Deck 1: Introduction

Question 1

Which one of the choices below represents the preferred practice regarding significant figures when adding the following: 12.4 + 14 + 67.37 + 4.201?

A) 98
B) 98.0
C) 97.97
D) 97.971

Answer 1

98

Question 2

Which one of the choices below represents the preferred practice regarding significant figures when multiplying the following: 10.5 * 8.9 *3.11?

A) 290.6295
B) 290.63
C) 291
D) 290

Answer 2

290

Question 3

A circle has an area of 2.0 m². A second circle has triple the radius of the first. The area of the second circle is _____ times that of the first.

A) 27
B) 9.0
C) 3.0
D) 0.67

Answer 3

9.0

Question 4

A room in a house has a floor area of 160 ft². Which of the following is most likely the approximate volume of the room?

A) 4000 m³
B) 400 m³
C) 40 m³
D) 4 m³

Question 5

Multiplying a 4 significant figure number by a 3 significant figure number and then dividing the product by a six significant figure number yields a number with how many significant figures?

A) 7/6
B) 3
C) 2
D) 13

Question 6

The prefixes which are abbreviated p, n, and T represent which of the following?

A) 10^-2, 10^-6, and 10¹⁵
B) 10^-9, 10⁶, and 10¹⁰
C) 10^-12, 10^-9, and 10¹²
D) 10^-15, 10^-6, and 10¹⁵

Question 7

In mechanics, physicists use three basic quantities to derive additional quantities. Mass is one of the three quantities. What are the other two?

A) length and force
B) power and force
C) length and time
D) force and time

Question 8

Two numbers, one with 4 significant figures and the other with 3 significant figures, are combined using the math operations given below. Which operation can give a result with fewer than 3 significant figures?

A) addition
B) subtraction
C) multiplication
D) division

Question 9

The ratio M/m of the prefixes M and m has what value?

A) 10³
B) 10⁶
C) 10⁹
D) 10¹⁸

Question 10

tripling the radius of a sphere results in increasing its volume by a factor of

A) 27 $\pi$
B) 27
C) 9
D) 3

Question 11

The current standard definition for the second has been based on which of the following?

A) characteristic frequency of the light from cesium atoms
B) average solar day
C) sidereal day
D) Greenwich Civil Time

Question 12

One year is about _____ seconds while one day is exactly _____ seconds.

A) 3.16 * 10⁷, 86,400
B) 5.26 * 10⁵, 86,400
C) 3.16 * 10⁷, 8640
D) 1.04 *10⁶, 36,000

Question 13

On planet Q the standard unit of volume is called the guppy. Space travelers from Earth have determined that one liter = 38.2 guppies. How many guppies are in 200 liters?

A) 70.2 guppies
B) 9.74 guppies
C) 5.24 guppies
D) 7640 guppies

Question 14

Modern electroplaters can cover a surface area of 55.0 m² with one troy ounce of gold (volume = 1.611 cm³). What is the thickness of the electroplated gold?

A) 3.64*10^-7 m
B) 1.46 *10^-9 m
C) 1.83 *10^-6 m
D) 2.93 *10^-8 m

Question 15

In 1983 the standard meter was redefined to what it is currently. What was the previous definition from 1960 based on?

A) specific alloy bar housed at Sevres, France
B) wavelength of light emitted by certain krypton atoms
C) distance from the Earth's equator to the North Pole
D) the distance light travels in a certain fraction of a second

Question 16

On planet Z, the standard unit of length is the foose. Ann the Astronaut is 5.90 feet tall on Earth. She lands on planet Z and is measured to be 94 foosi tall. Her partner Rachael is 83 foosi tall. How tall is Rachael on Earth?

A) 5.2 feet
B) 5.5 feet
C) 5.8 feet
D) 6.3 feet

Question 17

The number 0.0001070 has how many significant figures?

A) 2
B) 3
C) 4
D) 7

Question 18

Calculate (0.82 + 0.042) * (4.49 *10³), keeping only significant figures.

