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Generation Date: 02/15/2011
Generated By: Rachael Pringle
Plots and Diagrams
1. The following stem-and-leaf plot shows the average temperature over the last 10
months.
5 6 8
6 3 5 6
7 0 2 5
8 2 6
What is the highest average temperature over the last 10 months?
A. 66°
B. 82°
C. 86°
D. 89°
Patterns
2.
The pattern above is a segment of a long necklace. The pattern is repeated in the
necklace. If the necklace is 154 beads long, how many pattern segments will the
necklace have?
A. 28 segments
B. 15 segments
C. 14 segments
D. 13 segments
Pythagorean Theorem
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3.
*Note: Figure not drawn to scale.
If X = 3 cm and Z = 5 cm, what is the length of Y?
A. 16 cm
B. 5 cm
C. 3 cm
D. 4 cm
Estimate Solutions
4. Max has between 82 and 97 trees he needs to plant. He wants to make exactly 9
rows of trees keeping about the same number of trees in each row. Which of the
following is a reasonable number of trees Max should plant in each row?
A. 8
B. 10
C. 12
D. 6
Angles, Lines, & Objects
5. What three-dimensional object can be made by folding the following pattern?
A. cube
B. triangle
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C. pyramid
D. cone
Plots and Diagrams
6. This data set indicates the number of times a group of middle school students
went to the movies last month.
3, 1, 5, 2, 2, 4, 1, 3, 14, 2, 1, 4
Which of these entries is the outlier?
A. 2
B. 5
C. 1
D. 14
Patterns
7. Which expression below produces the n th term in the sequence?
29 , 34 , 39 , 44 , 49 , ...
A. 25 + 5n
B. 33 - 4n
C. 34 - 5n
D. 24 + 5n
Pythagorean Theorem
8.
*Note: Figure not drawn to scale.
If X = 6 cm and Y = 8 cm, what is the length of Z?
A. 10 cm
B. 7 cm
C. 8 cm
D. 11 cm
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Estimate Solutions
9. Jason earned $400 working at a restaurant. He spent $31.46 at a concert and
$20.52 at an arcade. He put the rest of the money in his savings account. About
how much money did Jason put in his savings account?
A. Between $335 and $345
B. Between $325 and $335
C. Between $315 and $325
D. Between $345 and $355
Angles, Lines, & Objects
10.
Lines AB and CD are parallel. If
Z?
X equals 52°, then what is the measurement of
A. 45°
B. 128°
C. 135°
D. 52°
Plots and Diagrams
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11.
How many students scored 61 or above on the final exam?
A. 23
B. 4
C. 26
D. 12
Patterns
12.
In the pattern above, how many blue dots will the diagram have in position 2?
A. 5
B. 3
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C. 2
D. 4
Pythagorean Theorem
13.
*Note: Figure not drawn to scale.
If X = 7.5 cm and Z = 19.5 cm, what is the length of Y?
A. 17 cm
B. 16 cm
C. 18 cm
D. 20 cm
Estimate Solutions
14. Don gets off of work at 6:30 and is planning on meeting some friends to watch
the football game. On the way to the game he plans to stop at a fast food
restaurant to get a quick bite to eat. At what time should he tell his friends he
will arrive at the game?
In the question above, does Don need to give his friends an exact time or an
estimated time that he will arrive at the game?
A. an exact time
B. an estimated time
Angles, Lines, & Objects
15. Angles
A and
B are supplementary. If
A is 71°, what is the measure of
B?
A. 19°
B. 71°
C. 109°
D. 119°
Plots and Diagrams
16. The following stem-and-leaf plot shows the range of 10 numbers.
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123 5
124 0 2 3
125 0 5 5
126 0 2 4
What is the highest number?
A. 126024
B. 1264
C. 126
D. 1260
Patterns
17.
In the sequence above, the triangle is the first shape. What would be the sixth
shape in this sequence?
A. 8-sided shape
B. 7-sided shape
C. 16-sided shape
D. 6-sided shape
Pythagorean Theorem
18. Ben is building a storage box for the sail of his boat. The left side of the box is
3 ft long and the right side of the box is 4 ft long. The left and right side form a
right angle, as shown in the picture below.
