AFM Unit #1 Test Preparation DO ALL OF YOUR WORK ON A SEPARATE PIECE OF PAPER!
1) Express these statements in symbols: a) r is non-negative b) p is at least -6 c) d is at most 10.
2) Represent the given intervals on a number line: a) [ -9 , 7), b) (4, 6) c) (-∞, 5]
3) Use interval notation to denote the set of all real numbers x that satisfy these inequalities:
a) x ≥ 12 b) r<-22 c) -4<p<23/2
For questions 4-7, solve the inequality for x and express your answer in interval notation
4) 3x +18 > -6 5) -3 ≤ 7 - 2x < 10 6) 3x + 2(x - 4) ≥ -x +(x -5) 7)
For questions 8 & 9, find the slope and y-intercept of the line whose equation is:
8) -8x + 4y = 7 9) 3(y-5) + (x-9) = 4(x +8) -1
10) Find the slope of the line through the points (-1, -8) and (9, -3).
11) Find the equation of the line with that passes through the point (3, -6)
12) Find the equation of the line that passes through the two points (5, -6) and (-8, 0)
13) Determine if the line that passes through the points R and S is parallel, perpendicular or neither to the line that passes through the points P and Q.
R = (-3,7), S = (2, 3) AND P = (-3, 6), Q = (2, 1)
14) For this set of data, find the following information. Note, let x = 0 correspond to 1900
a: The scatter plot of points. b) Find the equation of the best fit line through these data points and write it down. c) Does the best fit line look like a good fit?
Time / Minimum Hourly Wage1903 / .03
1911 / .11
1921 / .25
1933 / .38
For problems 15 -16, solve the absolute value inequalities and indicate the solution using interval notation.
15) 2 |3x-3 | >22 16) -|x+2| +5 ≤ 4
For problems 17 – 22 factor the polynomial completely.
17) 2x2 – 36
18) x2 + 8xy - 33 y2
19) x2 – 12x – 45
20) 3x2 +13x +4
21) 64c3 – 125d3
22) x2y −11xy +30y
23) (x -5)2 −z2
24) Write the equation for the line of this graph:
24) Write the domain and range of these graphs in interval notation.
a) b)
D: ______D: ______
R: ______R: ______
25) Complete the table of comparative notation:
Set Notation Interval Notation # line (graph)
X > -2[-3,8)
26) Find an equation for the line through (-2,5) and perpendicular to the line through (3,-2) and (2,-3).