This exam was adminstered in June 2026.
June 2026 Algebra, Part III
Each correct answer is worth up to 4 credits. Partial credit can be given. Work must be shown or explained.
31. A ball is tossed up into the air from the deck of a building. The distance that the ball is above the ground t seconds after it is tossed can be modeled by the function D(t) = −16t2 + 32t + 48, where the distance is measured in feet. On the set of axes below, graph D(t) = −16t2 + 32t + 48.
State the maximum number of feet above the ground that the ball will reach.
State the number of seconds after the toss it will take the ball to hit the ground.
Answer:
Use your graphing calculator to find the points that you need to plot before t = 0 and when h(t) = 0.
You'll get the following points: (0,48), (1,64), (2,48), (3,0). Plot these and draw the curve. Do not draw any arrows at the endpoints.
The ball will reach a maximum height of 64 feet.
The ball will hit the ground at 3 seconds.
32. Solve the following system of equations algebraically for all values of x and y:
y = x2 − 5x + 3
Answer:
Set the expressions equal to each other and solve the quadratic equation.
x2 − 5x + 3 = -2x + 3
x2 − 3x = 0
x(x - 3) = 0
x = 0 or x - 3 = 0
x = 0 or x = 3
Solve for y:
If x = 0, then y = -2(0) + 3 = 3.
If x = 3, then y = -2(3) + 3 = -3
33. The table below shows the number of years of experience, x, working as a salesperson and their corresponding salaries, y, in thousands of dollars.
State the linear regression equation for these data. Round all values to the nearest hundredth.
State the correlation coefficient for this data set, to the nearest hundredth.
State what the correlation coefficient indicates about the linear fit of the data.
Answer:
Put the data into Lists L1 and L2. Make sure that "DiagnosticOn" has been executed. (It's in the Catalogue.) Run a Linear Regression.
COPY THE ENTIRE WINDOW OF DATA ONTO YOUR TEST PAPER. The reason for this is if you entered any piece of information incorrectly, all of the following answers are likely to be incorrect. However, if you show the data that you were given by your calculator, you can still earn three of the four points.
The equation for the linear equation will be y = 4.61x + 11.93
The correlation coefficient is r = 0.98.
The correlation coefficient indicates a strong correlation.
There isn't much to say about this. Either you know how to enter the data and run the linear regression, or you do not.
34. Graph the system of inequalities on the set of axes below.
State the coordinates of a point that satisfies both inequalities. Justify your answer
3x + y ≥ 6
Answer:
Rewrite the inequalities, solving for y in terms of x and graph.
Remember that < means a borken line that gets shading underneath, and ≥ means a solid line that gets shaded above.
2y < x − 8
y < 1/2 x − 4
3x + y ≥ 6
y ≥ -3x + 6
Your graph should look like this:
Any point in the area labeled "S" is a valid point that satisfies both inequalities. Do NOT choose any point on the solid line.
For example: (8, -2) is in the double-shaded area, marked "S".
June 2025 Algebra, Part IV
A correct answer is worth up to 6 credits. Partial credit can be given. Work must be shown or explained.
35. At a department store in a tax-free state, Jane can either buy three tank tops and two sweatshirts for $52 or two tank tops and one sweatshirt for $30. If x represents the price of one tank top and y represents the cost of one sweatshirt, write a system of equations that could be used to model this situation. On the set of axes below, graph the system of equations.
State the coordinates of the point of intersection of your lines. Explain what each coordinate of the point of intersection means in the context of the problem.
Answer:
Write the equations from the first statement.
3x + 2y = 52 and 2x + y = 30
Rewrite these in slope-intercept form so you can graph them.
3x + 2y = 52
2y = -3x + 52
y = -3/2 x + 26
2x + y = 30
y = -2x + 30
Put these equations in your graphing calculator and plot the points from the tables of values.
Your graph will look like this.
The point of intersection is (8,14). In the context of the problem, tank tops cost $8 and sweatshirts cost $14.
End of Exam
How did you do?
Questions, comments and corrections welcome.
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