What is the length of the base of the box?
A. 7 ft
B. 4.5 ft
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C. 3.5 ft
D. 5 ft
Estimate Solutions
19. Jessica has a part-time job at the water park. She makes between $50.34 and
$60.73 a day. Which of the following is a reasonable amount of money Jessica
makes for working 9 days?
A. $483.00
B. $432.00
C. $609.00
D. $440.00
Angles, Lines, & Objects
20. Angles
B?
A and
B are complementary. If
A is 11°, what is the measure of
A. 11°
B. 79°
C. 169°
D. 78°
Plots and Diagrams
21. How would the number 55,133 be displayed on a stem-and-leaf plot?
A. stem leaf
55 133
B. stem leaf
5513 3
C. stem
leaf
55000 133
D. stem leaf
551 33
Patterns
22. What is the missing number in this sequence?
6 , -4 , -14 , ___ , -34
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A. -25
B. -22
C. -27
D. -24
Pythagorean Theorem
23.
*Note: Figure not drawn to scale.
If X = 7.5 cm and Y = 18 cm, what is the length of Z?
A. 20.5 cm
B. 18.5 cm
C. 21.5 cm
D. 19.5 cm
Estimate Solutions
24. Karen bought a sapphire bracelet for $7,140. She had to pay an additional 10
percent of the purchase price to cover the sales tax and to purchase jewel mount
insurance. Which of the following is the closest to the total amount paid by
Karen?
A. $7,550
B. $8,250
C. $8,600
D. $7,900
Angles, Lines, & Objects
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25.
Lines AB and CD are parallel. If
O?
X equals 32°, then what is the measurement of
A. 148°
B. 32°
C. 154°
D. 41°
Plots and Diagrams
26. Which of the following would be best displayed on a scatter plot?
A. the amount of money in a bank account over the course of a year
B. the percentage of students in each grade at Peterson High School
C. the size of a home and the household electricity bill
D. the type of car owned and the number of members in the family
Patterns
27.
In the pattern above there are 7 figures. If the pattern is repeated indefinitely,
what is the shape and color of figure 25?
A. red circle
B. green circle
C. yellow circle
D. purple diamond
Pythagorean Theorem
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28. Two friends leave school at the same time, Sarah is heading due north and Beth
is heading due east. One hour later they are 10 miles apart. If Sarah had
traveled 8 miles from the school, how many miles had Beth traveled?
A. 4 miles
B. 10 miles
C. 2 miles
D. 6 miles
Estimate Solutions
29. Frank bought a Y-Box for $57.00 during Game World's Semi-Annual Gaming
Blowout. If the original price of the Y-Box is $145.00, about what percentage of a
discount did Frank receive?
A. 65%
B. 50%
C. 55%
D. 60%
Angles, Lines, & Objects
30.
The pattern above could be folded to produce what kind of three-dimensional
figure?
A. triangle base pyramid
B. rectangular prism
C. rectangular base pyramid
D. triangular prism
Plots and Diagrams
31. Mrs. Franklin is having her broken window repaired. She has had the following
estimates done so far: $159, $140, $143, $144, $166, $149, $160, $171. How
many stems will be on a stem-and-leaf plot that displays this information?
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A. zero
B. three
C. four
D. eight
Patterns
32. What is the value of the 8th term in the sequence?
-5 , -9 , -13 , -17 , -21 , ...
A. -33
B. -31
C. -35
D. -37
Pythagorean Theorem
33. Mrs. Bird set-up her kindergarten classroom so that there was a right triangular
shaped reading area formed by the bookshelves. As shown in the picture below.
If bookshelf A is 6 feet long and bookshelf B is 8 feet long, what is the length of
bookshelf C?
A. 12 feet
B. 10 feet
C. 14 feet
D. 16 feet
Estimate Solutions
34. Every day on his way to school, Wally goes to breakfast and buys one bagel for
$1.67 and an orange juice for $3.33. Which of the following is a reasonable
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amount Wally would spend on 45 breakfasts?
