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# Basic Mathematics for Physics Practice Test

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By McGraw-Hill Professional
Updated on Sep 17, 2011

## Basic Mathematics for Physics Practice Test

A good score is at least 37 correct. Answers are given at the end. It is best to have a friend check your score the first time so that you won’t memorize the answers if you want to take the test again.

1. A constant that is a real number but is not expressed in units is known as

(a) a euclidean constant.

(b) a cartesian constant.

(c) a dimensionless constant.

(d) an irrational constant.

(e) a rational constant.

2. If someone talks about a gigameter in casual conversation, how many kilometers could you logically assume this is?

(a) 1,000

(b) 10,000

(c) 100,000

(d) 1 million

(e) 1 billion

3. In log-log coordinates,

(a) one axis is linear, and the other is determined according to an angle.

(b) both axes are logarithmic.

(c) all possible real-number ordered pairs can be shown in a finite area.

(d) all three values are determined according to angles.

(e) points are defined according to right ascension and declination.

4. Consider this sequence of numbers: 7.899797, 7.89979, 7.8997, 7.899, 7.89, .... Each number in this sequence has been modified to get the next one. This process is an example of

(a) truncation.

(b) vector multiplication.

(c) rounding.

(d) extraction of roots.

(e) scientific notation.

5. The expression 3 x (read “three sub x ”) is another way of writing

(a) 3 raised to the x th power.

(b) the product of 3 and x .

(c) 3 divided by x .

(d) The xth root of 3.

(e) nothing; this is a nonstandard expression.

6. Which of the following statements is true?

(a) A quadrilateral can be uniquely determined according to the lengths of its four sides.

(b) The diagonals of a parallelogram always bisect each other.

(c) Any given four points always lie in a single plane.

(d) If one of the interior angles in a triangle measures 90°, then all the interior angles in that triangle measure 90°.

(e) All of the above statements are true.

7. If you see the lowercase italic letter c in an equation or formula describing the physical properties of a system, it would most likely represent

(a) the exponential base, roughly equal to 2.71828.

(b) the ratio of a circle’s diameter to its radius.

(c) the square root of −1.

(d) the speed of light in free space.

(e) the 90° angle in a right triangle.

8. Suppose that an airplane is flying on a level course over an absolutely flat plain. At a certain moment in time you measure the angle x at which the airplane appears to be above the horizon. At the same moment the pilot of the aircraft sees you and measures the angle y at which you appear to be below the horizon. Which of the following statements is true?

(a) x < y .

(b) x = y .

(c) x > y .

(d) The relationship between x and y depends on the plane’s altitude.

(e) The relationship betwen x and y depends on the plane’s speed.

9. Suppose that you are told that the diameter of the sun is 1.4 × 10 6 kilometers and you measure its angular diameter in the sky as 0.50°. Based on this information, approximately how far away is the sun, to two significant figures?

(a) 1.6 × 10 8 kilometers

(b) 6.2 × 10 8 kilometers

(c) 1.6 × 10 7 kilometers

(d) 6.2 × 10 7 kilometers

(e) 6.2 × 10 6 kilometers

10. What is the diameter of a sphere whose volume is 100 cubic meters? (The formula for the volume V of a sphere in cubic meters, in terms of its radius R in meters, is V = 4π r 3 /3.)

(a) 2.88 meters

(b) 4.19 × 10 6 meters

(c) 5.76 meters

(d) 8.28 × 10 6 meters

(e) There is not enough information to determine this.

11. What is the difference, from the point of view of an experimental physicist, between 2.0000000 × 10 5 and 2.000 × 10 5 ?

(a) One expression has eight significant figures, and the other has four significant figures.

(b) Four orders of magnitude

(c) One part in 10,000

(d) One number is rounded, and the other is truncated.

(e) There is no difference whatsoever between these two expressions.

12. Refer to Fig. T-0-1. What is the domain of this function?

(a) All the real numbers between and including 0 and 1

(b) All real numbers greater than 0 but less than or equal to 1

(c) All real numbers greater than or equal to 0 but less than 1

Fig. T-0-1 Illustration for Part Zero Test Questions 12 and 13.

(d) All real numbers between but not including 0 and 1

(e) All real numbers

13. Refer again to Fig. T-0-1. What is the range of this function?

(a) All the real numbers between and including 0 and 1

(b) All real numbers greater than 0 but less than or equal to 1

(c) All real numbers greater than or equal to 0 but less than 1

(d) All real numbers between but not including 0 and 1

(e) All real numbers

14. Suppose that a car travels down a straight road at a constant speed. Then the distance traveled in a certain amount of time is equal to

(a) the product of the speed and the elapsed time.

(b) the speed divided by the elapsed time.

(c) the elapsed time divided by the speed.

(d) the sum of the speed and the elapsed time.

(e) the difference between the speed and the elapsed time.

15. A two-dimensional coordinate system that locates points based on an angle and a radial distance, similar to circular radar displays, is called

(a) the cartesian plane.

(b) semilog coordinates.

