Algebra Problems of the Day (Algebra 1 Regents, August 2022)

The following questions appeared on the August 2022 Algebra 1 Regents Exam

More Regents problems.

Algebra 1 Regents, August 2022

Part I: Each correct answer will receive 2 credits.


21. A swimmer set a world record in the women’s 1500-meter freestyle, finishing the race in 15.42 minutes. If 1 meter is approximately 3.281 feet, which set of calculations could be used to convert her speed to miles per hour?

1) 1500 meters / 15.42 min * 60 min / 1 hour * 1 meter / 3.281 feet * 1 mile / 5280 feet
2) 1500 meters / 15.42 min * 60 min / 1 hour * 3.281 feet / 1 meter * 1 mile / 5280 feet
3) 1500 meters / 15.42 min * 3.281 feet / 1 meter * 1 mile / 5280 feet
4) 1500 meters / 15.42 min * 60 min / 1 hour * 1 mile / 5280 feet

Answer: 2) 1500 meters / 15.42 min * 60 min / 1 hour * 3.281 feet / 1 meter * 1 mile / 5280 feet

You are starting with meters on top and minutes on the bottom. You want miles on top and hours on the bottom.

That means that you need to divide by meters so that the units will cancel (reduce to 1) and multiply the top by min so that the units will cancel (reduce to 1).

Choice (1) gives a result of meters * miles / (feet * feet). Eliminate Choice (1).

Choice (2) gives a result of miles) / hour. Choice (2) is the correct answer.

Choice (3) gives a result of miles / min, which isn't quite right. Eliminate Choice (3).

Choice (4) gives a result of (Meters * miles) / (hour * feet). Eliminate CHoice (4).

22. The diagram below shows the graph of h(t), which models the height, in feet, of a rocket t seconds after it was shot into the air.

The domain of h(t) is

1) (0,4)
2) [0,4]
3) (0,64)
4) [0,64]

Answer: 2) [0,4]

The domain is the set of all the x values, and the range is the set of all the y values. We care about x, not y. Or in this case, we want t, not h(t). Eliminate Choices (3) and (4).

THis would be a good time to mention that the choices are INTERVLS. They are NOT points on a coordintae plane.

The interval (0,4), with round brackets, or parentheses, means that the number is NOT included in the interval. It is only a boundary, like an open circle at the end of an inequality graph. The interval [0,4] with square brackets means that the values shown are included in the interval.

In the graph, t=0 and t=4 are valid values, and are included in the set. So Choice (2) is the correct answer.

10(x - 5) = -15

x - 5 = -15/10

x = 5 - 15/10 = 5 - 3/2 = 7/2 or 3 1/2 or 3.5

4 + 2(x - 2) = 9

2(x - 2) = 5

x - 2 = 5/2

x = 2 + 5/2 = 9/2 or 4 1/2 or 4.5

1/3 x = 3/2

x = 3(3/2) = 9/2 or 4 1/2 or 4.5

23. The table below shows the time, in hours, spent by students on electronic devices and their math test scores. The data collected model a linear regression.

What is the correlation coefficient, to the nearest hundredth, for these data?

1) -0.98
2) -0.95
3) 0.98
4) 0.95

Answer: 1) -0.98

You need a calculator that can handle lists and can do linear regression. However, you can tell from looking at the data that the correlation is negative -- as the input gets higher, the output gets lower. So you can eliminate Choices (3) and (4).

When you put it in the calculator and run the linear regression, you will see that the linear regression is -0.98.

24. The volume of a trapezoidal prism can be found using the formula V = 1/2 a(b + c)h. Which equation is correctly solved for b?

1) b = V / (2ah) + c
2) b = V / (2ah) - c
3) b = (2V) / (ah) + c
4) b = (2V) / (ah) - c

Answer: 4) D and B

Use inverse operations to isolate b.

V = 1/2 a(b + c)h.

2V = a(b + c)h

(2v) / ah = b + c

(2V) / ah - c = b

This is Choice (4).

End of Part I.

More to come. Comments and questions welcome.

More Regents problems.

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