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Ludus for Mathematics
Mathematics Grade 9/10 – B
Levels 10, 11, 12
Ver 2010JAN11
Barnacle Bill
Originator
Prepared for Learners in Adams County School District 50 to achieve proficient or advanced on all assessments
related to Mathematics topics contained herein. Use Permissions Contact: [email protected] Not for sale or
publishing. Classroom use only.
Barnacle Bill
Synthesizer
Science Content
Questions
Topics
1-10
Solving Problems with Measures
11-20
Reviewing Scale Drawings
21-30
Using Number Sense
31-40
Perimeter, Area, Volume
41-50
What Happens When Dimensions
Change?
51-60
Transformations on a Coordinate Plane
61-70
Congruence, Parallelism, and
Perpendicularity
Mathematics Grade 9
Levels 10, 11, 12
2
3
4
5
6
7
Directions: Click on the
yellow numbered buttons to
select a question. They are
active.
8
9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
Question 1
A nylon rope 7 feet in length was
divided in half. Each half length is now
_____.
a. 3 ft
b. 3 ft 4 in
c. 3 ft 6 in
d. 3 ft 8 in
Answer
Answer 1
c. 3 ft 6 in
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Question 2
Four measurements were
recorded for the length of a
corn field. Select the most
precise measurement.
f. 0.03 km
g. 30 m
h. 3000 cm
j. 30,000 mm
Answer
Answer 2
j. 30,000 mm
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Question 3
Place these measurements in order of
least precise to most precise.
cup, pint, quart, gallon
a. gallon, quart, pint, cup
b. cup, pint, quart, gallon
c. quart, gallon, cup, pint
d. gallon, quart, cup, pint
Answer
Answer 3
a. gallon, quart, pint, cup
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Question 4
Person A is 6 ft 1 in tall. Person B is
4 ft 8 in tall. Determine the
difference in height between the two
persons.
f. 5 in
g. 1 ft 5 in
h. 2 ft 5 in
j. 2 ft 7 in
Answer
Answer 4
g. 1 ft 5 in
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Question 5
Determine the total capacity of 8
containers of perfume if each container
holds 800 mL.
a. 6 L 100 mL
b. 6 L 400 mL
c. 6 L 600 mL
d. 7 L 200 mL
Answer
Answer 5
b. 6 L 400 mL
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Question 6
Determine the number of grams there are in
3 Kg 264 g.
f. 3.264
g. 32.64
h. 326.4
j. 3264
Answer
Answer 6
j. 3264
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Question 7
If
4,
a.
b.
c.
d.
you multiply 6 qt 20 fl oz by
how many fl oz do you get?
848
768
586
104
Answer
Answer 7
a. 848
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Question 8
The length of a hallway is 5 m 27
cm. Determine this length in cm.
f. 5.27
g. 52.7
h. 527
j. 5270
Answer
Answer 8
h. 527
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Question 9
Order these units of measure from most precise
to least precise.
meter, centimeter, millimeter, kilometer
a.
b.
c.
d.
millimeter, centimeter, meter, kilometer
kilometer, meter, centimeter, millimeter
kilometer, meter, millimeter, centimeter
millimeter, meter, centimeter, kilometer
Answer
Answer 9
a. millimeter, centimeter, meter,
kilometer
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Question 10
Three boxes of Ramen each
weigh 6 lb 12 oz. Determine the
total weight of the boxes.
f. 19 lb 4 oz
g. 19 lb 8 oz
h. 20 lb 2 oz
j. 20 lb 4 oz
Answer
Answer 10
j. 20 lb 4 oz
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Question 11
How do you know 42 is divisible by 6?
I can apply the Divisibility Rule:
a. The sum of the digits is divisible
by 6.
b. The last two digits form a number
divisible by 6.
c. The number is divisible by both 2
and 3.
d. The sum of the digits is divisible
by 6.
Answer
Answer 11
c. The number is divisible by
both 2 and 3
42 is divisible by both 2 and 3.