(c) cylindrical coordinates.

(d) circular coordinates.

(e) polar coordinates.

16. The expression 6! is equivalent to

(a) the common logarithm of 6.

(b) the natural logarithm of 6.

(c) .

(d) 21.

(e) 720.

17. Suppose that you come across a general single-variable equation written in the following form:

( xq )( xr )( xs )( xt ) = 0

This can be classified as a

(b) cubic equation.

(c) quartic equation.

(d) quintic equation.

(e) linear equation.

18. Suppose that you have a pair of equations in two variables. What is the least number of common solutions this pair of equations can have?

(a) None

(b) One

(c) Two

(d) Three

(e) Four

19. Suppose that you have a brick wall 1.5 meters high and you need to build a ramp to the top of this wall from some point 3.2 meters away on level ground. Which of the following plank lengths is sufficient to make such a ramp without being excessively long?

(a) 4.7 meters

(b) 4.8 meters

(c) 3.6 meters

(d) 1.7 meters

(e) There is not enough information given here to answer that question.

20. In a cylindrical coordinate system, a point is determined relative to the origin and a reference ray according to

(c) three angles.

(d) height, width, and depth.

(e) celestial latitude and longitude.

21. What is the standard quadratic form of ( x + 2)( x − 5)?

(a) 2 x − 3 = 0

(b) x 2 − 10 = 0

(c) x 2 − 3 x − 10 = 0

(d) x 2 + 7 x + 10 = 0

(e) There is no such form because this is not a quadratic equation.

22. Suppose that a piston has the shape of a cylinder with a circular cross section. If the area of the circular cross section (the end of the cylinder) is 10 square centimeters and the cylinder itself is 10 centimeters long, what, approximately, is the volume of the cylinder?

(a) 10 square centimeters

(b) 100 square centimeters

(c) 62.8 cubic centimeters

(d) 100 cubic centimeters

23. Suppose that you see this equation in a physics paper: z 0 = 3 h + sin q . What does sin q mean?

(a) The logarithm of the quantity q

(b) The inverse sine (arcsine) of the quantity q

(c) The sine of the quantity q

(d) The exponential of the quantity q

(e) None of the above

24. The expression −5.44E + 04 is another way of writing

(a) −5.4404

(b) −544,004

(c) −5.44 × 10 −4

(d) −54,400

(e) nothing; this is a meaningless expression.

25. When two equations in two variables are graphed, their common approximate solutions, if any, appear as

(a) points where the curves cross the x axis.

(b) points where the curves cross the y axis.

(c) points where the curves intersect each other.

(d) points where the curves intersect the origin (0, 0).

(e) nothing special; the graphs give no indication of the solutions.

26. What is the product of 5.8995 × 10 −8 and 1.03 × 10 6 ? Take significant figures into account.

(a) 6.0764845 × 10 −2

(b) 6.076485 × 10 −2

(c) 6.07648 × 10 −2

(d) 6.076 × 10 −2

(e) 6.08 × 10 −2

27. Suppose that you see the following expression in a physics thesis:

sech −1 x = ln[ x −1 + ( x −2 − 1) 1/2 ]

What does the expression ln mean in this context?

(a) Some real number multiplied by 1

(b) The common logarithm

(c) The natural logarithm

(d) The inverse secant

(e) The square root

28. Suppose that there are two vectors a and b , represented in the cartesian plane as follows:

a = (3, 5)

b = (−3, −5)

What is the sum of these vectors in the cartesian plane?

(a) a + b = −34

(b) a + b = (0, 0)

(c) a + b = (6, 10)

(d) a + b = (−9, −25)

(e) There is no such sum, because the sum of these vectors is not defined.

29. How many points does it take to uniquely define a geometric plane?

(a) One

(b) Two

(c) Three

(d) Four

(e) Five

30. Refer to Fig. T-0-2. What does this graph represent?

(a) The sine function

(b) The cosine function

(d) A linear equation

(e) A logarithmic function

31. Refer again to Fig. T-0-2. The coordinate system in this illustration is

(a) polar.

(b) spherical.

(c) semilog.

Fig. T-0-2 Illustration for Part Zero Test Questions 30 and 31.

(d) log-log.

(e) trigonometric.

32. Suppose that there are two vectors. Vector a points straight up with a magnitude of 3, and vector b points directly toward the western horizon with a magnitude of 4. The cross product a × b has the following characteristics:

(a) It is a scalar with a value of 12.

(b) It is a vector pointing toward the southern horizon with a magnitude of 12.

(c) It is a vector pointing upward and toward the west with a magnitude of 5.

(d) It is a vector pointing straight down with a magnitude of 5.

33. Using a calculator, you determine the power of 2 (that is, 2 ) to four significant figures. The result is

(a) 1.587.

(b) 2.828.

(c) 4.000.

(d) 8.000.

(e) The expression 2 is not defined and cannot be determined by any means.

34. The numbers 34 and 34,000 differ by

(a) a factor of 10.

(b) three orders of magnitude.

