Show:
Equations and Inequalities
Sets/Scientific Notation
Functions/Slope
Linear Equations
Systems of Equations
100
What is -(x+3)=4 solved for x?
x = -1
100
Find the union and intersection of the pair of sets. M = {1, 6, 8}; N = {3, 6, 8, 14, 15}
M ∪ N = {1, 3, 6, 8, 14, 15};M ∩ N = {6, 8}
100
Which of the following relations is a function? a. {(1, 0),(1, -1),(2, 0),(2, -1),(3, 0),(3, -1)} b. {(1, 3),(-1, 5),(2, 7),(-2, 7),(3, 5),(-3, 3)} c. {(-2, -1),(1, -2),(0, 0),(-1, -1),(-2, -2)} d. {(0, 3),(1, 3),(-3, 3),(1, 2),(-3, 2),(1, 3)}
b. {(1, 3),(-1, 5),(2, 7),(-2, 7),(3, 5),(-3, 3)} There are no repeating Domains
100
Find the slope of the line that contains the points (1,− 1) and (−2,8)
m = -3
100
Write an equation for the line that has a y-intercept of 2 and is perpendicular to the line 3x+y = 6.
y=1/3x+2
200
What is the solution to 2a+3= 1/2(6+4a)
Infinitely many solutions since both sides of the equation balance out: 2a+3=3+2a Solving for a will leave 0=0
200
Find the intersection of the pair of sets. M = {1,2,3,4,5,6}; N = {2,3,4,5,6,7}
M ∩ N = {2,3,4,5,6}
200
Give the domain and range of the relation. x y 3 7 6 13 0 0 –7 –13
b. D: {–7, 0, 3, 6}; R: {–13, 0, 7, 13}
200
There were T people waiting for buses at the station. When the first bus arrived, n people boarded it. The remaining p people waited for buses to other places. Use the equation T − n = p, to find n, the number of people who boarded the first bus.
n=T-p
200
What is the equation of the line that has x-intercept = −2 and y-intercept = −4? a. y = −2x−4 c. y = −2x+4 b. y = 2x−4 d. y = −1/2 x−4
y=-2x-4
300
What is the value of y: 3y-5=y+2y-9
-5=-9 (Think back, is this possible? No, therefore there are no solutions. These equations would be graphed as parallel lines.
300
Find the intersection of the pair of sets. W = the set of whole numbers P = the set of nonzero integers a. {} c. the set of negative integers b. {0} d. the set of positive integers
d
300
18. Given f(x) = x^2 +1 with domain D: (−2,−1,0,1,3) The symbol ^ indicates we are finding the square of the value. What is the range, R?
Range: (1,2,5,10)
300
You’ve already earned $48 washing cars and plan to earn $12 for each additional car you wash. Write an equation to represent d, the amount earned in dollars, as a function of c, the number of additional cars you wash.
d=12c+48
300
Solve 2x + 3y = 4 3x − 3y = −9
x= -1 y= 2
400
(a-2)/9=2/3
a=8
400
Surprise Question! Multiply (x + 7)(x − 7).
x^2-49
400
Give the domain and range of the function y=x^2 Remember the ^ indicates we are finding the value of x squared.
Domain = (all real numbers) Range = (y is greater than or equal to 0)
400
A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. The equation below represents this situation where m is the number of movies rented each month. 7.50 +1.00m = 2.50m Which of the following is the number of movies that need to be rented each month for the total fees to be the same from either store?
5 movies
400
Solve 3x − y = 7 2x − y = 5
x=2 y=-1
500
Gloria earns 1.5 times her normal hourly pay for each hour that she works over 40 hours in a week. Her normal pay is p dollars per hour. Last week Gloria worked 47 hours and earned $489.85. The following equation represents this situation where p is Gloria’s normal hourly pay in dollars per hour. 40p +7(1.5p) = 489.85 What is Gloria’s normal hourly pay?
$9.70
500
40 candidates apply for a unique job. The job has both a height requirement and a weight requirement. The following information is known about the candidates: 21 candidates meet the height requirement; 17 candidates meet the weight requirement; 8 candidates meet both the weight and height requirements. How many candidates meet only the height requirement?
13
500
For f(x) = 24 − 2x, find f(2)
f(x) = 20
500
Latisha is on page 30 of her book and reads 3 pages every night. Sal is on page 40 of the same book and reads 2 pages every night. How long will it take Latisha to be further in the book than Sal?
11 nights
500
Which system has an infinite number of solutions a.x + 2 = y b.2y + 6 = 4x 4 = 2y − x −3 = y − 2x c.y + 3 = 2x d. y = 2x − 5 4x = 2y − 3 −2 = y − 2x
b. 2y+6 = 4x and -3 = y -2x because they are the same line when both solved for y or x. They will be graphed the same.