The following are some of the multiple questions from the January 2019 New York State Common Core Algebra I Regents exam.

### January 2019 Algebra I, Part II

Each correct answer is worth up to 2 credits. Partial credit can be given. Work must be shown or explained.

**25.** *
Solve algebraically for x: 3600 + 1.02x < 2000 + 1.04x
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**Answer: **

Subtract 2000 from both sides. Then subtract 1.02x from each side.

Finally, divide both sides by 0.02.

3600 + 1.02x < 2000 + 1.04x

1600 < 0.02x

80000 < x

**26.** *
The number of people who attended school's last six basketball games increased as the teamed neared the state sectional games. The table below shows the data.
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Game | 13 | 14 | 15 | 16 | 17 | 18 |

Attendance | 348 | 435 | 522 | 609 | 696 | 783 |

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State the type of function that best fits the given data. Justify your choice of a function type.
**Answer: ** Note that you don't need to understand anything about basketball or what "sectional games" are.

A linear function is best because there is a constant rate of change of 87.

435 - 348 = 87

522 - 435 = 87

609 - 522 = 87, etc.

At this point, even if the rest weren't exactly 87, a linear function would still be the best fit.

**27.** *
Solve x*^{2} - 8x - 9 = 0 algebraically

Explain the first step you used to solve the given equation.

**Answer: ** If you graph it on the calculator, you will not get full credit. However, you can graph it if you wish to check your answer.

If you look for the factors of -9 that add up to -8, you will get -9 and +1

So x^{2} - 8x - 9 = 0 factors into

(x - 9)(x + 1) = 0

Then x - 9 = 0 or x + 1 = 0

So x = 9 or x = -1
You could have also, for example, completed the square or used the quadratic formula. In either case, you needed to explain what you were doing to get the second point.

**28.** *
The graph of f(t) models the height, in feet, that a bee is flying above the grown with respect to the time it traveled in t seconds.
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State all time intervals when the bee's rate of change is zero feet per second. Explain your reasoning.
**Answer: **

When the bee's rate of change is zero, the slope of the line will be zero. This means the parts of the graph that are horizontal line segments.

This intervals are between 2 and 6 seconds and again at 14-15 seconds.

**29.** *
Graph the function f(x) = 2*^{x} - 7 on the set of axes below.

If g(x) = 1.5x - 3, determine if f(x) > g(x) when x = 4. Justify your answer.

**Answer: **

The graph will look like the exponential parent function y = 2^{x} but translated seven units down.

g(4) = 1.5(4) - 3 = 6 - 3 = 3.

f(4) = 2^{4} - 7 = 9. (You didn't have to show this if you included the point (4, 9) on the graph.

So f(4) > g(4).

You also could have graph g(x) to compare the points. If you did this, be sure to label both lines!

**30.** *
Determine algebraically the zeroes of f(x) = 3x*^{3} + 21x^{2} + 36x

**Answer: **

As with the earlier problem, if you graph the equation, you can check your answer, but you will not get full credit for doing it that way.

Any time you have a number greater than one as a coefficient for the first term, or if the exponent is greater than 2, look for common factors you might be able to remove.

3 is a factor of all three terms, and so is x.

f(x) = 3x^{3} + 21x^{2} + 36x

f(x) = 3x(x^{2} + 7x + 12)

f(x) = 3x(x + 3)(x + 4)
If 3x(x + 3)(x + 4) = 0 then

x = 0 or x = -3 or x = -4.

The zeroes of f(x) are 0, -3 and -4.

**31.** *
Santina is considering a vacation and has obtained high-temperature data from the last two weeks for Miami and Los Angeles.
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Which location has the least variability in temperatures? Explain how you arrived at your answer.
**Answer: **

The range of temperatures in Miami is 87 - 60 = 27

The range of temperatures in Los Angeles is 74 - 61 = 13

Los Angeles had less variability.

A similar question came up on the August Regents, and there were multiple acceptable answers.

For example, you could have used the Interquartile Range (Q3 - Q1), which you could have gotten if you had put all the data into two separate lists on your calculator and performed "1-Var Stats".

Or you could have compared standard deviations, similarly by making lists in your calculator.

These methods require extra work. Some students may have chosen these because comparing the range might appear to be "too easy".

**32.** *
Solve the quadratic equation below for the exact values of x.
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*4x*^{2} - 5 = 75
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**Answer: **

Since there is no x^{1} term, it would be easier to use square roots than trying to factor the equation (in this blogger's opinion).

Add 5 to both sides: 4x^{2} = 80

Divide by 4: x^{2} = 20

Square root: x = __+__ SQRT(20)

Note that "exact value" means leave it in radical form. DO NOT write a rounded decimal, not even one that has 10 decimal places. It won't be the exact value.

**End of Part II**

How did you do?

Questions, comments and corrections welcome.