(c) five orders of magnitude.

(d) seven orders of magnitude.

(e) the same ratio as a foot to a mile.

35. Right ascension is measured in

(a) degrees.

(c) linear units.

(d) logarithmic units.

(e) hours.

36. Consider the function y = 2 x with the domain restricted to 0 < x < 2. What is the range?

(a) 0 < y < 1/2

(b) 0 < y < 1

(c) 0 < y < 2

(d) 0 < y < 4

(e) There is not enough information given to answer this question.

37. The fifth root of 12 can be written as

(a) 12 1/5 .

(b) 12/5.

(c) 12 5 .

(d) 5 12 .

(e) 5 1/12 .

38. Suppose that you are given the equation x 2 + y 2 = 10. What does this look like when graphed in rectangular coordinates?

(a) A straight line

(b) A parabola

(c) An elongated ellipse

(d) A hyperbola

(e) A circle

39. Suppose that an experimenter takes 10,000 measurements of the voltage on a household utility line over a period of several days and comes up with an average figure of 115.85 volts. This is considered the nominal voltage on the line. Suppose that a second experimenter takes a single measurement and gets a value of 112.20 volts. The percentage departure of the single observer’s measurement from the nominal voltage is approximately

(a) −0.03 percent.

(b) +0.03 percent.

(c) +3 percent.

(d) −3 percent.

(e) impossible to determine from the data given.

40. Suppose that there is a four-sided geometric figure that lies in a single plane and whose sides all have the same length. Then the perimeter of that figure is

(a) the product of the base length and the height.

(b) the square of the length of any given side.

(c) the sum of the lengths of all four sides.

(d) half the sum of the lengths of all four sides.

41. Suppose that you view a radio tower on a perfectly flat plain and find that it appears to extend up to a height of 2.2° above the horizon. How far away is the base of the tower from where you stand, expressed to two significant figures?

(a) 0.5 kilometer

(b) 1.0 kilometer

(c) 1.5 kilometers

(d) 2.2 kilometers

42. The product of 3.88 × 10 7 and 1.32 × 10 −7 is

(a) 5.12.

(b) 5.12 × 10 14 .

(c) 5.12 × 10 −14 .

(d) 5.12 × 10 49 .

(d) 5.12 × 10 −49 .

43. The cosine of a negative angle is the same as the cosine of the angle. Knowing this and the fact that the cosine of 60° is equal to 0.5, what can be said about the cosine of 300° without making any calculations?

(b) The cosine of 300° is equal to 0.5.

(c) The cosine of 300° is equal to −0.5.

(d) The cosine of 300° can be equal to either 0.5 or −0.5.

(e) The cosine of 300° is equal to zero.

44. The slope of a vertical line (a line parallel to the ordinate) in cartesian rectangular coordinates is

(a) undefined.

(b) equal to 0.

(c) equal to 1.

(d) variable, depending on how far you go from the origin.

(e) imaginary.

45. Which of the following statements is false?

(a) A triangle can be uniquely determined according to the lengths of its sides.

(b) A triangle can be uniquely determined according to the length of one side and the measures of the two angles at either end of that side.

(c) A triangle can be uniquely determined according to the measures of its three interior angles.

(d) All equilateral triangles are similar to each other.

(e) An isosceles triangle has two sides whose lengths are the same.

46. The equation −4 x 2 + 17 x = 7 is an example of

(a) a two-variable equation.

(b) a linear equation.

(d) an exponential function.

(e) none of the above.

47. The sum of a real number and an imaginary number is

(a) undefined.

(b) an irrational number.

(c) a rational number.

(d) a transcendental number.

(e) a complex number.

48. In astronomy, the equivalent of celestial longitude, based on the vernal equinox and measured relative to the stars, is called

(a) longitude.

(b) azimuth.

(c) right ascension.

(d) arc span.

(e) meridian.

49. Consider a plane that contains the axis of a true parabolic dish antenna or mirror. The dish or mirror intersects this plane along a curve that can be defined by

(a) imaginary numbers.

(b) a linear equation.

(d) a cubic equation.

(e) no particular equation.

50. Suppose that you are given two positive numbers, one of them 25 orders of magnitude larger than the other and both expressed to four significant figures. If you add these numbers and express the sum to four significant figures,

(a) the smaller number vanishes into insignificance.

(b) you must write both numbers out in full.

(c) you must have the aid of a computer.

(d) the sum is 25 orders of magnitude bigger than the larger number.

(e) you must subtract the numbers and then take the negative of the result.

1. c

2. d

3. b

4. a

5. e

6. b

7. d

8. b

9. a

10. c

11. a

12. e

13. b

14. a

15. e

16. e

17. c

18. a

19. c

20. a

21. c

22. d

23. c

24. d

25. c

26. e

27. c

28. b

29. c

30. e

31. c

32. b

33. a

34. b

35. e

36. d

37. a

38. e

39. d

40. c

41. e

42. a

43. b

44. a

45. c

46. c

47. e

48. c

49. c

50. a

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