**New York State Algebra 1 (Common Core) Regents**exam, Part 2. There were 8 questions, each worth 2 credits. Partial credit may be earned for correct work on a problem without a solution, or for a problem with a solution that contains

**one**computational or conceptual error. All work must be shown. In general, a correct answer without any work is worth 1 credit, unless that answer is given as a choice and an explanation is required.

Link to Part 1

### Part 2

**25. ** *Each day Toni records the height of a plant for her science lab. Her data are shown in the table below*

*The plant continues to grow at a constant daily rate. Write an equation to represent h(n), the height of the plant on the nth day.*

The plant is growing at a constant rate, so use any two points to find the slope. Let's use (1, 3.0) and (2, 4.5). m = (4.5 - 3)/(2 - 1) = 1.5/1 = 1.5

Solve for b: 3 = 1.5(1) + b; b = 3 - 1.5 = 1.5

The function is **h(n) = 1.5n + 1.5**

Even if the slope or the y-intercept were obvious to you, show the work anyway. It helps.

**26. ** *On the set of axes below, graph the inequality 2x + y > 1.*

Things they will be looking for: the correct slope and y-intercept, a broken line, proper shading.

In slope-intercept form: 2x + y > 1 becomes y > -2x + 1. Shade above the line.

**27. ** *Rachel and Marc were given the information shown below about the bacteria growing in a Petri dish in their biology class.
*

*Rachel wants to model this information with a linear function. Marc wants to use an exponential function. Which model is the better choice? Explain why you chose this model.*

The better choice is **exponential** because the function isn't growing at a constant rate.

If you find the **rate of change** for each pair of numbers, you will get the following: 60, 70, 80, 90, 110, 140, 170, 210, 270, 340. Not only is it NOT constant, it's growing with each passing hour.

If you divide B(2)/B(1), you get 1.27... Divide B(3)/B(2), you get 1.25. B(4)/B(3), you get 1.257.

You probably don't need to go all the way to 10 -- it's only a 2-point question -- but you can see that the growth factor is approximately 25%.

**28. ** *A driver leaves home for a business trip and drives at a constant speed of 60 miles per hour for 2 hours. Her car gets a flat tire, and she spends 30 minutes changing the tire. She resumes driving and drives at 30 miles per hour for the remaining one hour until she reaches her destination.
*

*On the set of axes below, draw a graph that models the driver’s distance from home.
*

*Graph a line with a slope of 60 from time 0 to time 2. Graph a horizontal line (slope 0) from 2 to 2.5. Graph a line with a slope of 30 from time 2.5 to 3.5.
*

**29. ** *How many real solutions does the equation x ^{2} - 2x + 5 = 0 have? Justify your answer.*

None. If you complete the square, you will get (x - 1)^{2} = -4, which has no real roots.

Or you could find the

**discriminant**(of the quadratic formula):

Alternatively, I don't know if you would get credit for just saying that you graphed y = x

^{2}- 2x + 5 and it didn't have any roots, or it didn't cross the x-axis. On the other hand, if you

*show*that the minimum point for the parabola is above the x-axis and, therefore, has no roots, that might have been acceptable.

**30. ** *The number of carbon atoms in a fossil is given by the function y = 5100(0.95) ^{x}, where x represents the number of years since being discovered.
What is the percent of change each year? Explain how you arrived at your answer.*

There is a 5% decrease each year. The decay factor is .95, and 1.00 - .95 = .05, which is 5%.

If you left it at .05, you probably lost a point because it asked for percent. If you didn't say "decrease", you probably lost a point.

**31. ** *A toy rocket is launched from the ground straight upward. The height of the rocket above the ground, in feet, is given by the equation h(t)= 16t ^{2} + 64t, where t is the time in seconds.
Determine the domain for this function in the given context. Explain your reasoning.*

The domain of the function is 0 __<__ t __<__ 4.

Time cannot be negative. At t=0, h(0) = -16(0)^{2} + 64(0) = 0 + 0 = 0

At t=1, h(1) = -16(1)^{2} + 64(1) = -16 + 64 = 48

At t=1, h(2) = -16(2)^{2} + 64(2) = -64 + 128 = 64

At t=1, h(3) = -16(3)^{2} + 64(3) = -144 + 192 = 48

At t=1, h(4) = -16(4)^{2} + 64(4) = -256 + 256 = 0. The rocket hits the ground.

If t > 4, the rocket would have negative height, which is impossible.

**32. ** *Jackson is starting an exercise program. The first day he will spend 30 minutes on a treadmill. He will increase his time on the treadmill by 2 minutes each day. Write an equation for T(d),
the time, in minutes, on the treadmill on day d.
*

*Find T(6), the minutes he will spend on the treadmill on day 6.*

First part: T(d) = 30 + 2(d - 1), 30 minutes for the first day, plus 2 more each additional day.

Second part: T(6) = 30 + 2(6 - 1) = 30 + 2(5) = 30 + 10 = 40 minutes,

## 6 comments:

did you do number 37 yet?

nevermind...

Thanks for your hardwork

.m a big gan

For number 32 why is it 2 (d-1) though?

In question 32, he runs 30 minutes on Day 1, and 32 on Day 2. You don't start counting on Day 0, so you need to subtract 1 from the day before multiplying by 2.

it would be either 30 + 2(d - 1) or just 28 + 2d.

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