This exam was adminstered in January 2024 .

More Regents problems.

__January 2024 __

__January 2024__

Part III: Each correct answer will receive 4 credits. Partial credit can be earned.

*33. While playing golf, Laura hit her ball from the ground. The height, in feet, of her golf ball can be
modeled by h(t) = - 16t + 48t, where t is the time in seconds.
Graph h(t) on the set of axes below.
*

What is the maximum height, in feet, that the golf ball reaches on this hit?

How many seconds does it take the golf ball to hit the ground?

What is the maximum height, in feet, that the golf ball reaches on this hit?

How many seconds does it take the golf ball to hit the ground?

**Answer: **

Look at the graph below. You can put the equation in the graphing calculator. You might want to set it so that it shows every 0.5 increment of x because the high point is going to happen at x = 1.5

The maximum height the ball reaches is 36 feet (which happens at 1.5 seconds).

It takes 3 seconds for the ball to hit the ground.

*34. The table below shows the number of SAT prep classes five students attended and the scores they received on the test.*

State the linear regression equation for this data set, rounding all values to the nearest hundredth.

State the correlation coefficient, rounded to the nearest hundredth.

State what this correlation coefficient indicates about the linear fit of the data.

State the linear regression equation for this data set, rounding all values to the nearest hundredth.

State the correlation coefficient, rounded to the nearest hundredth.

State what this correlation coefficient indicates about the linear fit of the data.

**Answer: **

Enter all the data into two lists in your graphing calculator. You will have to run a linear regression. Make sure you have DIAGNOSTICS ON set on your calculator.

When you run the linear regression, you will get a = 40.48 and b = 363.81, rounded to the nearest hundredth.

So the equation is y = 40.48x + 363.81

The correlation coefficient, r, is 0.84.

There is a strong positive correlation between the number of SAT prep courses attended and the score on the Math SAT.

*35. Julia is 4 years older than twice Kelly’s age, x. The product of their ages is 96.*

Write an equation that models this situation.

Determine Kelly’s age algebraically.

State the difference between Julia’s and Kelly’s ages, in years.

Write an equation that models this situation.

Determine Kelly’s age algebraically.

State the difference between Julia’s and Kelly’s ages, in years.

**Answer: **

Kelly's age is

*x*. Write an expression for Julia in terms of x. The product of that expression and x will be 96. Solve the quadratic equation that results from it.

J = 2x + 4

x(2x + 4) = 96

2x^{2} + 4x = 96

2x^{2} + 4x - 96 = 0

x^{2} + 2x - 48 = 0

(x + 8)(x - 6) = 0

x + 8 = 0 or x - 6 = 0

x = -8 or x = 6

Throw out the negative answer because age cannot be negative. Therefore, Kelly is 6 years old.

Julia is 2(6) + 4 = 16. The difference between their ages is 10 years.

If you messed up the signs and thought that Kelly was 8 years old, then Julia would 20, and the difference would be 12 years. If you made one mistake, you would have lost only one point if the rest of your answers were consistent with that mistake.

*36. On the set of axes below, graph the following system of inequalities:*2x - y > 4

x + 3y > 6

Label the solution set S.

x + 3y > 6

Label the solution set S.

*Is (4,2) a solution to this system? Justify your answer.
*

**Answer: **

Rewrite the inequalities into slope-intercept form. Remember when you divide an inequality by a negative number, you have to flip the direction of the inequality symbol.

2x - y > 4

- y > -2x + 4

y < 2x - 4

x + 3y > 6

3y > -x + 6

y > -1/3 x + 2

Both inequalites will have broken lines. Shade above the line y > 1/3x + 2, and below y < 2x - 4. Mark the area with the crisscross with a big "S". This is your solution.

(4,2) is a solution to the system because it's in the double-shaded area.

End of Part III

How did you do?

More to come. Comments and questions welcome.

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