A) 3870.8
B) 3870
C) 3879
D) 3900

Question 19

The length and width of a standard sheet of paper is measured, and then the area is found by calculation to be 93.500 in². The number of significant figures in the width measurement must be at least:

A) 5
B) 4
C) 3
D) 2

Question 20

The basic function of an automobile's carburetor is to atomize the gasoline and mix it with air to promote rapid combustion. Assume that 40 cm³ of gasoline is atomized into N spherical droplets. Each droplet has a radius of 2.0 *10^-5 m. Find the total surface area of these N spherical droplets.

A) 60,000 cm²
B) 24,000 cm²
C) 20,000 cm²
D) 2800 cm²

Question 21

Note the expression: y = x². Which statement is most consistent with this expression?

A) if y doubles, then x quadruples
B) y is greater than x
C) if x doubles, then y doubles
D) if x doubles, then y quadruples

Question 22

The unit slug has what dimensions?

A) L
B) M
C)
D)

Question 23

Water flows into a swimming pool at the rate of 12 gal/min. The pool is 16 ft wide, 32 ft long and 6.0 ft deep. How long does it take to fill? (1 U.S. gallon = 231 cubic inches)

A) 32 hours
B) 64 hours
C) 48 hours
D) 24 hours

Question 24

When NASA was communicating with astronauts on the moon, the time from sending on the Earth to receiving on the moon was 1.28 s. Find the distance from Earth to the moon. (The speed of radio waves is 3.00 *10⁸ m/s.)

A) 240,000 km
B) 384,000 km
C) 480,000 km
D) 768,000 km

Question 25

The information on a one-gallon paint can is that the coverage, when properly applied, is 270 ft². One gallon is 231 in³. What is the average thickness of the paint in such an application?

A) 0.0036 in.
B) 0.0059 in.
C) 0.043 in.
D) 0.053 in.

Question 26

Volume can be measured in units of Which of the following unit combinations also result in volume?

A)
B)
C)
D)

Question 27

The distance to the Andromeda Galaxy is estimated at about 2 * 10⁶ light years. A light year is the distance traveled by light in one year; if the speed of light is 3 * 10⁸ m/s, about how far is it from our galaxy to Andromeda? (1 year = 3.15 *10⁷ s)

A) 10 * 10¹⁵ m
B) 1 * 10¹⁸ m
C) 2 * 10²² m
D) 6 * 10¹² m

Question 28

When SI units are plugged into an equation, it is found that the units balance. Which of the following can we expect to be true for this equation?

A) The equation will be dimensionally correct.
B) The equation will be dimensionally correct except sometimes in cases when the right-hand side of the equation has more than one term.
C) The equation will not be dimensionally correct.
D) All constants of proportionality will be correct.

Question 29

If v is velocity, x is position, and t is time, then which equation is not dimensionally correct?

A) t = x/v
B) = v²/x²
C) v = t/x
D) t² = 2x²/v²

Question 30

Areas always have dimensions _____ while volumes always have dimensions _____.

A) m², m³
B) L², L³
C) Both a and b are correct.
D) No answer is correct because of the "always."

Question 31

A cement truck can pour 40 cubic yards of cement per hour. Express this in ft³/min.

A) 2/3 ft³/min
B) 18 ft³/min
C) 6 ft³/min
D) 2.0 ft³/min

Question 32

Suppose an equation relating position, x, to time, t, is given by x = bt³ + ct⁴, where b and c are constants. The dimensions of b and c are respectively:

A) T³, T⁴.
B) 1/T³, 1/T⁴.
C) L/T³, L/T⁴.
D) L²*T³, L²*T⁴.

Question 33

A furlong is a distance of 220 yards. A fortnight is a time period of two weeks. A horse is running at a speed of 4.00 yards per second. What is his speed in furlongs per fortnight?

A) 2200 furlongs/fortnight
B) 4980 furlongs/fortnight
C) 11,000 furlongs/fortnight
D) 22,000 furlongs/fortnight

Question 34

If the displacement of an object, x, is related to velocity, v, according to the relation x = Av, the constant, A, has the dimension of which of the following?

A) volume
B) length
C) time
D) area

Question 35

Which of the following conversion factors is not exact?

A) 12 in. = 1 ft
B)
C)
D)

Question 36

The mass of the Sun is 2.0 *10³⁰ kg, and the mass of a hydrogen atom is 1.67 *10^-27 kg. If we assume that the Sun is mostly composed of hydrogen, how many atoms are there in the Sun?