A. $225
B. $2,250
C. $45
D. $180
Angles, Lines, & Objects
35.
Lines AB and CD are parallel. If
of Y?
N equals 39°, then what is the measurement
A. 39°
B. 141°
C. 28°
D. 49°
Plots and Diagrams
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36.
How many more students scored between 81 and 90 than between 71 and 80?
A. 3
B. 10
C. 14
D. 7
Patterns
37.
If the 7-bead segment above is repeated several times to create a necklace with
28 beads, how many oval-shaped beads will the necklace have?
A. 8
B. 12
C. 4
D. 6
Pythagorean Theorem
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38.
*Note: Figure not drawn to scale.
If Y = 16 cm and X = 12 cm, what is the length of Z?
A. 20 cm
B. 22 cm
C. 24 cm
D. 19 cm
Estimate Solutions
39. Mrs. Walker has $2,281.22 to give out to her 19 grandchildren. She wants to
give the same amount to each grandchild. Which of the following is the best
estimate of how much each grandchild should receive?
A. Between $135 and $145
B. Between $115 and $125
C. Between $105 and $115
D. Between $95 and $105
Angles, Lines, & Objects
40.
Which of the following are alternate exterior angles?
A.
B and
E
B.
A and
H
C.
E and
H
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D.
A and
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E
Plots and Diagrams
41.
This box plot represents the number of absences in middle school classes this
year. What can be interpreted from this box plot?
A. 50% of the classes had ten absences.
B. 50% of the classes had eight or fewer absences.
C. 50% of the classes had fewer than four absences.
D. 50% of the classes had nine or more absences.
Patterns
42. What is the pattern for this sequence?
11 , 8 , 5 , 2 , -1 , ...
A. The sequence decreases by multiples of 4: first by 4, then 8, then 12, then 16.
B. Each number in the sequence is 2 less than the previous number.
C. Each number in the sequence is 3 less than the previous number.
D. The sequence decreases by multiples of 3: first by 3, then 6, then 9, then 12.
Pythagorean Theorem
43. Anthony was mapping out a route to ride his bike. The route he picked forms a
right triangle, as shown in the picture below.
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If the route takes him 10 miles on Forrest Lane and 26 miles up Cedar Drive,
how far will Anthony ride down Pine Avenue?
A. 24 miles
B. 16 miles
C. 30 miles
D. 36 miles
Estimate Solutions
44. Jed lives on a busy street. Six to nine cars pass by Jed's house every five
minutes. Which of the following is a reasonable number of cars which pass by
Jed's house in 60 minutes?
A. 69
B. 96
C. 124
D. 134
Angles, Lines, & Objects
45.
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Lines AB and CD are parallel. If
Z?
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X equals 36°, then what is the measurement of
A. 140°
B. 36°
C. 35°
D. 144°
Plots and Diagrams
46. Jeremy is doing a project for his health class. He wants to know if there is a
correlation between the month a person is born and their heart rate. He collected
some data and displayed it in the scatter plot below.
What can be interpreted from this data?
A. There is a positive correlation between the month a person is born and their heart rate.
B. There is no correlation between the month a person is born and their heart rate.
C. There is a negative correlation between the month a person is born and their heart rate.
D. There is both a positive and negative correlation between the month a person is born and their
heart rate.
Patterns
47.
INPUT (n) OUTPUT
11
30
12
33
15
42
17
19
54
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21
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60
What number sentence would you use to figure out what number goes in the
empty box above?
A. n + 21
B. n + 24 - 5
C. n - 1 × 3
D. (n - 1) × 3
Pythagorean Theorem
48. Raymond was riding a zip-cable from the top of a viewing post. The cable is 60
yards long. The viewing post is 48 yards high and forms a right angle with the
ground, as shown in the picture below.
Given this information, how far is the bottom of the cable from the base of the
viewing post?
A. 36 yards
B. 72 yards
C. 48 yards
D. 24 yards
Estimate Solutions
49. Bobby went to the store and bought 12 boxes of oranges. The lightest box
weighed 38.75 pounds. The heaviest box weighed 45.85 pounds. Which of the
following could be the total weight of the orange boxes?
