Download Benchmark 4 Study Guide

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Benchmark 4 Study Guide 2010-2011
Use the Venn diagram to answer the following questions.
U
A
B
4
14
2
6
8
16
12
20
10
18
1.) What are the elements of set A?
2.) True or False: B is a subset of A?
3.) What is the Union of Sets A and B?
4.) What is the Intersection of sets A and B?
Use the Venn diagram to answer the following questions.
5. What is the union of the two sets?
6. What is the intersection
7. True or False: Horses are neither duck-billed or small and furry.
8. Out of forty students, 14 are taking English Composition and 29 are taking Chemistry. If five students are in
both classes, how many students are in neither class? How many are in either class? What is the probability that
Name:________________________________
a randomly-chosen student from this group is taking only the Chemistry class? Create a Venn diagram and
solve.
9. In set A = {s, u, m, m, e, r} and set B = {f, u, n} find A  B  __________
Identify intersections, and unions in problems 10 and 11.
10. A: {2, 4, 6, 8,}
B: {4, 6, 8, 10}
11. C: {a, e, i, o, u}
D: {a, b, c, d, e, f, g, h, i, j, k}
12. Draw a Venn diagram to show the relationship between the sets.
X = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
Y = {5, 10, 15, 20, 25, 30, 35, 40}
13. Which of these sets contains the subset {June, July}?
a.
b.
c.
d.
{School Year}
{March, April, May, June}
{Summer Break}
{July, August, September}
14. {5, 10, 15, 20, 25}  {10, 20, 30, 40, 50}
a.
b.
c.
d.
{}
{10, 20}
{10, 20, 30, 40, 50}
{5, 10, 15, 20, 25, 30, 40, 50}
15. Set A = {c, a, t}, Set B = {d, o, g}, Set C = {m, o, u, s, e}
Which statement is true?
e. A  B
f. B  A
g. o  B  C
h. c  A
16. Set C = {b, i, r, t, h}, Set L = {d, a, y}, Set W = {c, a, k, e}
Which statement is true?
a. e  C  L
b. W  L
c. b  C  L
d. a  L  W
Name:________________________________
17. Set A = {all even numbers}, what is the complement of A?
A. {2, 4, 6, 8, 10}
B. {all positive integers}
C. {3, 6, 9, 12}
D. {all odd numbers}
18. Set B = {January, February, March, April, May, June, and July}, what is the complement of B?
A. {February, March, April}
B. {August, September, October, November, December}
C. {winter months}
D. {summer months}
19. Find the union and intersection of the sets
X  2  x  12
Y  4  x  16
20. Identify the union, intersection, and subset.
X<8
X>6
-6
Complete the following probability problems.
21. How many different ways can lunch be ordered from a menu if you can have one choice from each
category?
Main Course: Hamburger, Chicken Fingers, Hot Dog, Pizza, Veggie
Sides: French Fries, Onion Rings, Salad, Corn
Drinks: Lemon Lime, Cola, Orange, Diet Cola
A. 13
B. 21
C. 80
D. 95
Name:________________________________
22. The Frozen Treat shop offers 4 types of ice cream (vanilla, chocolate, cookie dough, strawberry), 2 types of
cones (sugar, waffle cone) and 4 types of toppings (chocolate, caramel, sprinkles, whipped cream). How many
possible ways can a frozen treat be made with one choice from each category?
A. 32
B. 45
C. 125
D. 10
23. Shirts at Teez R Us can be purchased in 4 sizes (S, M, L, XL), short or long sleeves, and 3 colors (brick,
orange, sage). Use this information to draw a tree diagram and answer the following question:
How many possible arrangements of size, sleeve style, and color are available? _________
If I know I want a sage colored shirt, how many shirt possibilities are available? __________
24. One bag of marbles contains 1 white, 1 yellow, 2 blue, and 2 orange marbles. A second bag contains 2
white, 3 yellow, 1 blue, and 2 orange marbles. What is the probability of drawing a blue marble from each bag?
25. One bag of marbles contains 3 red, 4 green, 7 black, and 2 yellow marbles. What is the probability of
drawing a green marble? What is the probability of drawing a green marble, removing it from the bag and then
drawing another green marble?
26. Using the same bag of marbles without replacement, what is the probability of drawing a red marble and
then drawing a black marble?