A) 1.2 * 10⁵⁶ atoms
B) 3.4 * 10⁵⁶ atoms
C) 1.2 * 10⁵⁷ atoms
D) 2.4 * 10⁵⁷ atoms

Question 37

A cereal box has the dimensions of 0.19 m *0.28 m *0.080 m. If there are 3.28 feet per meter, then what is the volume of the box in cubic feet?

A) 0.0043 cubic feet
B) 0.15 cubic feet
C) 0.046 cubic feet
D) 0.0014 cubic feet

Question 38

The speed of a boat is often given in knots. If a speed of 5 knots were expressed in the SI system of units, the units would be:

A) m
B) s
C) m/s
D) kg/s

Question 39

Which expression is dimensionally consistent with an expression that would yield a value for time ^{- 1}?(v is velocity, x is distance, and t is time)

A) v/x
B) v²/x
C) x/t
D) v²t

Question 40

Which formula is dimensionally consistent with an expression yielding a value for velocity? (v is velocity, x is distance, and t is time)

A) v/t²
B) vx²
C) v²/t
D) v²t/x

Question 41

Note the expression: y = A/x². Which statement is most consistent with this expression?

A) y is less than A
B) if x is doubled, y is multiplied by a factor of four
C) if x is halved, y is multiplied by a factor of four
D) y is greater than x

Question 42

If $\varphi$ = 90° - $\theta$ , what is the value of sin² $\varphi$ + sin² $\theta$ ?

A) "0"
B) "1"
C) "-1"
D) "The answer depends on $\theta$ ."

Question 43

Which of the following is an example of a vector quantity?

A) velocity
B) temperature
C) volume
D) mass

Question 44

Which type of quantity is characterized by both magnitude and direction?

A) scalar
B) vector
C) trigonometric
D) algebraic variable

Question 45

For which of the values below is x > x³?

A) x = -1.5
B) x = 0
C) x = 1.0
D) x = 1.5

Question 46

Which point is nearest the y axis?

A) (-3, 4)
B) (4, 5)
C) (-5, 3)
D) (5, -2)

Question 47

Each edge of a cube has a length of 50.8 cm. What is the length of a diagonal of the cube going through the center of the cube?

A) 20.0 in
B) 28.8 in
C) 34.6 in
D) 50.8 in

Question 48

If point A is located at coordinates (2, -3) and point B is located at coordinates (-3, 9), what is the distance from A to B if the units of the coordinated system are meters?

A) 17 m
B) 10 m
C) 13 m
D) 20 m

Question 49

A train slowly climbs a 600-m mountain track which is at an angle of 10.0° with respect to the horizontal. How much altitude does it gain?

A) 86.8 m
B) 104 m
C) 106 m
D) 492 m

Question 50

Four vectors all have the same magnitude. Vector 1 is at 30 $\degree$ , Vector 2 is at 110 $\degree$ , vector 3 is at 240 $\degree$ , and Vector 4 is at 315 $\degree$ . Which vector has the greatest magnitude x component and which vector has the least magnitude y component?

A) Vector 1, Vector 2
B) Vector 4, Vector 4
C) Vector 1, Vector 1
D) Vector 3, Vector 2

Question 51

Vectors have magnitudes 6, 11, and 22. When these vectors are added, what is the least possible magnitude of their addition?

A) 25
B) 15
C) 5
D) 3

Question 52

Vector 1 is 7 units long and is at 70 $\degree$ . Vector 2 is 5 units long and is at 155 $\degree$ . Vector 3 is 3 units long and is at 225 $\degree$ . Which vector has equal magnitude components?

A) Vector 1
B) Vector 2
C) Vector 3
D) None of the vectors has equal magnitude components.

Question 53

If and are each first quadrant angles, which of the following must be true if ?

A)
B)
C)
D)

Question 54

When we subtract a velocity vector from another velocity vector, the result is:

A) another velocity.
B) an acceleration.
C) a displacement.
D) a scalar.

Question 55

A right triangle has sides 5.0 m, 12 m, and 13 m. The largest angle not 90° of this triangle is nearest:

A) 21°.
B) 23°.
C) 67°.
D) Not attainable since this is not a right triangle.

Question 56

Of vectors with lengths 5 m, 3 m, and 4 m, which has the greatest magnitude x component?

