Deck 1: Introduction

Question 1

last page of a book is numbered 814 and the book is $3.00 \mathrm{~cm}$ thick. What is the average thickness of each page?

A) $2.54 \times 10^{3} \mathrm{~cm}$
B) $2.54 \times 10^{-3} \mathrm{~cm}$
C) $3.92 \times 10^{-3} \mathrm{~cm}$
D) $7.37 \times 10^{-3} \mathrm{~cm}$

Answer 1

$7.37 \times 10^{-3} \mathrm{~cm}$

Question 2

The volume of a sphere is $8.00 \mathrm{~m}$ . The radius of the sphere is

A) $1.24 \mathrm{~m}$ .
B) $2.65 \mathrm{~m}$ .
C) $2.00 \mathrm{~m}$ .
D) $3.00 \mathrm{~m}$ .

Answer 2

$1.24 \mathrm{~m}$ .

Question 3

The radius of a sphere is $2.00 \mathrm{~m}$ . The surface area of the sphere is

A) $72.5 \mathrm{~m}^{2}$ .
B) $50.3 \mathrm{~m} 2$ .
C) $75.0 \mathrm{~m}^{2}$ .
D) $36.7 \mathrm{~m}^{2}$ .

Answer 3

$50.3 \mathrm{~m} 2$ .

Question 4

1.0 kilometer equals how many nanometers?

A) 1.0 times 10¹²
B) $1.0 \times 10^{4}$
C) $1.0 \times 10^{6}$
D) $1.0 \times 10^{-3}$

Question 5

1.0 centimeter equals how many micrometers?

A) $1.0 \times 10^{-3}$
B) $1.0 \times 10^{6}$
C) $1.0 \times 10^4$
D) $1.0 \times 10^ {12}$

Question 6

1.0 micrometer equals how many millimeters?

A) $1.0 \times 10^{3}$
B) $1.0 \times 10^{-6}$
C) $1.0 \times 10^{6}$
D) $1.0 \times 10^{-3}$

Question 7

The length $4.221 \mathrm{~cm}$ is added to $0.01 \mathrm{~cm}$ . The appropriately rounded sum is

A) $4.231 \mathrm{~cm}$ .
B) $4.22 \mathrm{~cm}$ .
C) $4.21 \mathrm{~cm}$ .
D) $4.2 \mathrm{~cm}$ .
E) $4.23 \mathrm{~cm}$ .

Question 8

The length $3.76 \mathrm{~mm}$ is multiplied by $0.05 \mathrm{~mm}$ . The appropriately rounded product is

A) $0.2 \mathrm{~mm}^{2}$ .
B) $0.1881 \mathrm{~mm}^{2}$ .
C) $0.18 \mathrm{~mm}^{2}$ .
D) $0.19 \mathrm{~mm}^{2}$ .
E) $0.29 \mathrm{~mm}^{2}$ .

Question 9

The length $3.76 \mathrm{~mm}$ is multiplied by $0.0232 \mathrm{~mm}$ . The appropriately rounded product is

A) $0.0872 \mathrm{~mm}^{2}$ .
B) $0.08723 \mathrm{~mm}^{2}$ .
C) $0.09 \mathrm{~mm}^{2}$ .
D) $0.082 \mathrm{~mm}^{2}$ .
E) $0.087 \mathrm{~mm}^{2}$ .

Question 10

The length $3.76 \mathrm{~mm}$ is divided by $6 \mathrm{~mm}$ . The appropriately rounded ratio is

A) 0.627 .
B) 0.6267 .
C) 0.62666 .
D) 0.63 .
E) 0.6 .

Question 11

A cube is 1.0 inch in length on the side ( $1 \mathrm{in}=2.54 \mathrm{~cm}$ ). The volume of the cube is

A) $1.64 \times 10^{1} \mathrm{~cm}^{3}$ .
B) $1.6 \times 10^{1} \mathrm{~cm}^{3}$ .
C) $1.639 \times 10^1 \mathrm{~cm}^{3}$ .
D) $1.6387 \times 10^{1} \mathrm{~cm}^{3}$ .

Question 12

The number of seconds in exactly 30 days is

A) $2.5920 \times 106$ .
B) $2.592000 \times 106$ .
C) $2.59 \times 106$ .
D) $2.592 \times 106$ .