Divisibility Rule for 6
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Question 12
Which of the following numbers is
a perfect square? Why?
a. 20
b. 50
c. 100
d. 150
Answer
Answer 12
c. 100
10 x 10 = 100
A number x itself forms a
perfect square.
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Question 13
A _____ is a comparison of two
numbers by division.
Answer
Answer 13
A ratio is a comparison of two
numbers by division.
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Question 14
Express each rate as a unit rate.
$50 for 4 days of work
3 feet of snow in 5 hours
Answer
Answer 14
$50 for 4 days of work
Divide the both the numerator &
denominator by 4.
$50/4d = $12.50/1d
3 feet of snow in 5 hours
Divide the both the numerator &
denominator by 5
3ft/5h = 0.6ft/1h
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Question 15
Simplify.
(ab4)(ab2)
(p5q4)(p2q)
(-7c3)(4c)
Answer
Level 11
Answer 15
Simplify.
(ab4)(ab2)
(p5q4)(p2q)
(-7c3)(4c)
a(1+1)b(4+2)
p(5+2)q(4+1)
(-7.4)c(3+1)
a2b6
p7q5
-28c4
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Question 16
Select the factor form numbers from
below.
a. 6,345
b. 6.345 x 103
c. 6.345 x 10 x 10 x 10
d. 0.006345
e. 6.345 x 10-3
f. 6.345 x 10-1 x 10-1 x 10-1
Answer
Answer 16
Select the standard form numbers from
below.
c. 6.345 x 10 x 10 x 10
f. 6.345 x 10-1 x 10-1 x 10-1
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Question 17
A value in a matrix is called a(n)
a. array
b. element
c. dimension
d. equality
Answer
Answer 17
elements
elements
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Question 18
An exponential function can be
written in the form (standard form)
_____.
a. y = ax
b. y = ax2 + bx + c
c. y = bx + c
Answer
Answer 18
a. y = ax
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Question 19
8 1/3 ÷ 6 2/3 = ?
a.
b.
c.
d.
e.
1 ¼
1 2/3
2 ½
2 2/3
55 4/9
Answer
Answer 19
a. 1 ¼
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Question 20
The science lab measures 14 ft
by 20 ft. If you were to make a
scale drawing of the room, what
scale would you use on a sheet of
paper that measures 8.5 in by 11
in ?
Answer
Answer 20
Possible answers include:
½ in = 1 ft
¼ in = 1 ft
1 in = 2 ft
An answer that will not work is
1 in = 1 ft
because it will not fit on the paper.
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Question 21
How do you know 2,324 is divisible by 4?
I can apply the Divisibility Rule:
a. the sum of the digits is divisible by 4.
b. The last two digits form a number divisible
by 4.
c. The number is divisible by both 2 and 3.
d. The sum of the digits is divisible by 4.
Answer
Answer 21
d. The last two digits form a
number divisible by 4.
Divisibility Rule for 4
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Question 22
Which of the following numbers is a
perfect square? Why?
a. 121
b. 144
c. 169
d. 196
Answer
Answer 22
a, b, c, and d are all
perfect squares.
11 x 11 = 121
12 x 12 = 144
13 x 13 = 169
14 x 14 = 196
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Question 23
When a ratio compares a number to
100, it can be written as a _____.
Answer
Answer 23
percent
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Question 24
For the 2000 census, the population of
Texas was about 20,900,000 and the
population of Illinois was about
12,500,000. There were 30 members of
the U.S. House of Representatives from
Texas and 19 from Illinois. In which state
did a member represent more people?
Answer
Answer 24
Texas: 20,900,000 people ≈ 700,000 people
30 representatives
1 representative
Divide numerator & denominator by 30.
Illinois: 12,500,000 people ≈ 660,000 people
19 representatives 1 representative
Divide the numerator &
denominator by 19.