A. 436 pounds
B. 503 pounds
C. 582 pounds
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D. 563 pounds
Angles, Lines, & Objects
50.
Which of the following are alternate interior angles?
A.
A and
D
B.
C and
F
C.
F and
G
D.
D and
F
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Answers
1.
C
2.
C
3.
D
4.
B
5.
C
6.
D
7.
D
8.
A
9.
D
10. B
11. C
12. B
13. C
14. B
15. C
16. B
17. A
18. D
19. A
20. B
21. B
22. D
23. D
24. D
25. B
26. C
27. A
28. D
29. D
30. D
31. C
32. A
33. B
34. A
35. A
36. D
37. A
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38. A
39. B
40. B
41. B
42. C
43. A
44. B
45. D
46. B
47. D
48. A
49. B
50. B
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Explanations
1.
The leaf is always the last digit in the number (the ones place) and the stem is the entire number
except the last digit (that is the tens place or the tens place and hundreds place). The highest
value of a stem is 8; the highest value among its leaves is 6.
8 |2 6
8 | 6 = 86
2.
Each segment has 11 beads. If the necklace is 154 beads long, 154 divided by 11 (the beads in
each segment) is 14. So, there are 14 segments in the necklace.
3.
Use the Pythagorean theorem.
3 2 + Y2 = 5 2
9 + Y2 = 25
Y2 = 25 - 9
Y2 = 16
Y = 4
4.
To find a range for the possible number of trees per row, divide the number of trees by the number
of rows.
82 trees ÷ 9 rows = 9.11 trees per row
97 trees ÷ 9 rows = 10.78 trees per row
The range is from 9.11 to 10.78.
The only answer choice within the range is 10.
5.
When the end points are brought together to form a three-dimensional object, this star shape
creates a pyramid.
6.
The outlier is the one piece of data that is outside the range of the other values. When a box plot
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is made of this data, "14" falls well beyond the range of the other entries.
7.
Each number in the sequence is 5 more than the previous number.
In sequences that have a common difference, find the expression for the nth term, t n, using the
following formula, where t 1 is the first term, d is the common difference, and n is the term
number.
t n = t 1 + d(n - 1)
Since 29 is the first term and 5 is the common difference, plug in 29 for t 1 and 5 for d.
t n = 29 + 5(n - 1)
= 29 + 5n - 5
= 24 + 5n
So, the expression that produces the n th term in the sequence is 24 + 5n.
8.
Use the Pythagorean theorem.
6 2 + 8 2 = Z2
36 + 64 = Z2
100 = Z2
10 = Z
9.
Round the amounts he spent:
$31.46 to $30.00
$20.52 to $20.00
He spent about $50.00 altogether.
Subtract $50.00 from $400.00 to find out about how much money Jason put in his savings account.
$400.00 - $50.00 = $350.00
$350.00 is between $345 and $355
10. In this picture, X and Z are supplementary angles. Therefore, subtract 52° from 180° to find the
measurement of angle Z.
180° - 52° = 128°.
11. The lowest interval on this histogram is 61-70. Therefore, all test scores shown in this histogram
are above 60. So, add all the numbers together.
4 + 8 + 11 + 3 = 26
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12. The pattern should be consistent from diagram to diagram. In each of these diagrams, the red dots
make up the perimeter of the triangles, with the blue dots filling in the rest. The triangle perimeters
increase by 3 dots with each consecutive diagram.
Keeping with this pattern, diagram 2 would have 3 blue dots.
13. Use the Pythagorean theorem.
Y2 + 7.5 2 = 19.5 2
Y2 + 56.25 = 380.25
Y2 = 380.25 - 56.25
Y2 = 324
Y = 18
14. Since this is just a group of friends meeting at a sporting event as spectators, the time of arrival is
not critical. Therefore, Don can give his friends an estimated time of his arrival.
