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Pre-AP Algebra II – Chapter 2 Test Review
Standards/Goals:
 A.1.d. I can solve a single step or multi-step linear inequality that has only one variable.
 A.1.f./ A.REI.12./A.CED.1.:
o I can understand linear equations and can apply them to solving real-life problems.
o I can understand the relationship between slope & parallel & perpendicular lines.
o I can write linear equations in standard form & slope intercept form.
o I can write a linear equation in slope-intercept form when given two points, a point and the
slope, or from the graph of an equation.
o I can graph equations on the coordinate axes with labels and scales.
o I can solve and graph a linear inequality.
o I can graph the solution of a linear inequality in a half-plane.
o I can write and graph linear equations in point-slope form.
 A.1.g./A.CED.1.: I can determine the x & y intercepts of a linear equation.
 D.1.a./A.CED.1.:
o I can solve and graph inequalities and equations that involve absolute value.
o I can solve compound inequalities containing the words ‘or’ and ‘and’.
o I can create and solve absolute value equations and inequalities and graph their solutions.
 D.1.b.: I can solve and graph compound inequalities that involve both “or” and “and.”
 D.1.c./A.CED.2.: I can solve systems of THREE linear equations using various methods, including
substitution and the use of matrices.
 D.2.a.:
o I can graph the solution set to a system of linear inequalities in two variables as the
intersection of the corresponding half-planes.
o I can graph a system of linear inequalities in two variables with and without technology to find
the solution set to the system.
 D.2.b.: I can solve linear programming problems by finding maximum and minimum values of a
function over a region defined by linear inequalities.
 I.1.e./A.REI.8/N.VM.8.:
o I can solve a system of linear equations using a single matrix equation and inverses and
determinants.
 F.IF.4:
o I can interpret the key features of graphs and sketch key features given the known intercepts,
through the use of a scatter plot.
o I can use graphs and linear models to make predictions from linear data displaying
relationships between quantities.
What are the x & y intercepts of
#1. 4x + 7y = 28?
#2. 3x + y = 6
#3. A factory wants to make ball bearings that have a standard diameter, ‘d’ of 58.255 mm. Ball
bearings that are deemed to be “acceptable” measure within ±0.155 mm of this standard. Determine
the solution set for the diameter of these ball bearings.
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#4. Free Response Practice
The table and scatterplot below show the relationship between student enrollment (in thousands) and
total number of property crimes (burglary and theft) in 2006 for eight colleges and universities in a
certain U.S. state.
Enrollment (in No. of
1000s) (x)
Property
Crimes (y)
16
201
2
6
9
42
10
141
14
138
26
601
21
230
19
294
Predictor
COEF
Constant
-112.58
X
21.83
a. Write the equation of the least-squares regression line in the format of: ̂
Define any variables used. State whether the correlation is positive or negative.
.
b. Use your ‘line of best fit/LSRL’ to predict the number of property crimes when there are 20,000
students enrolled.
c. Use your equation from part #1 to predict the number of property crimes (in thousands) for an
enrollment of 15,000 students.
d. Suppose that a college in fact had 15,000 students and there was an actual amount of 198
crimes. Based on your prediction in #3., was your prediction and overestimate or an
underestimate and by approximately how much?
e. Interpret the slope of the equation in the context of the problem. Does the intercept have any
meaningful interpretation? Should be written in the following format:
“For every _______ additional __________________________________, we predict/expect
a(n) ___________ of _________ of ____________________________________________.”
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Write an absolute value inequality or equation for each number line shown:
#5.
#6.
#7.
#8.
Solve AND graph the following. Write answers in set and interval forms.:
#9. 4x + 8 < 12 OR 5 – 8x ≤ -35
#10. |
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#11. |
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#13.
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#12. |
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#14.
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#15.
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#16.
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Consider an equation with a slope of -1/2 and passes through the point (-12, 10).
#17. Write the equation of the line in point-slope form.
#18. Write the equation of the line in slope-intercept form.
#19. Write the equation of the line in standard form.
#20. Write the equation of the line that would be parallel to this line in both standard and slopeintercept forms.
#21. Write the equation of the line that would be perpendicular to this line in both standard and slopeintercept forms.
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Graphing linear inequalities.
#22. What is the area of the figure determined by
this system of inequalities?
Use the graph provided below, if you wish.
{
#23. Graph this system of constraints and show its feasible region. Write the vertices down, and the
point that achieves the maximum and minimum for the objective function: P(x, y) = 4x + 2y.
{
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What systems of inequalities are shown in the graphs?
#24.
#25.
#27. For the following, graph the system of
constraints. Name ALL vertices and then find the
values of ‘x’ and ‘y’ that maximize or minimize
the objective function. Use the graph provided.
{
Maximum for P = x + 3y
#26.
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EXTRA REVIEW PROBLEMS:
#1. Line ‘n’ contains (5, -5) and is perpendicular to the line 5x + 3y = 12. What is the equation of line ‘n’
in slope-intercept form and standard form?
#2. What would the slope be of a line parallel to y = ¼ x + 9 look like?
#3. What would the slope of a line perpendicular to y = 5x – 10 look like?
MULTIPLE CHOICE QUESTIONS:
#1. What is the solution of 1 < 2x + 3 < 9?
a. -1 > x < 2
b. 2 < x < 3
c. -1 < x < 2
d. -1 < x < 3
#2. Which expression best represents the value of ‘x’ in y = mx + b?
a. m(y – b)
b.
c.
d.
#3. The hourly rate of a waiter is $4 plus tips. On a particular day, the waiter worked 8 hours and
received more than $150 in pay. Which could be the amount of tips the waiter received?
a. $18.75
b. $32
c. $118
d. $120.75
#4. Which expression best represents a simpler form of 4m + 3(m + n)?
a. 7m + 3n
b. 4m + 3mn
c. 3m + 4n
d.
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Throwback Topic: “Boxplots”
Twenty-six samples of Romano-British pottery were found at four different kiln sites. The percentage of
oxides of two metals, magnesium and iron, measured by atomic absorption spectrophotometry, are
displayed in the given boxplots.
a. Approximate the IQR for both the Iron and Magnesium distributions.
b. Which metal (Iron or Magnesium) has a higher measure of center (median) and by how much?
c. Between what two values do the higher 75% of data approximately lie for the Iron distribution?
d. Between what two values do the middle 50% of the data approximately lie for the Magnesium
distribution?
e. Is the mean of the Iron distribution going to be less than or greater than the median value?