CPM Algebra 1 - Chapter 9 Group Test
1.
The local blood bank has a very low supply of blood. They know they’ll run
out if a large disaster occurs in the near future. If the blood bank is not back
up to its normal stock of more than 1350 pints of blood in 15 weeks, then the
bank must spend several thousand dollars on an advertising campaign to
refresh the supply. The bank currently has 72 pints of blood and is receiving
donations of 61 pints per week. Will the blood bank have more than 1350
pints in time?
a.
Discuss with your study team whether an inequality or an equation is
appropriate for this situation. State your reasoning.
b.
Write an appropriate mathematical sentence and solve it to determine the
number of weeks that it will take to have more than 1350 pints of blood.
Will they have to spend the money on advertising?
c.
The blood bank can only safely handle 2000 pints of blood. Write an
additional mathematical sentence and solve it to determine when the
blood bank has to end the blood drive.
[ a: Answers vary. b: 72 + 61x ! 1350 ; x ! 20.95 weeks; they will not
have enough blood in 15 weeks, so they will need to spend the money,
c: 72 + 61x ! 2000 , x ! 31.6 weeks. ]
2.
With your study team, test points A through G graphed below to determine
whether they are solutions to the inequality y ! 5x " 6 . Write “true” or
“false” next to each point’s label on your paper. Then show the entire
solution region on the graph. How many solutions are there?
y A D C F x B E G [ A, B, C, and E solve the inequality and the others do not. There are an
infinite number of solutions. ]
3. y Examine the graph at right with your study team. a.
Write an inequality for the graph.
b.
Which points on the graph are
solutions for the inequality?
(0, 6) -­‐(5, 0) c.
Is the origin a solution? How do you
know? Justify your answer using the
graph and the inequality.
d.
If the other side of the line were shaded and the current shading were
gone, how would the inequality that you wrote in part (a) be different?
Explain why.
[ a: y ! 56 x + 6 , b: All points in the shaded region and all points on the
line are solutions for the inequality, c: Yes; it makes the inequality true
and lies in the shaded region, d: The ≤ symbol would become ≥. ]
x 4.
Graph the inequality y > 6x 2 ! 4 and, with your study team, describe the
solution. Demonstrate that a test point from the shaded region of your graph
makes the inequality true.
[ The graph is a parabola opening up with vertex at (0, – 4) and a dashed
boundary line. The shaded region lies above the parabola. Students
should select any point in the shaded region and use it to prove the
inequality true. ]
5.
Graph the system of inequalities below on one set of axes.
i.
ii.
y > 4x ! 4
y ! " 12 x + 3
a.
Is the boundary line for each inequality included in the solution?
Explain.
b.
Which points are solutions to this system?
c.
Verify your solution region algebraically. Be sure to check each
inequality and show your work.
d.
How can your team be sure this region is the only set of points that
makes both inequalities true?
[ a: only the boundary line for inequality (ii) is included, b: All points in
the combined shaded region and on the boundary line for inequality (ii)
(to the left of the point of intersection) are solutions, c: Students should
choose a point that falls in the combined shaded region and test it in both
inequalities, d: Select several points that do not fall in the combined
shaded region and test them in each inequality; at least one inequality
should be false in each case. ]