15. Two angles are supplementary if the sum of their measures equals 180°.
16. The highest number on the stem side is 126; the highest number on the leaf side for that stem is
4.
126 | 4 = 1264
17. In the pattern above, each shape has one more side than the previous shape. The fourth shape has
6 sides. The sixth shape is two shapes after the fourth shape.
So, the sixth shape will have 6 + 2 = 8 sides.
18. Let x represent the length of the left side, y represent the length of the right side, and z represent
the length of the base. Now, use the Pythagorean theorem.
x 2 + y 2 = z2
(3 ft) 2 + (4 ft)2 = z2
25 ft2 = z2
5 ft = z
So, the length of the base is 5 feet.
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19. First, round the high and low amounts of money she makes.
$50.34 to $50.00
$60.73 to $60.00
Then, multiply the dollar amounts by the number of days she works to find a range for the total
amount of money she can make.
9 × $50.00 = $450.00
9 × $60.00 = $540.00
The range is from $450.00 to $540.00.
The only answer choice in this range is $483.00.
20. Two angles are complementary if the sum of their measures equals 90°.
21. When the number is broken into a "stem" and a "leaf," the leaf is always the last digit in the
number (the ones place) and the "stem" is the entire number except the last digit (in this example,
it's the digits in the tens, hundreds, thousands, and ten-thousands place).
22. Each number in the sequence is 10 less than the previous number.
23. Use the Pythagorean theorem.
7.5 2 + 18 2 = Z2
56.25 + 324 = Z2
380.25 = Z2
19.5 = Z
24. Karen bought the bracelet for $7,140 plus an additional 10 percent.
Total price = purchase price + tax & insurance
= $7,140 + ($7,140)(10%)
= $7,140 + ($7,140)(0.1)
= $7,140.00 + $714.00
= $7,854.00
So, $7,900 is the closest amount to the actual price paid.
25.
X and
O are alternate interior angles. Therefore, they are congruent.
26. Scatter plots are used to examine two sets of data -- such as the size of a home and the household
electricity bill -- and to investigate the correlation between the two variables; that is, to see if one
event has an effect on the other.
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27. There are 7 figures in the pattern. Using division, 25 figures divided by 7 gives us 3 patterns with 4
left over. Starting at the left, 4 figures over is a red circle.
28. Let x represent the distance traveled by Sarah, y represent the distance traveled by Beth, and z
represent the distance between the two friends. Now, use the Pythagorean theorem.
x 2 + y 2 = z2
(8 miles) 2 + y2 = (10 miles) 2
64 miles 2 + y2 = 100 miles 2
y2 = 100 miles 2 - 64 miles 2
y2 = 36 miles 2
y = 6 miles
So, Beth traveled 6 miles east.
29. The original price of the Y-Box is $145.00 and the sale price is $57.00.
Original Price - Sale Price = Price Discount
$145.00 - $57.00 = Price Discount
$88.00 = Price Discount
Now, calculate the discount as a percentage
Price Discount
Original Price
$88.00
$145.00
= % Off
= % Off
0.607 = % Off
So, Frank bought the Y-Box for approximately 60% off.
30. This pattern contains 2 triangles and 3 rectangles. They could only be combined to form a
triangular prism.
31. The stem is the entire number except the last digit (that is the tens place or the tens place and
hundreds place). In this plot, the stems are:
15, 14, 14, 14, 16, 14, 16, 17. Notice some of the numbers are duplicates.
Therefore, there are four stems in this plot.
32. To figure out the 8 th term in the sequence, first figure out the equation for the n th term. Each
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number in the sequence is 4 less than the previous number.
(-5 + 4) - 4n
-1 - 4n
Now plug in 8 for n:
-1 - (4 × 8) = -33
33. Let x represent the length of bookshelf A, y represent the length of bookshelf B, and z represent
the length of bookshelf C. Now, use the Pythagorean theorem.
x 2 + y 2 = z2
(6 ft) 2 + (8 ft)2 = z2
100 ft2 = z2
10 ft = z
So, the length of bookshelf C is 10 feet.