27. John has 18 CD’s on his shelf. There are 8 Rap CD’s, 7 R&B CD’s and 3 Pop CD’s. Without looking, what
is the probability that John chooses a CD that is NOT Rap?
28.
In the following diagram, identify the following types of angles:
Vertical
Corresponding
A
B
3
C
4
5
8
7
6
Alternate Exterior
* Using the diagram, identify all CONGRUENT angles.
2
1
Alternate Interior
_____________________________________________
_____________________________________________
_____________________________________________
_____________________________________________
_____________________________________________
_____________________________________________
Name:________________________________
29. Write a congruency statement these two figures: __________  __________
A
B
Q
2X
(Y – 3)°
P
C
120°
R
120°
15
15°
F
E
O
D
S
18
T
30. Given that the two figures are congruent, solve for X.
X= _____________.
31. Given that the two figures are congruent, solve for Y.
Y= _____________.
32. If figure ABCDE  figure VWXYZ then W   __________?
A
9
33. In the diagram BE is parallel to CF . What is the length of x ?
X=___________
34. In the diagram BE is parallel to CF . What is the length of y ?
Y=______________
C
12
D
35. Multiply the Binomials. (4n  4)(5n  8)
a. 20n 2  12n  32
b. 20n 2  32n  12
c. 20n 2  12n  32
d. 8n  32
36. Multiply the Binomials. (k  2)(k  2) or (k  2) 2
a. k 2  4
b. 2k 2  4k  4
c. k 2  k  2
d. k 2  4k  4
37. Multiply the Binomials. (m  5)( m  5)
a. m2  10m  25
b. m2  25
c. m2  10m  25
d. m2  25
38. Find the Quadratic Trinomial expression.
a. 16  4x 2  x5  x9
b. m2  25
c. 20n 2  12n  32
d. 5x  6
B
x
6
6
E
2
y
F
4
G
Name:________________________________
39. Find the monomial with a degree of 7.
a. 2a 3b5
b. 7x 2 y3 z
c. 8m2 n 2 o 2
d. 12h5 j 2
40. Factor the Trinomial n 2  4n  12
a.
b.
c.
d.
 n  6
 n  6 n  2
 n  6 n  2
 n  6 n  2
2
41. Factor the Trinomial x 2  15 x  50
a.
b.
c.
d.
 x  5
 x  25 x  2
 x 10 x  5
 x 10 x  5
2
42. Solve the equation with fractions.
1
1
 6 x  24   20  12 x  72 
3
4
43. Solve the equation with fractions.
1
4 1
2
x  x 2
5
5 3
3
44. Determine which fraction is bigger in each set.
4 2
or
a.
5 3
5 5
or
b.
8 3
9
7
or
c.
10 8
4 6
or
d.
7 7
Name:________________________________
Answers:
1.
2.
3.
4.
5.
4, 8, 14, 16
False
4, 6, 8, 12, 14, 16, 20
8, 16
Edmontosorum, geese, swans, platypus,
moles, my cat, rabid skunks
6. Platypus
7. True (compliment)
8.
Composition
9
23. 24 possible arrangements size, sleeve, color
8 sage possibilities
24. 1/24
25. Probability of green:
Probability of green & green without
replacement:
24
2
neither class : 2
either class: 38
probability taking only chemistry: 24/40=60 %
9.
=u
10.
=
=
11.
12.
29. Congruency statement for the figures:
2 4 6
8 12
14 16
18
10
20
C
B
G
D
D
B
X  Y  4  x  12
X  Y  2  x  16
20.
 X  8  X  6  all integers
 X  8  X  6  6  X  8
6   X  8
21. C
22. A
ABCDEF  OPQRST
Y
X
13.
14.
15.
16.
17.
18.
19.
1
20
26. Probability of red, then black without
replacement: 7/80
27. Probability of not rap: 5/9
28. Identification of angles:
Vertical Angles
Corresponding Angles
2&4
1&8
1&3
4&7
5&7
2&5
6&8
3&6
Alternate Interior
Alternate Exterior
3&8
1&6
4&5
2&7
Congruent Angles
1, 3, 8 & 6
2, 4, 5 & 7
Chemistry
5
1
4
5
25
35
15
30
40
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
X=9
Y= 18
W  B
X=3
Y = 10
C
B
B
C
D
C
C
X=6
X=12
4
5
5
b.
3
9
c.
10
6
d.
7
44. a.