## Saturday, February 10, 2024

### January 2024 Algebra 1 Regents Part II

This exam was adminstered in January 2024.

More Regents problems.

### January 2024

Part II: Each correct answer will receive 2 credits. Partial credit can be earned. One mistake (computational or conceptual) will lose 1 point. A second mistake will lose the other point. It is sometimes possible to get 1 point for a correct answer with no correct work shown.

25. Student scores on a recent test are shown in the table below.

 85 96 92 82 90 90 88 95 85 88 90 87 96 82 85 92 96 85 92 87

On the number line below, create a dot plot to model the data

State the median test score for the data set.

For each number in the table place a dot about that value on the number line. Make them all the same size so that, say, 3 dots above one number are the same height as 3 dots above another. Don't make any boxes or bars. You should have 20 dots when you are finished. If you have a different number of dots, you either left something out or repeated some piece of data.

Note that having exactly 20 dots is not a guarantee that you put them in the right place, but having 19 or 21 is definitely an error.

Your graph should look like this one:

There are 20 pieces of data, so the median test score will be the average of the 10th and the 11th. The 10th is 88 and the 11th is 90. The number in the middle of 88 and 90 is 89, which is the median.

26. State whether 2√(3) + 6 is rational or irrational. Explain your answer.

2√(3) is an irrational number and the sum of a rational and an irrational number is always irrational.

If you mentioned that the decimal value goes on forever you must mention that it doesn't have a repeating pattern.

27. The table below shows data from a recent car trip for the Burke family.
 Hours After Leaving (x) 1 2 3 4 5 Miles from Home (y) 45 112 178 238 305

State the average rate of change for the distance traveled between hours 2 and 4. Include appropriate units.

Divide the difference of the miles at hour 4 and miles at hour 2 by the difference of 4 minus 2.

(238 - 112) / (4 - 2) = 63 mph.

It says to add appropriate units, so if you don't specify mph or miles per hour, you will lose a point.

28. On the set of axes below, graph the equation 3y + 2x = 15.

Explain why (-6,9) is a solution to the equation.

Rewrite the equation into slope-intercept form to graph (or to put in your graphing calculator).

3y + 2x = 15
3y = -2x + 15
y = -2/3 x + 5

The slope is -2/3 and the y-intercept is 5. Start at (0,5) and use the rise (-2) and run (3) to find points on the line. Or use the table of values in the calclulator.

Your graph will look like this:

The point (-6,9) is a solution to the equation because it is a point on the line. All points on the line are solutions to the equation.

29.Using the quadratic formula, solve 3x2 - 2x - 6 = 0 for all values of x.

Plug the values into the quadratic formula and evaluate. Don't forget to find two solutions.

Use a = 3, b = -2, and c = -6.

x = ( -b + √( (b)2 - 4(a)(c) ) / ( 2a )

x = ( -(-2) + √( (-2)2 - 4(3)(-6) ) / ( 2(3) )

x = ( 2 + √( 4 + 72) ) / (6)

x = ( 2 + √( 76) ) / (6) or x = ( 2 - √( 76) ) / (6)

x = 1.7862... or x = -1.1196...

x = 1.79 or x = -1.12

30. The piecewise function f(x) is given below.
f(x) = { 2x - 3, x > 3;
-x2 + 15, x < 3 }

State the value of f(3).

Since 3 is not great than 3, but three is less than or equal to 3, use the second piece of the function.

f(3) = -(3)2 + 15 = -9 + 15 = 6

If you evaluate the top piece instead, you will get 1 credit.

31. Express the equation x2 - 8x = -41 in the form (x - p)2 = q.

Complete the square by adding 16 to both sides. Half of -8 is -4 and (-4) square is 16.

x2 - 8x = -41
x2 - 8x + 16 = -41 + 16
(x - 4)2 = -25

32. Factor 36 - 4x2 completely.

Remember that when it says "completely", there is usually more than one step. In this case there is a common factor of 4 in the two terms.

36 - 4x2
4(9 - x2)
4(3 - x)(3 + x)

The difference of two perfect squares always factors into two conjugates. (That is, two binomials with the same two terms, except that one has a + and the other has a -.)

End of Part II

How did you do?

More to come. Comments and questions welcome.

More Regents problems.

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