34. Round the prices for the bagel and the juice.
$1.67 to $2
$3.33 to $3
Wally spends about $5 per day on breakfast.
In 45 days, Wally will spend about $5 × 45 = $225.
35.
N and
Y are alternate exterior angles. Therefore, they are congruent.
36. The bar for interval 81 to 90 goes up to 14.
The bar for interval 71 to 80 goes up to 7.
The difference between these two intervals is 14 - 7 = 7.
37. One segment has 2 oval beads and 7 beads total. First, find out how many segments will be in a
necklace of 28 beads by dividing 28 by 7:
28 ÷ 7 = 4 segments
Since there are 2 oval beads per segment, multiply the number of segments by 2 to find the total
number of oval beads in the necklace:
4 × 2 = 8 oval beads
So, the necklace will have 8 oval beads.
38. Use the Pythagorean theorem.
16 2 + 12 2 = Z2
Z2
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256 + 144 = Z2
400 = Z2
20 = Z
39. First, round $2,281.22 to $2,280.00.
Then, divide the rounded dollar amount by the number of grandchildren.
$2,280.00 ÷ 19 = $120.00
$120.00 is between $115 and $125
40. Lines 1 and 2 are parallel and they are intersected by line 3. By definition,
alternate exterior angles and B and G are alternate exterior angles.
A and
H are
41. The median -- the middle value -- represents 50% of the data. The median is indicated in the box
plot by a vertical line drawn through the box. In this box plot the median is 8, which indicates 50%
of the classes had eight or fewer absences.
42. To determine the rule of this sequence, find the difference between consecutive terms.
8 - 11 = -3
5 - 8 = -3
2 - 5 = -3
-1 - 2 = -3
Therefore, each number in the sequence is 3 less than the previous number.
43. Let x represent how far Anthony rode on Forrest Lane, y represent how far he rode down Pine
Avenue, and z represent how far he rode up Cedar Drive. Now, use the Pythagorean theorem.
x 2 + y 2 = z2
(10 miles) 2 + y2 = (26 miles) 2
100 miles 2 + y2 = 676 miles 2
y2 = 676 miles 2 - 100 miles 2
y2 = 576 miles 2
y = 24 miles
So, Anthony rode 24 miles down Pine Avenue.
44. In 60 minutes, there are 12 sets of five minutes.
If every 5 minutes, about 6 to 9 cars pass by Jed's house, then in 60 minutes, 12 times that
amount of cars will pass by.
Find the range of cars which pass by Jed's house in 60 minutes.
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6 × 12 = 72 cars
9 × 12 = 108 cars
The range is from 72 to 108.
The only answer choice in this range is 96.
45. In this picture, X and Z are supplementary angles. Therefore, subtract 36° from 180° to find the
measurement of angle Z.
180° - 36° = 144°.
46. Study the data points on the plot. The points follow no particular trend. Therefore, there is no
correlation.
47. Try to recognize a pattern.
Look at the numbers in the first row of the table.
30 is equal to 3 times one less than 11.
(11 - 1) × 3 = 30
Now, look at the numbers in the second row.
33 is equal to 3 times one less than 12.
(12 - 1) × 3 = 33
Checking the other rows, we see that the pattern continues.
So, the number sentence describing the input-output table is (n - 1) × 3.
48. Let x represent the height of the viewing post, y represent the how far the base of the viewing post
is from the end of the cable, and z represent the length of the cable. Now, use the Pythagorean
theorem.
x 2 + y 2 = z2
(48 yd)2 + y2 = (60 yd)2
2,304 yd2 + y2 = 3,600 yd2
y2 = 1,296 yd2
y = 36 yd
So, the end of the cable is 36 yards from the base of the viewing post.
49. Use the lightest and heaviest weights of the boxes to get a weight range for 12 boxes.
12 × 38.75 = 465 pounds
12 × 45.85 = 550.2 pounds
The range is from 465 to 550.2 pounds.
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The only answer choice within this range is 503 pounds.
50. Lines 2 and 3 are parallel and they are intersected by line 1. By definition,
alternate interior angles and D and E are alternate interior angles.
C and
F are
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