Question 13

The population of the United States (in 2019) is approximately 329,000,000. Write this number in scientific notation.

A) $329 \times 106$
B) $32.9 \times 10^{7}$
C) $3.29 \times 10^{7}$
D) $3.29 \times 10^{8 }$
E) $3.3 \times 10^{7}$

Question 14

Using the following unit conversions: 1.00 fluid ounce $=29.573 \mathrm{ml}, 1.00 \mathrm{~L}=1000 \mathrm{~cm}^{3}$ , density of water = $1.00 \mathrm{~g} / \mathrm{cm}^{3}$ , the number of fluid ounces in a $\mathrm{kg}$ of water is

A) 33.8 fluid ounces.
B) 40.1 fluid ounces.
C) 48.8 fluid ounces.
D) 25.7 fluid ounces.

Question 15

If the radius of the Earth is $6400.0 \mathrm{~km}$ and the atmosphere is $10.0 \mathrm{~km}$ high, then the volume of air around the Earth is

A) $5.16 \times 1018 \mathrm{~m} 3$ .
B) $5.2 \times 1018 \mathrm{~m}^{3}$ .
C) $5.1552 \times 10^{9} \mathrm{~m}^{3}$
D) $3.605 \times 10^{16} \mathrm{~m}^{3}$ .

Question 16

Approximately how many square centimeters are in 1 square foot $(1 \mathrm{in}=2.54 \mathrm{~cm})$ ?

A) $30.5 \mathrm{~cm}^{2}$
B) $144 \mathrm{~cm}^{2}$
C) $22.3 \mathrm{~cm}^{2}$
D) $366 \mathrm{~cm}^{2}$
E) $929 \mathrm{~cm}^{2}$

Question 17

One angstrom $=10^{-10} \mathrm{~m}$ and one fermi $=10^{-15} \mathrm{~m}$ . What is the relationship between these units?

A) 1 angstrom $=10^{-25}$ fermi
B) 1 angstrom $=10^{25}$ fermi
C) 1 angstrom $=10^{-5}$ fermi
D) 1 angstrom $=10^{ 5}$ fermi

Question 18

To be dimensionally consistent, distance $[\mathrm{L}]$ , velocity $[\mathrm{L} / \mathrm{T}]$ , and acceleration $[\mathrm{L} / \mathrm{T} 2]$ must be related as follows.

A) distance $=$ velocity $\times$ acceleration ${ }^{2}$
B) distance $=$ velocity $2 \times$ acceleration
C) distance $=$ velocity $2 /$ acceleration
D) distance $=$ velocity/acceleration

Question 19

To be dimensionally consistent, velocity $[\mathrm{L} / \mathrm{T}]$ , pressure $\left[\mathrm{M} / \mathrm{LT}^{2}\right]$ , and density $\left[\mathrm{M} / \mathrm{L}^{3}\right]$ must be related as follows.

A) velocity $=$ pressure $/$ density 2
B) velocity $=$ pressure/density
C) velocity $^{2}=$ pressure/density
D) velocity $^{2}=$ pressure $/$ density 2

Question 20

To be dimensionally consistent, force $\left[M L / \mathrm{T}^{2}\right]$ , pressure $\left[\mathrm{M}^{\mathrm{L}} \mathrm{LT}^{2}\right]$ , and length $[\mathrm{L}]$ must be related as follows.

A) force $=$ pressure $\times$ length 2
B) force $=$ pressure $2 \times$ length 2
C) force $=$ pressure $\times$ length
D) force $=$ pressure $^{2} \times$ length

Question 21

To be dimensionally consistent, distance $[\mathrm{L}]$ , acceleration $\left[\mathrm{L} / \mathrm{T}^{2}\right]$ , and time $[\mathrm{T}]$ must be related as follows.

A) distance $=$ acceleration $2 \times$ time
B) distance $=$ acceleration $^{2} \times$ time $^{2}$
C) distance $=$ acceleration $\times$ time
D) distance $=$ acceleration $\times$ time $^{2}$

Question 22

To be dimensionally consistent, velocity $[\mathrm{L} / \mathrm{T}]$ , acceleration $\left[\mathrm{L} / \mathrm{T}^{2}\right]$ and time $[\mathrm{T}]$ must be related as follows.