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Question 25
Express the area of the
figure as a monomial.
a2b
a2b
Answer
Answer 25
Express the area of the
figure as a monomial.
a2b = s
a2b = s
Area = side . side
A = s . s
A = a2b . a2b
A = a(2+2)b(1+1)
A = a4b2
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Question 26
Select the scientific notation numbers
from below.
a. 12,322
b. 8.423 x 107
c. 6.3457 x 10 x 10 x 10 x 10
d. 0.000006345
e. 3.895 x 10-8
f. 2.345 x 10-1 x 10-1 x 10-1
Answer
Answer 26
Select the scientific notation numbers
from below.
b. 8.423 x 107
e. 3.895 x 10-8
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Question 27
State the dimensions of the matrix below.
Answer
Answer 27
2 x 3
2 rows and 3 columns
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Question 28
The y-intercept for the exponential function
graphed below is _____.
Answer
Answer 28
y = 1
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Question 29
In a group of 25 students, 16 are female. What
percentage of the group are female?
a. 16%
b. 40%
c. 60%
d. 64%
e. 75%
Answer
Answer 29
d. 64%
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Question 30
An advantage of sexual reproduction over asexual
reproduction is that it allows _____.
a. protection for the offspring.
b. more offspring to be produced.
c. more genetic variation among the offspring.
d. all of the above.
e. none of the above.
Answer
Answer 30
c. more genetic variation
among the offspring.
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Question 31
How do you know 567 is divisible by 9?
I can apply the Divisibility Rule:
a. The sum of the digits is divisible
by 3.
b. The last two digits form a number
divisible by 9.
c. The number is divisible by both 2
and 3.
d. The sum of the digits is divisible
by 9.
Answer
Answer 31
d. The sum of the digits is
divisible by 9.
Divisibility Rule for 9
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Question 32
Determine the square root
of 225 (√225).
a. 14
b.15
c. 16
d. 17
Answer
Answer 32
b. 15
√225 = 15
15 x 15 = 225
In this case multiplying the
square roots together for the
perfect square 225.
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Question 33
If Juan answered 8 out of 10 questions
correctly, which diagram represents this ratio?
B
A
C
Answer
Answer 33
B
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Question 34
You have a Trail Mix Recipe for six
people. This recipe requires you to
combine 3 cups of raisins with 6 cups
of peanuts. But only you and your
significant other will be going on the
hike in El Dorado Canyon. How do you
modify the recipe for only two
people?
Answer
Answer 34
6 people
Raisins
2 people
Divide the 6
people by 3 and
divide the recipe
proportions by 3.
Peanuts
1 cup of raisons & 2 cups
of peanuts for 2 people.
Raisins
Peanuts
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Question 35
Simplify each expression.
x0y 4
y2
2x3y2z5
10xy3z4
Answer
Answer 35
Simplify each expression.
x 0y4
y2
2x3y2z5
10xy3z4
y(4-2)
0.2x(3-1)y(2-3)z(5-4)
y2
0.2x2y-1z1
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Question 36
Show that 2.35 x 10-5 < 1 and
2.35 x 103 > 1 by creating a
table.
Answer
Answer 36
Show that 2.35 x 10-5 < 1 and
2.35 x 103 > 1.
Scientific
Factor Form
Standard
Notation
Form
2.35 x 10-5 2.35 x 10-1 x 10-1 x 10-1 x 10-1 x 10-1 0.0000235< 1
2.35 x 103
10-1 = 1/10 = 0.1
2.35 x 101 x 101 x 101
2350 > 1
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Question 37
Two matrices are considered _____ when
they have the same dimensions and if each
element of one matrix is equal to the
corresponding element of the other matrix.
a. square matrices
b. zero matrices
c. row matrices
d. column matrices
e. equal matrices
Answer
Answer 37
e. equal matrices
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Question 38
Select the graph representing a growth curve.
