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Accelerated Math 1 Benchmark 2 Study Guide
Name ______________________
(Chance of Winning, Algebra in Context, Coordinate Geometry)
1. Fifty tickets are numbered 1 to 50 and placed in a box. Three tickets are drawn at random
without replacement. What is the probability that their numbers are all greater than 32?
18 numbers are greater than 32; (18/50) * (17/49) * (16/48) = 4896/117600 = .04
2. An ice cream store has 31 flavors of ice cream and 10 toppings. A regular sundae has one
flavor of ice cream one topping, and comes with or without whipped cream. How many
different ice cream sundaes can be ordered?
31 * 10 * 2 = 620 different sundaes
3. Find the number of committees of five persons that can be formed from a group of ten
people.
This is combinations:
10
C5 
10!
10! 10 * 9 * 8 * 7 * 6 * 5! 30240



 252
5!10  5! 5!5! 5 * 4 * 3 * 2 *1* 5!
120
4. A rock concert producer has scheduled an outdoor concert. If it is warm that day, she
expects to make a $20,000 profit. If it is cool that day, she expects to make a $5,000 profit.
If it is very cold that day, she expects to suffer a $12,000 loss. Based upon historical records,
the weather office has estimated the chances of a warm day to be .60; the chances of a cool
day to be .25. What is the producer’s expected profit?
(20,000 * .60) + (5,000 * .25) + (-12,000 * .15) = 12,000 + 1,250 – 1,800 = 11,450
5. The sample mean is an unbiased estimator for the population mean. This means:
a)
b)
c)
d)
e)
The sample mean always equals the population mean.
The average sample mean, over all possible samples, equals the population mean.
The sample mean is always very close to the population mean.
The sample mean will only vary a little from the population mean.
The sample mean has a normal distribution.
B; if I were to take the data from a sample and take the average, it would equal the
population mean.
6. Event A has probability 0.4. Event B has probability 0.5. If A and B are mutually exclusive,
then what is the probability that both events occur.
P(A and B) = P(A) * P(B) = .4 * .5 = .2
7. The weights of male and female students in a class are summarized in the following boxplot:
Which of the following is NOT correct?
a) About 50% of the male students have weights between 150 and 185 lbs.
b) About 25% of female students have weights more than 130 lbs.
c) The median weight of male students is about 162 lbs.
d) The mean weight of female students is about 120 because of symmetry.
e) The male students have less variability than the female students.
Because the median breaks the data in half, then the upper and lower quartiles break the
data into fourths.
E; the male students have more variability due to how wide of a range their data spans.
8. The average salary of all female workers is $35,000. The average salary of all male workers
is $41,000. What must be true about the average salary of all workers?
a)
b)
c)
d)
e)
It must be $38,000.
It must be smaller than $38,000.
It must be larger than $38,000.
It could be any number between $35,000 and $41,000.
There is no conclusion that could be drawn from this setting.
D; since we are given the averages of both the male and female salaries, then the
average of all workers would fall somewhere between those two values.
9. An example of random sampling would be
a) Put names in a hat and draw them out.
b) Select the first 3 people who enter the cafeteria and the last 3 people who enter the
cafeteria.
c) Let people volunteer.
d) Pick all of the apples in my sample from the low branches of the tree.
e) All of these are good examples of random sampling.
A; that is the only example that doesn’t have any other factors involved in the decision.
All names are on separate slips and drawn out at random.
10. What is the distance between (1, -2) and (-7, 9)?
d
Use the distance formula:
d
9  22   7  12
2
112   8
d  121  64
d  185  13.6
11. Find the coordinates of the other endpoint of a segment with an endpoint of (13, 5) and
midpoint at (8, 3).
The midpoint is half the length of the segment. Find the difference fro the endpoint to the
midpoint and then subtrack that to the midpoint coordinates.
The change in the y-values: 5-3 = 2; The change in the x-values: 13-8 = 5
Subtract from the midpoint: (8-5, 3-2) = (3, 1)
12. A line segment has endpoints (-6, 2) and (-2, -4). What are the coordinates of the
midpoint?
  6  2 2  4 
m
,

2
2 

8  2
Use the midpoint formula: m  
,

 2 2 
m  (4,1)
13. The coordinates of a parallelogram are (4, 0), (6, 3), (11, 1), and (x, y) and x > 11. What is
the value of x + y?
Graph the three points. Since x>11 than we need to find the slope between (4, 0) and
(6, 3). The slope is 3/2. Then we use the point (11, 1) and add on the slope, making the
new point (14, 3). Then I add x + y = 14 + 3 = 17.
14. Solve 5  2 x  4  11
Subtract 5 from both sides to get the radical on one side by itself.
2x  4  6
Take the square of both sides.
2 x  4  36
Add 4 to both sides.
2 x  40
Divide both sides by 2.
x  20
x 2  49
15. Solve
3
x7
x 2  49
3
x7
Factor the numerator.
( x  7)( x  7)
3
x7
x7 3
Add 7 to both sides.
x  10
16. Solve for x:
6
5

x4 x3
Take the cross products.
6( x  3)  5( x  4)
6 x  18  5 x  20
Get all variables on one side.
x  18  20
Add 18 to both sides.
x  2
17. Solve for x:
3x  2  2
3x  2  2
Take the square of both sides.
3x  2  4
Add 2 to both sides.
3x  6
Divide both sides by 3.
x2
18. Based on the portions of the graphs of the functions f and g shown above, what are all
values of x between -6 and 6 for which g(x) > f (x) ?
a)
b)
c)
d)
e)
-6 < x < -3 only
-3 < x < 0 only
0 < x < 3 only
3 < x < 6 only
-6 < x < -3 and 0 < x < 3
When you look at the graph, look and see where the graph of g(x) is above the graph of
f(x). Then give the x value range between which that happens.
Therefore, the answer is B. g(x) is only greater than f(x) between the values of -3 and 0.
19. Solve for x: x 2  9 x  0
x 2  9x  0
Factor out an x.
x( x  9)  0
Set each part equal to 0.
x  0; x  9  0
Solve for x in both parts.
x  0; x  9
20. Which of the following functions are neither even nor odd?
I.
II.
III.
I.
II.
III.
f x   15x
f x   2 x  3
f x   x 3  3x  217
even
neither; does not have rotational symmetry anymore because of the y-intercept
neither; does not have rotational symmetry anymore because of the y-intercept
Therefore, both 2 and 3 are neither.
21. Solve by factoring. x2 + 16x + 48 = 0
x 2  16 x  48  0
( x  12)( x  4)  0
Set both parts equal to 0.
x  12  0; x  4  0
Solve for x.
x  12; x  4