A) velocity $=$ acceleration $2 \times$ time $^{2}$
B) velocity $=$ acceleration $2 \times$ time
C) velocity $=$ acceleration $\times$ time $^{2}$
D) velocity $=$ acceleration $\times$ time

Question 23

Estimate the number of dollar bills ( $15.5 \mathrm{~cm}$ wide), placed end to end, that it would take to circle the Earth (radius $=6.40 \times 10^{3} \mathrm{~km}$ ).

A) $9.5 \times 10^{8}$
B) $3.7 \times 10^{7}$
C) $8.5 \times 10^{6}$
D) $1.2 \times 10^{7}$
E) $2.6 \times 10^{8}$

Question 24

Find the equation $x=a t^{2}+b$ that fits the following data.

$\begin{array}{|l|l|l|l|l|l|l|}\hline \mathrm{t}(\mathrm{sec})& 0 & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm{x}(\mathrm{m}) & -16 & -12 & 0 & 20 & 48 & 84 \\\hline\end{array}$

A) $x=4 t^{2}-16$
B) $x=4 t^{2}+16$
C) $x=2 t^{2}+16$
D) $x=2 t^{2}-16$

Question 25

the equation $x=a t^{2}+b$ that fits the following data.

$\begin{array}{|l|l|l|l|l|l|l|}\hline \mathrm{t}(\mathrm{sec}) & 1 & 3 & 5 & 7 & 9 & 11 \\\hline \mathrm{x}(\mathrm{m})& 2 & 18 & 50 & 98 & 162 & 242 \\\hline\end{array}$

A) $x=t^{2}+18$
B) $x=4 t^{2}-2$
C) $x=2 t^{2}$
D) $x=t^{2}+1$

Question 26

Find the equation $x=a t^{2}+b$ that fits the following data.

$\begin{array}{|l|l|l|l|l|l|l|}\hline \mathrm{t}(\mathrm{sec})& 0 & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm{x}(\mathrm{m} \mathrm{I}) & 60 & 58 & 52 & 42 & 28 & 10 \\\hline\end{array}$

A) $x=5 t^{2}+60$
B) $x=-2 t^{2}+60$
C) $x=-4 t^{2}+60$
D) $x=3 t^{2}+60$

Question 27

Find the equation $x=a t^{2}+b t$ that fits the following data.

$\begin{array}{|l|l|l|l|l|l|l|}\hline \mathrm{t}(\mathrm{sec}) & 1 & 3 & 5 & 7 & 9 & 11 \\\hline \mathrm{x}(\mathrm{m}) & 3 & 21 & 55 & 105 & 171 & 253 \\\hline\end{array}$

A) $x=6 t^{2}-3 t$
B) $x=2 t^{2}+2 t$
C) $x=2 t$
D) $x=t^{2}+2 t$

Question 28

Find the equation $v^{2}=a h+b$ that fits the following data.

$\begin{array}{|l|l|l|l|l|l|l|}\hline \mathrm{h}(\mathrm{m}) & 2 & 4 & 6 & 8 & 10 & 12 \\\hline \mathrm{v}(\mathrm{m} / \mathrm{s}) & 0 & 200 & 2.83 & 3.46 & 400 & 4.47 \\\hline\end{array}$

A) $v^{2}=2 h-4$
B) $v^{2}=h-2$
C) $v^{2}=2 h+4$
D) $v^{2}=3 h-6$

Question 29

Lake Superior has a shoreline of length 2726 miles. What would be its diameter in $\mathrm{km}$ if it were a perfectly circular lake? One mile is $1.609 \mathrm{~km}$ .

A) $1396 \mathrm{~km}$
B) $539 \mathrm{~km}$
C) $847 \mathrm{~km}$
D) $270 \mathrm{~km}$
E) $698 \mathrm{~km}$
F) $1694 \mathrm{~km}$

Question 30

Lake Superior has a shoreline of length 2726 miles. What would be its area in $\mathrm{km}^{2}$ if it were a perfectly circular lake? One mile is $1.609 \mathrm{~km}$ .