Answer
Answer 38
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Question 39
At the end of the season, a team’s ratio
of wins to losses was 3:5. If there were
no ties, what percentage of its games
did the team win?
f. 33 1/3%
g. 37 ½%
h. 40%
j. 60%
k. 62 ½%
Answer
Answer 39
g. 37 ½%
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Question 40
What is the greatest of the numbers 132, 361,
36, 312, and 123?
a. 132
b. 361
c. 36
d. 312
e. 123
Answer
Answer 40
d. 312
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Question 41
How do you know 525 is divisible by 5?
I can apply the Divisibility Rule:
a. The sum of the digits is divisible by 5.
b. The last digit is a number divisible by
5.
c. The number is divisible by both 2 and
5.
d. The sum of the last two digits is
divisible by 5.
Answer
Answer 41
b. The last digit is a number
divisible by 5.
Divisibility Rule for 5
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Question 42
√625 = ?
a. 15
b.20
c. 25
d. 30
Answer
Answer 42
c. 25
√625 = 25
25 x 25 = 625
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Question 43
Complete the ratios for the diagram below. (Yellow &
Total) Which answer is the fraction format?
___ out of ___
____ : ____
____ / ____
Answer
Answer 43
31 out of 88
31:88
31/88 
fraction format
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Question 44
Express each ratio in simplest form:
14 chosen out of 70 who applied
28 out of 100 doctors (and then convert
to percent)
153 points in 18 games
Answer
Answer 44
Express each ratio in simplest form:
14 chosen out of 70 who applied
1 chosen out of 5 applicants
1 chosen / 5 applicants
1 chosen : 5 applicants
28 out of 100 doctors (and then convert to percent
7 out of 25 doctors
7/25 doctors
7 : 25 doctors
153 points in 18 games
17 points in 2 games
17 points/2 games
17 points : 2 games
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Question 45
Old Technology – The first
transatlantic cable has 51 amplifiers
along its length. Each amplifier
strengthens the signal on the cable 106
times. After it passes through the
amplifier, the signal has been boosted
106.106 times. Simplify this
expression.
Answer
Answer 45
Old Technology – The first
transatlantic cable has 51 amplifiers
along its length. Each amplifier
strengthens the signal on the cable
106 times. After it passes through the
amplifier, the signal has been boosted
106.106 times. Simplify this
expression.
106.106 = 10(6+6) = 1012
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Question 46
Travel – The number of
visitors from various
countries to the United
States in a recent year
are listed in the table.
Order the countries
according to the number
of visitors from greatest
to least.
Country
Number of
Visitors
Canada
1.46 x 107
France
1.1 x 106
Germany
1.8 x 106
Japan
5.1 x 106
Mexico
1.03 x 107
United Kingdom
4.7 x 106
Answer
Answer 46
Country
Number of
Visitors
Greatest to
Least
Canada
1.46 x 107
1
France
1.1 x 106
6
Germany
1.8 x 106
5
Japan
5.1 x 106
3
Mexico
1.03 x 107
2
United Kingdom
4.7 x 106
4
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Question 47
Add the two matrices below. Be sure
to show your method.
Answer
Answer 47
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Question 48
The amount of money spent at the Outlet Mall
continues to increase as modeled by T(x)=12.(1.12)x.
T(x) is in millions of dollars. Two marks on the domain
axis represents 1 year. A mark
on the range axis
represents 5 million
dollars. How much
money was spent at
the mall in 1995
(year 0)? How much
was spent in 2006
(year 10)?
Answer
Answer 48
Calculated for 2006:
T(x) = 12(1.12)10
= $37.3 million
About 37 million dollars
spent in 2006
About 12 million dollars
spent in 1995
Calculated for 1995:
T(x) = 12(1.12)0
= $12 million
2006 or
10 y
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Question 49
(-2)-3 + (-3)-2 =?
f. -17/72
g. -1/72
h. 0
j. 1/17
k. 17/72
Answer
Answer 49
g. -1/72
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Question 50
If x = -5, then 2x2 -6x
+5 = ?
a.-15
b.15
c.25
d.85
e.135
Answer
Answer 50
c. 25
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Question 51
How do you know 138 is divisible by 3?
