Thursday, January 18, 2018

August 2017 Common Core Algebra 1 Regents, Part 3

Continuing with the August 2017 Algebra 1 Regents.
Here are the Part I questions, answers, and explanations.
Here are the Part II questions, answers, and explanations.

August 2017, Algebra 1 (Common Core), Part III

Each correct answer will receive 4 credits. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

33. Loretta and her family are going on vacation. Their destination is 610 miles from their home. Loretta is going to share some of the driving with her dad. Her average speed while driving is 55 mph and her dad’s average speed while driving is 65 mph.

The plan is for Loretta to drive for the first 4 hours of the trip and her dad to drive for the remainder of the trip. Determine the number of hours it will take her family to reach their destination.

After Loretta has been driving for 2 hours, she gets tired and asks her dad to take over. Determine, to the nearest tenth of an hour, how much time the family will save by having Loretta’s dad drive for the remainder of the trip.

Answer: Loretta drives 55 mph for 4 hours. Distance = rate X time, d = rt
Loretta drives d = (55)(4) = 220 miles of the 610 miles of the trip.
Her Dad will drive the remaining 610 - 220 = 390 miles
Using d = rt again, 390 = (65)t
t = 6 hours her Dad drives.

Note: you will neither gain nor lose a point whether or not you capitalize the "d" in "Dad", but I'm a "Dad", so there. But I digress.

The total number of hours it should take it 4 + 6 = 10 hours of total driving time.

Second part: If Loretta only drives 2 hours, then they have only traveled 55 * 2 = 110 miles.
Dad has to drive 610 - 110 = 500 miles
500 / 65 = 7.69... or 7.7 hours
To the nearest tenth, the family will drive for 2 + 7.7 = 9.7 hours.
The family will save 0.3 hours in this situation.

34. The heights, in feet, of former New York Knicks basketball players are listed below

Using the heights given, complete the frequency table below

Based on the frequency table created, draw and label a frequency histogram on the grid below.

Determine and state which interval contains the upper quartile. Justify your response

Answer: The frequency table will look like the following. Note that you could have just the tally marks or just the numerical value, and you would receive credit for this portion of the question.

Note that they wanted a frequency histogram, not a bar graph, line graph or anything cumulative. It's important to leave a blank column between 0 and the first bar to indicate the gap, and you should include the little squiggle (which they are inconsistent about demanding).
Remember to add title, labels, scale, etc. Also, do not shade or draw anything to represent 0 for 6.6-6.7.

You can find the upper quartile by either writing out the numbers in order, then finding the median and quartiles. (There are 29 numbers, the 15th is the median, and the upper quartile is between the 7th and 8th numbers of the top half of data. This will give you 6.5.) Otherwise, you can say that 29 divided by 4 is 7.25, and if you could back from the last tally mark on the frequency table, you will find that the 7th and 8th marks are both in the interval 6.4-6.5.

33. Solve the following system of inequalities graphically on the grid below and label the solution S.

3x + 4y > 20 x < 3y - 18

Is the point (3,7) in the solution set? Explain your answer.

Answer: Remember to label the axis. The inequalities used are greater than and less than, so neither will have a solid line.
If you are using the graphing calculator to help with the graph, you need to rewrite the equations is slope-intercept form.

3x + 4y > 20
4y > -3x + 20
y > -3/4 x + 5
x < 3y - 18
x + 18 < 3y
(1/3)x + 6 < y
y > (1/3)x + 6

(3, 7) is NOT a solution because it is on the broken line, and the line is not part of the solution.

33. An Air Force pilot is flying at a cruising altitude of 9000 feet and is forced to eject from her aircraft.
The function h(t) = -16t2 + 128t + 9000 models the height, in feet, of the pilot above the ground, where t is the time, in seconds, after she is ejected from the aircraft.

Determine and state the vertex of h(t). Explain what the second coordinate of the vertex represents in the context of the problem.

After the pilot is ejected, what is the maximum number of feet she was above the aircraft's cruising altitude? Justify your answer.

Answer: The vertex can be found from the axis of symmetry, which is x = (-b) / (2a), where a = -16 and b = 128.
x = -(128) / (2(-16)) = -128 / -32 = 4
y = h(4) = -16(4)^2 + 128(4) + 9000 = 9256
Oddly, in this particular problem, no actual work was needed, and if you found the answer in your calculator by graphing and finding the maximum, you would have been fine. I do not recommend that approach, except to check your math.

The coordinates of the vertex are (4, 9256) where the second coordinate is the height of the pilot above ground level in feet.

The maximum number of feet the pilot will rise above the plane is 9256 - 9000 = 256 feet.

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