of each.
  1. Give an example of each of these properties:
  2. Distributive Property
  3. Associative Property of Addition
  4. Inverse Property of Addition
  5. Commutative Property of Addition
  1. Simplify:
  2. -5(-7+3*6 – 4)2
  3. 5(6 – 42*3 + 7)
  1. Write an expression for “twice the sum of two consecutive odd integers and two consecutive even integers” where (x+2) represents the first odd integer and (y+4) represents the first even integer.
  1. Where is the vertex of y = |5x-10| - 7
  1. Solve (x2-z)/y2 = 1/z for y
  1. Write the variation equations for the following:
  2. Y varies jointly with m and n where the constant of variation is 7.
  3. Y varies inversely with 15z where “k” is the constant of variation.
  1. Which domain number causes this relation NOT to be a function?

{(5,3),(-5,3),(7,-2),(1,1),(-1,-1),(7,-3),(3,-5)}

  1. Given g(x) = 3x2-5 and f(x) = x-2, find
  2. f(g(x))
  3. (f o g)(-1)
  4. g(f(x))
  5. (g o f)(2)
  1. Given f(x) = -7(x + 3), find f-1(x)
  1. Change y = -4(2x-3) into Standard Form
  1. For m = kg/n, k is a constant. Which two letters are in:
  2. DIRECT variation?
  3. Inverse variation?
  1. Be able to write the equation of any line in slope intercept form given the graph of the line.
  1. Be able to identify the slope and y-intercept of a line given the graph of the line.
  1. What is the slope of the line perpendicular to
  2. y = -(2/3)x + 7 ?
  3. y= 0.5x – 3
  1. Are the following lines horizontal, vertical or neither?
  2. y = 7
  3. x = -3
  4. y = 2x
  5. x = -5y
  6. y = x
  7. x = 2
  1. State the slope and explain WHY the slope is what it is for:
  2. Vertical line (what is the slope and why?)
  3. Horizontal line (what is the slope and why?)
  1. Solve the following:
  2. Five times the sum of two consecutive integers is 45. Find the integers.
  3. Three times the sum of two consecutive even integers is 72. Find the integers.

19. Give an equation for a horizontal line.

20. What is the equation of the x axis?

21. Solve the equation showing all steps. -5x – 12 = 2x + 10

22. Solve the equation showing all steps. 4 – (x+3) = x – 1

23. Describe the graph of the solution for 2x3x-9.

24. Find the slope and y intercept for the equation. 8x-12=4y+8

25. What is the slope of a line perpendicular to the line y=4x+1

26. Write the equation of the line that goes through the points (4,1) and (3,6). Show work.

Answers:

  1. There are numbers that cannot be expressed as a fraction, and these numbers are called irrational because they are not rational. Rational numbers are all numbers of the form , where a and b are integers (but b cannot be zero). Irrational numbers are non-terminating and non-repeating. Rational numbers are always terminating or repeating.

Irrational numbers include: sqrt(2), pi, 1.121121112…, etc

Rational numbers include: ½, 5, -sqrt(4), 0.33333…, etc.

  1. Properties:
  2. Distributive: 2(x + 3) = 2(x) + 2(3)
  3. Associative Prop of Addition: (2+3)+4 = 2 + (3+4)
  4. Inverse Property of Addition: -3 + 3 = 0
  5. Commutative Prop of Addition: 5 + 6 = 6 + 5
  1. Simplify using PEMDAS:
  2. -245
  3. -175

  1. 2(x +2 + x+4 + y + 4 + y + 6)
  1. (2,-7)
  1. Y = ±sqrt[z(x2-z)]
  1. Variation equations:
  2. Y = 7mn
  3. Y = (k/15z)
  1. 7
  1. Compound Functions:
  2. 3x2-7
  3. -4
  4. 3x2-4x-1
  5. 3
  1. – (x+21)/7
  1. 8x + y = 12
  1. a) m and g b) m and n
  1. Review section 1.16
  2. Review section 1.16
  1. a) 3/2 b) -2
  1. Horizontal, Vertical, or Niether?
  2. Horizontal
  3. Vertical
  4. Niether
  5. Niether
  6. Niether
  7. Vertical
  1. To answer this question, first draw the lines on a graph select two points on each. Use the points and the slope formula to find the slopes of each type of line. Keep in mind that a fraction with a zero in the denominator is called “undefined”. The slope formula is: slope = (y2-y1)/(x2-x1). Be able to use a sentence to explain why the slopes are what they are. One is “zero” and one is “undefined”. You can do it!
  2. a) 4 and 5 b) 11 and 13
  1. y = 6
  2. y = 0
  3. x = 1
  4. open dot at x = 9 shaded to the left
  5. m = 2 and b = -5