I can apply the Divisibility Rule:
a. The sum of the digits is divisible by
3.
b. The last two digits form a number
divisible by 3.
c. The number is divisible by both 2 and
3.
d. The product of the digits is divisible
by 3.
Answer
Answer 51
a. a. the sum of the digits is
divisible by 3.
Divisibility Rule for 3
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Question 52
The square root of 289 is _____.
a. 9
b.14
c. 17
d. 22
Answer
Answer 52
c. 17
√289 = 17
17 x 17 = 289
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Question 53
Write an equivalent fraction for
2/5 with a denominator of 100.
Answer
Answer 53
numerator
denominator
2 x 20
5 x 20
40
100
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Question 54
Express each rate as a unit rate:
$25 for 5 dozen donuts
21.5 lbs in 12 weeks
400 m in 48.5 s
Answer
Answer 54
unit rate:
$25 for 5 dozen donuts
Divide both numerator & denominator by 5.
$5/1doz
21.5 lbs in 12 weeks
Divide both the numerator & the denominator by 12.
≈ 1.8 lbs/1 week
400 m in 48.5 s
Divide both the numerator & the denominator by 48.5.
≈ 8.25 m/1 s
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Question 55
Old Technology – The first
transatlantic cable has 51 amplifiers
along its length. Each amplifier
strengthens the signal on the cable
106 times. Represent the number of
times the signal has been boosted
after it has passed through the
first four amplifiers as a power of
106. Then simplify the expression.
Answer
Answer 55
Old Technology – The first transatlantic
cable has 51 amplifiers along its length.
Each amplifier strengthens the signal on
the cable 106 times. Represent the
number of times the signal has been
boosted after it has passed through the
first four amplifiers as a power of 106.
Then simplify the expression.
(106)4 = 10(6x4) = 1024
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Question 56
Electromagnetic
Wavelength
Electromagnetic Spectrum –
Radiation
Astronomers observe
Radiowave
10 km
electromagnetic radiation
X rays
4.5 x 10-1 nm
(including visible and non-visible)
UV rays
6.5 x 101 nm
at various wavelengths to gain
Red
6.5 x 102 nm
information and understandings
Violet
425 nm
about our cosmos. The table
Microwaves
5 x 101 mm
contains some typical
Gamma rays
800 x 10-5 nm
wavelengths of the spectrum.
Place them in order of the Hint: Convert to the same unit.
1 km = 1000 m
smallest to the largest
100 cm = 1 m
10mm = 1cm
wavelength.
1000 μm = 1 mm 1000 nm = 1 μm
Answer
Answer 56
Electromagnetic Wavelength
Radiation
Conversion to nm
10 km (1000m/km) x
(100cm/m)(10mm/cm) x
(1000μm/mm)(1000nm/μm) =
1 x 1013
Smallest to Largest
Wavelength
Radio wave
10 km
X ray
4.5 x 10-1 nm
4.5 x 10-1
2
UV ray
6.5 x 101 nm
6.5 x 101
3
Red
6.5 x 102 nm
6.5 x 102
5
Violet
425 nm
4.25 x 102
4
Microwave
5 x 101 mm
Gamma ray
800 x 10-5 nm
55 mm (1000μm/mm) x
(1000nm/μm) = 5.5 x 107
8.0 x 10-3
7
6
1
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Question 57
Answer
Answer 57
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Question 58
Which of the following equations
represents exponential growth of
compound interest?
a. y = C(1 + r)t
b. A = P(1 + r/n)nt
c. y = C(1-r)t
Answer
Answer 58
b. A = P(1 + r/n)nt
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Question 59
The formula for the lateral surface area S
of a right circular cone is S = πr√(r2 + h2),
where r is the radius of the base and h is
the altitude. What is the lateral surface
area, in square feet, of a right circular cone
with base radius 3 feet and altitude 4 feet?
f. 3π√5
g. 3π√7
h. 15π
j. 21π
k. 75π/2
Answer
Answer 59
h. 15π
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Question 60
If xyz ≠ 0, which of the following is
equivalent to
x 2y3z4
(xyz2)2
a. 1/y
b. 1/z
c. Y
d. x/yz
e. xyz
Answer
Answer 60
a. 1/y
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Question 61
Using mental math determine if
965,476 is divisible by 2, 3, 4, 5,
6, 9, or 10.
