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 rocket was launched from the ground into the air at an initial velocity of 80 feet per second.
The path of the rocket can be modeled by h(t) = -16t2 + 80t, where t represents the time after
the rocket has been launched, and h(t) represents the height of the rocket.
Sketch the function on the set of axes below.
State how many seconds it will take for the rocket to reach its maximum height.
State the maximum height, in feet, of the rocket.
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: (0,0), (1,64), (2,96), (3,96), (4,65), (5,0).
If the zeros of the rocket's path are 0 and 5, then the highest point occurs when t = 2.5. It should be "obvious" that the rocket does not just hang in the air at 96 feet for an entire second.
You can adjust the calculator to show increases of .5 for t (or x, on the calculator). When t = 2.5, h(t) = 100.
Your graph should look like this:
Do not draw arrows below the ground.
The rocket reached its maximum height at 2.5 seconds. The rocket reached a maximum height of 100 feet.
32. Use the quadratic formula to solve 2x2 -4x - 3 = 0, and express the answer in simplest radical form.
Answer:
Use the quadratic formula with a = 2, b = -4, and c = -3. Make sure you use parentheses around the negative numbers!
( -(-4) + √( (-4)2 - 4(2)(-3) ) ) / ( 2(2))
( 4 + √( 16 - (-24) ) ) / 4
( 4 + √(40) ) / 4
( 4 + √( (4)(10) ) ) / 4
( 4 + 2√(10) ) / 4
1 + 1/2 √(10)
Either of the last two lines are acceptable. So long as the radical is simplified, it doesn't matter if the fraction is.
33. The table below shows the ages of drivers and the annual cost of their car insurance.
Write the linear regression equation for this set of data. Round all values to the nearest hundredth.
State the correlation coefficient of this line of best fit, to the nearest hundredth.
State what this correlation coefficient indicates about the linear fit of the data set.
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 = -56.97x + 2352.22
The correlation coefficient is r = -0.98.
The correlation coefficient indicates a strong negative 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. Solve the following system of inequalities graphically.
Label the solution set S
Is the point (0, 3) in the solution set? Explain your answer.
2x + y > 3
Answer:
Rewrite the inequalities, solving for y in terms of x and graph.
Remember that < means a solid line that gets shading underneath, and > means a broken line that gets shaded above.
2y < x + 6
y < 1/2 x + 3
2x + y > 3
y > -2x + 3
Your graph should look like this:
(0,3) is not in the solution because it's on the broken line, which is not part of the solution.
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. Acme Athletics purchases shoes from a supply company. In January the store bought 30 pairs
of running shoes and 10 pairs of basketball shoes for $3700. In March they bought 15 pairs of
running shoes and 20 pairs of basketball shoes for $3575. The supply company kept their prices
constant.
If x represents the cost of one pair of running shoes and y represents the cost of one pair of
basketball shoes, write a system of equations that models this situation.
Jacob says that a pair of running shoes costs the store $80 each, and a pair of basketball shoes costs
the store $130 each. Is he correct? Justify your answer.
Solve your system of equations algebraically to find the exact cost, in dollars, of one pair of running shoes and the exact cost, in dollars, of one pair of basketball shoes.
Answer:
The second sentence give us 30x + 10y = 3700. The third sentence gives us 15x + 20y = 3575. (The fourth sentence tells us to use x and y, so use them!)
Check Jacbo's answer by substituting his values into both equations.
30(80) + 10(130) = 2400 + 1300 = 3700 (check)
15(80) + 20(130) = 1200 + 2600 = 3800, not 3575.
Jacob is incorrect.
Solve the system of eqautions.
30x + 10y = 3700
15x + 20y = 3575
60x + 20y = 7400
15x + 20y = 3575
45x = 3825
x = 85
Solve for y:
30(85) + 10y = 3700
2550 + 10y = 3700
10y = 1150
y = 115
End of Exam
How did you do?
Questions, comments and corrections welcome.
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