A) the one with length 5 m
B) the one with length 3 m
C) the one with length 4 m
D) It could be any of the three.

Question 57

Consider the cosine of any angle between 35° and 40°. If the angle were doubled, what would happen to the cosine of the angle.

A) It would halve.
B) It would decrease to less than half its original value.
C) It would decrease but be more than half its original value.
D) In different cases, it could do any of the above.

Question 58

A high fountain of water is in the center of a circular pool of water. You walk the circumference of the pool and measure it to be 170 meters. You then stand at the edge of the pool and use a protractor to gauge the angle of elevation of the top of the fountain. It is 51°. How high is the fountain?

A) 17 m
B) 23 m
C) 30 m
D) 33 m

Question 59

A triangle has sides of lengths 14 cm and 50 cm. If the triangle is a right triangle, which of the following could be the length of the third side?

A) 26 cm
B) 36 cm
C) 48 cm
D) 64 cm

Question 60

Suppose the interior angles of a triangle are , , and , with . Which side of the triangle is the shortest?

A) The side opposite .
B) The side opposite .
C) The side opposite .
D) More information is needed unless the triangle is a right triangle.

Question 61

I walk six miles in a straight line in a direction north of east, and I end up four miles north and several miles east. How many degrees north of east have I walked?

A) 19 $\degree$
B) 42 $\degree$
C) 60 $\degree$
D) 71 $\degree$

Question 62

Find the sum of the following two vectors: (i) 50 units due east and (ii) 100 units 30 $\degree$ south of west.

A) 100 units 30 $\degree$ south of west
B) 62 units 54 $\degree$ south of west
C) 87 units 60 $\degree$ south of west
D) 62 units 15 $\degree$ south of west

Question 63

Arvin the Ant travels 30 cm eastward, then 25 cm northward, and finally 10 cm westward. In what direction is Arvin now in with respect to his starting point?

A) 59 $\degree$ N of E
B) 29 $\degree$ N of E
C) 29 $\degree$ N of W
D) 51 $\degree$ N of E

Question 64

A taxicab moves five blocks due north, five blocks due east, and another three blocks due north. Assume all blocks are of equal size. How far is the taxi from its starting point?

A) 13 blocks
B) 9.4 blocks
C) 9.2 blocks
D) 8.6 blocks

Question 65

Vector points north and vector points east. If , then vector points:

A) north of east.
B) south of east.
C) north of west.
D) south of west.

Question 66

When three vectors are added graphically and form a closed triangle, the largest enclosed angle between any two of the vectors cannot be greater than:

A) 60 $\degree$
B) 90 $\degree$ .
C) 180 $\degree$ .
D) No maximum exists.

Question 67

In a 2-dimensional Cartesian coordinate system the x component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and y axis?

A) sine
B) cosine
C) tangent
D) cotangent

Question 68

In a 2-dimensional Cartesian system, the y component of a vector is known, and the angle between vector and x axis is known. Which operation is used to calculate the magnitude of the vector (taken with respect to the y component)?

A) dividing by cosine
B) dividing by sine
C) multiplying by cosine
D) multiplying by sine

Question 69

Vector is 3.0 units in length and points along the positive x axis; vector is 5.0 units in length and points along a direction 150 $\degree$ from the positive x axis. What is the magnitude of the resulting vector when vectors and are added?

A) 7.0
B) 6.7
C) 2.8
D) 2.1

Question 70

A student adds two vectors with magnitudes of 200 and 70. Which one of the following is the only possible choice for the magnitude of their sum?

A) 100
B) 280
C) 200
D) 70

Question 71

Vector is 5 m long and vector is 12 m long. The length of the sum of the vectors must be:

A) some value from 7 m to 17 m.
B) 13 m.
C) 17 m.
D) 8 m.

Question 72

In a 2-dimensional Cartesian coordinate system the y component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and x axis?

A) sine
B) cosine
C) tangent
D) cotangent

Question 73

Vector is 3.0 units in length and points along the positive x axis; vector is 5.0 units in length and points along a direction 150 $\degree$ from the positive x axis. What is the direction of their sum with respect to the positive x axis?

A) 62 $\degree$
B) 13 $\degree$
C) 118 $\degree$
D) 103 $\degree$