Answer
Answer 61
965,476 is divisible by 2 and 4.
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Question 62
The square root of 16 is _____.
a. 1
b. 2
c. 3
d. 4
e. 5
Answer
Answer 62
d. 4
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Question 63
Write each of the fractions below as a percent.
17/20
3/5
2/25
Answer
Answer 63
Write each of the fractions below as a percent.
17/20
3/5
2/25
17 x 5
20 x 5
3 x 20
5 x 20
2 x 4
4 x 25
85/100
60/100
8/100
85%
60%
8%
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Question 64
Given: 1 mi = 5280 ft
1 min = 60 s
1 h = 60 min
1 gal = 64 oz
1 h = 3600 s
Convert the following rate:
180 gal/h = _____oz/min
Answer
Answer 64
Given: 1 mi = 5280 ft
1 gal = 64 oz
1 min = 60 s
1 h = 3600 s
1 h = 60 min
Convert the following rate:
180 gal/h = _____oz/min
180 gal x 64 oz x 1 h = 192 oz/min
1 h x 1 gal x 60 min
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Question 65
The length of a rectangle is five times
the width of the rectangle. If the width
of the rectangle is q units, what is the
area of the rectangle?
a. 5q units2
b. 5q2 units2
c. q + 5 units2
d. 5q(q + 5) units2
Answer
Answer 65
The length of a rectangle is five times
the width of the rectangle. If the width
of the rectangle is q units, what is the
area of the rectangle?
b. 5q2 units2
5q
q
Area = length x width
A = 5q x q = 5q(1+1) = 5q2
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Question 66
The smallest unit of time is
the yoctosecond, which equals
0.0000000000000000000000
01 second. Write this number
in scientific notation.
Answer
Answer 66
The smallest unit of time is the
yoctosecond, which equals
0.000 000 000 000 000 000 000 001
second. Write this number in scientific
notation.
1 x 10-24 s
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Question 67
Complete the matrix subtraction
problem below.
Answer
Answer 67
0
-6
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Question 68
For the exponential equations below for
growth, compound interest, and decay,
y = C(1 + r)t
A = P(1 + r/n)nt
y = C(1-r)t
match the letters with what they represent.
A
C
n
P
r
t
initial value
time
principal
current value
number of times
rate
Answer
Answer 68
For the exponential equations below for
growth, compound interest, and decay,
y = C(1 + r)t
A = P(1 + r/n)nt
y = C(1-r)t
match the letters with what they represent.
A
C
n
P
r
t
initial value
time
principal
current value
number of times
Category
rate
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Question 69
The two rectangles in the figure below
have the same area. What is a
expressed in terms of b?
f. 2b/3
b
g. 3b/2
b + 3
h. 2/3b
a + 2
j. 3/2b
k. b-1
a
Answer
Answer 69
f. 2b/3
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Question 70
Which of the following is the solution
statement for the inequality -3<4x – 5 ?
a. x >2
b.x > ½
c. x < -2
d. x < ½
e. x < 2
Answer
Answer 70
b. x > 1/2
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Credits
Triumph Learning and Colorado Educators (2002) CSAP Coach, Mathematics, Grade 9. New York, NY: Triumph
Learning, Inc.
Questions and Answers were either taken directly from these sources or modified for inclusion into this learning
activity and added to the synthesizers own questions.
Used for Educational Purposes Only.