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Unit 2A (Mod 6-9) Final Exam Review
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Gravity
Terms in this set (36)
What are the x- and y-intercepts?
point where the line crosses the x- and y-axies
What are the x- and y-intercepts of this problem?
y = 3x + 1
y = 1 or (0, 1)
x = -1/3 or (-1/3, 0)
What equation matches this recursive rule?
f(n) = f(n-1) - 3
a) 2, 5, 8, 11,...
b) -1, -4, -7, -10,...
b) - common difference of -3
What is the inverse function of f(x) = 3x - 1?
f-1(x) = 1/3x + 1/3
What is the correlation coefficient chart?
-1 = negative correlation
0 = no correlation
1 = positive correlation
What is the correlation coefficient of this problem?
age and value of a car
-1 = negative correlation
What is the correlation coefficient of this problem?
age and height of a tree
1 = positive correlation
What is the correlation coefficient of this problem?
a city's population and the number of letters in its name
0 = no correlation
Solve this system of equations using elimination:
3x - 2y = 9
5x + y = 2
(1, -3)
Solve this system of equations using substitution:
y - 2 = 4x
5y - 2x = 1
(-0.5, 0)
Jones watches a movie for $2 plus $3 every time he watches it. Anna watches the same movie for $5 with $2 every time she watches it. How many times does both Jones and Anna have to watch the movie for them to pay the same price?
3 times
- set J(x) and G(x) equal to each other and solve for x
How do you graph a slope of a line?
start at y-int and move through rise/run
If a line has a y-intercept of 3, a slope of 1, and a x-intercept of -3, what would be the equation?
y = x + 3
If f(x) = 3x - 4 and g(x) = -2x + 1, what is f(x) - g(x)?
5x - 5
If f(x) = 3x - 4 and g(x) = -2x + 1, what is f(x) + g(x)?
x - 3
Using the equation s = 0.8t + 0.5, what is the predicted s value if t = 13? If the actual value was 9.5, what would be the residual and squared residual?
10.9
- residual: -1.4
- squared residual: 1.96
What does RAP mean?
residual = actual value - predicted value
What is the y-intercept of this equation?
y = 3x
b = 0
How do you know which side to shade on for system of inequalities?
plug in (0, 0)
- if it works, shade towards (0, 0)
- if it is wrong, shade the other way
How do you know to use a dotted or solid line?
dotted = < >
solid = ≤ ≥
What are the four main qualities to see if an equation is linear?
1) x has the power of 1
2) x cannot be in a denominator
3) x cannot be multiplied by y
4) there is a constant slope
see page 156 in 6.1
Are these equations linear? Compare them.
y = 2x + 3
y = 2x - 1
yes
- both have same slope but different y-intercepts
Find the slope of a line that has its x-intercept at -2 and y-intercept at 7.
7/2
Brandon's gym membership is y = 45x + 5 and Lisa's gym membership is y = 15x + 25 where "x" is the amount of weeks they go to the gym. What are the meanings of the slopes? Describe differences in their graphs.
- slopes mean the amount of $$ the gym charges each time they go to their gyms
- Brandon has steeper line = higher slope rise
- Lisa has a higher line = y-int starts higher
Write a recursive and explicit rule for this arithmetic equation:
10, 5, 0, -5
RECURSIVE: f(n) = f(n-1) - 5
EXPLICIT: f(n) = 10 - 5(n-1)
The line of best fit is I = 1.32x + 25 with "I" being income earned in thousands of dollars per year while "x" is the years of experience. What would the coefficient be and what would be the prediction for 40 years?
COEFFICIENT: 1
PREDICTION: $77,800 (remember income in THOUSANDS of dollars in a year = turn 77.8 into $77,800)
If the line of best fit is y = 3.18x - 6.27, what would the prediction be if x = 2? If the actual value was 0.06, what would the residual and squared residual be?
PREDICTION: 0.09
RESIDUAL: -0.03
SQ RESIDUAL: 0.0009
What is the y-intercept of 2x + 5y = 15?
(0, 3) or y = 3
What is the solution for this problem?
3x - 1 > (9x + 6)/3
(9x + 6 over 3)
no solution
Which is not a linear function?
a) xy = 6
b) 6y = x
a)
Which equation is the solution to the point (1, 2)
a) 3y + x = 7; x - y = -1
b) 2x + 2y = 2; 7x = 4y
a)
Which ordered pair is a solution to the system of inequalities: y > 3x - 1 and 2x + y < 1?
a) (4, 4)
b) (-2, 3)
b)
If a car is rented and driven x miles, make a linear function that describes the total amount owned to the car company that charges a flat rate of $100 and $1 per mile?
C(x) = x + 100
What is a solution to the system of equations of 2x + 3y = 7 and 4x - 2y = -2?
a) (2, 1)
b) (1/2, 2)
b)
If a 6-foot snowman is built and begins to melt with a rate of 6 inches per day, what would the equation that represents the height "y" *(in feet) after x days? What are the x- and y-intercepts and their meanings?
EQ: y = -0.5x + 6
y = 6: 6 feet originally
x = 12: 12 days until the snowman melts
If the perimeter is 30 cm and the height is 3 cm more than twice its width, write a system of linear equations and solve to find the height and width of the rectangle.
SYSTEM: 2h + 2w = 30; h = 2w + 3
W = 4 cm
H = 11 cm
(you could have a different system, just make sure you have the right width and height)
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