A) $9.51 \times 10^{5} \mathrm{~km}^{2}$
B) $4.87 \times 10^{5} \mathrm{~km}^{2}$
C) $6.12 \times 10^{6} \mathrm{~km}^{2}$
D) $5.91 \times 10^{5} \mathrm{~km}^{2}$
E) $4.81 \times 10^{6} \mathrm{~km}^{2}$
F) $1.53 \times 10^{6} \mathrm{~km}^{2}$

Question 31

The surface area of Antarctica is 13.2 million square kilometers. If 1 acre is equivalent to $4047 \mathrm{~m}^{2}$ , what is the surface area of Antarctica in acres?

A) $8.05 \times 10^{6}$ acres
B) $3.26 \times 10^{3}$ acres
C) $8.05 \times 10^{3}$ acres
D) $3.26 \times 10^{9}$ acres
E) $3.26 \times 10^{6}$ acres
F) $8.05 \times 10^{9}$ acres

Question 32

Acceleration has dimension [L/T2]. Use dimensional analysis to determine the ratio of accelerations for car A to car B, if, everything else being equal, car A travels a given distance in half the time required by car B.

A) 4
B) $1 / \sqrt{2}$
C) $\sqrt{ } 2$
D) $1 / 2$
E) $1 / 4$
F) 2

Question 33

You can reason that the time required for a ball to fall is related to the height from which it falls and to the acceleration due to gravity. Time is measured in seconds, height in meters, and gravitational acceleration in meters per second squared. Using dimensional analysis, determine how the time to fall from height $\mathrm{h}$ compares to the time required to fall from height $2 \mathrm{~h}$ .

A) It takes $\sqrt{2}$ times as long.
B) It takes $1 / 4$ as long.
C) It takes 2 times as long.
D) It takes $1 / 2$ as long.
E) It takes 4 times as long.
F) It takes $\frac{1}{\sqrt{2}}$ as long.

Question 34

What is the approximate volume of the average adult human body?

A) $0.1 \mathrm{~m}^{3}$
B) $1 \mathrm{~m}^{3}$
C) $0.5 \mathrm{~m}^{3}$
D) $0.01 \mathrm{~m}^{3}$

Question 35

What is the approximate volume of an adult human's head?

A) $1.0 \mathrm{~m}^{3}$
B) $0.001 \mathrm{~m}^{3}$
C) $0.02 \mathrm{~m}^{3}$
D) $0.1 \mathrm{~m}^{3}$
E) $0.005 \mathrm{~m}^{3}$

Question 36

Estimate the surface area of an adult human's head.

A) $0.01 \mathrm{~m}^{2}$
B) $0.1 \mathrm{~m}^{2}$
C) $1.0 \mathrm{~m}^{2}$
D) $0.5 \mathrm{~m}^{2}$

Question 37

A graph of $x$ vs. $t$ is linear, and it intercepts the vertical axis at $-15 \mathrm{~m}$ and the horizontal axis at $5 \mathrm{~s}$ . What is the value of $x$ corresponding to $t=3 \mathrm{~s}$ ?

A) $-9 \mathrm{~m}$
B) $-6 \mathrm{~m}$
C) $6 \mathrm{~m}$
D) $9 \mathrm{~m}$
E) $26 \mathrm{~m}$
F) $-26 \mathrm{~m}$

Question 38

A graph of $x$ vs. $t^{2}$ is linear, and intercepts the vertical axis at $12 \mathrm{~m}$ and the horizontal axis at $4 \mathrm{~s}^{2}$ . What is the function?

A) $x=12 \mathrm{~m}-\left(3 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}$
B) $x=12 \mathrm{~m}+\left(6 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}$
C) $x=12 \mathrm{~m}-\left(6 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}$
D) $x=12 \mathrm{~m}+\left(3 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}$

Question 39

A 2.0 kg object is moving at a speed of $v=12.0 \mathrm{~m} / \mathrm{s}$ . The drag force is $6.0 \mathrm{~N}$ . If the drag force is given by the equation $F=b v^{2}$ , then the value of $b$ is

A) $4.2 \times 10^{-2} \mathrm{~kg} / \mathrm{m}$ .
B) $7.5 \times 10^{-3} \mathrm{Ns}^{2} / \mathrm{m}^{2}$ .
C) $4.2 \times 10^{-1} \mathrm{~N} / \mathrm{m}^{2}$ .
D) $3.9 \times 10^{-1} \mathrm{~kg} / \mathrm{m}^{2}$ .
E) $1.5 \times 10^{-2} \mathrm{Ns} 2 / \mathrm{m}^{2}$