Physics Math Review

Practice Problems:

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Physics Math Review

Express the following numbers in scientific notation:

  1. 156.90 ______
  2. 12 000 ______
  3. 0.0345 ______
  4. 0.00 890 ______

Expand the following numbers

  1. 1.23 x 106 ______
  2. 2.5 x 10-3 ______
  3. 1.54 x 104 ______
  4. 5.67 x 10-1 ______

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Physics Math Review

Solve the following and put you answer in scientific notation.

  1. 6.6 x 10-8 =

3.3 x 10-4 ______

  1. 7.4 x 1010 =

3.7 x 103 ______

  1. 2.5 x 108 =

7.5 x 102 ______

  1. (2.67 x 10 –3) – (9.5 x 10-4) = ______
  2. (1.56 x 10-7) + (2.43 x 10-8) = ______
  3. (2.5 x 10-6) x (3.0 x 10-7) = ______
  4. (1.2 x 10-9) x (1.2 x 107) = ______
  5. (2.3 x 104) + (2.0 x 10-3) = ______

Give the number of significant digits in the following measurements.

17) 2.9910 m ______

18) 5600 km ______

19)  0.00670 kg ______

20)  809 g ______

21)  2804 m ______

22)  0.0029 m ______

23)  4.06 x m ______

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Physics Math Review

Solve the following problems and give the answer in the correct number of significant digits.

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Physics Math Review

24) = ______m

25) 5.25 L x 1.3 L = ______L

26) 9.0 cm + 7.66 cm + 5.44 cm = ______cm

27) 10.07 g – 3.1 g = ______

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Physics Math Review

Briefly give the rule for sig-figs when using multiplication or division:

Briefly state the rule for sig-figs when employing addition and subtraction:

Solve for x in the following problems.

28) ______

29) ______

30) ______

31) ______

Make the following conversions. Use the factor label method and show your work.

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Physics Math Review

32) 4008 g = ______g

33) 48 mL = ______mL

34) 239 mm = ______mm

35) 38 kg = ______kg

Be sure that you know the following metric prefixes and the exponent that you would use to state a measured quantity as a base unit.

Example: m: ______Ans: milli, exponent: 10-3, e.g., 22.3 mm = 22.3 x 10-3 m

T: ______G: ______

M: ______k: ______

c: ______m: ______

m: ______n: ______

p: ______f: ______

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Physics Math Review

Answer the questions that refer to the following triangles.

I. II. III.

36) For triangle I, what is the cosine of angle A? ______

37) What is the tangent of angle A for triangle I? ______

38) Find side c for triangle II. ______

39) For triangle III, express side b in terms of trigonometric function of angle B and side c.

______

a. b. c. d.

40) Which graph represents an inverse relationship? ______

41) Which graph could have the equation y = kx2? ______

42) Plot a graph of the data given in the following table.

50
40
30
20
10
0 / 1 / 2 / 3 / 4 / 5
x / y
0 / 2
0.5 / 8
1 / 14
2 / 26
3 / 38
4 / 50
  1. What is the slope of the line? ______
  2. What is the value of Y when x = 4? ______
  3. What is the value of y when x = 6? ______
  4. What is the value of x when y = 0? ______

Convert each of the following units.

43) 4 m = ______cm

44) 50.0 cm = ______m

45) 15 cm = ______mm

46) 567 mg = ______g

47) 4.6 x 103 m = ______mm

48) 8.3 x 104 g = ______kg

49) 7.3 x 105 mL = ______L

50) 8.4 x 1010 m = ______km

51) 3.8 x 104 m2 = ______mm2

52) 6.9 x 1012 cm2 = ______m2

53) 6.3 x 1021 mm = ______cm

Word Problems:

54) A rectangular floor has a length of 15.72 m and a width of 4.40 m. Calculate the area of the floor.

55) A water tank has a mass of 3.64 kg when it is empty and a mass of 51.8 kg when it is filled to a certain level. What is the mass of the water in the tank?

56) The sides of a quadrangular plot of land are 132.68 m, 48.3 m 132.736 m and 48.37 m. What is the perimeter of the plot?

57) If a sample of aluminum has a mass of 13.5 g and a volume of 5.0 cm3. What is its density?

Qualitative versus Quantitative:

58) A candle has burned during an experiment. Classify each of the following attributes as quantitative or qualitative:

______the candle is 5.4 cm tall

______the flame of the candle is blue

______the candle burned for 10.1 s

______the temperature of the flame is 400°F

______the candle is made of wax

Accuracy and Precision: circle all that apply

59) A basketball is being tossed into a basket

a) the basketball goes into the basket 99 out of 100 times

accurate precise not accurate not precise

b) the basketball hits the rim of the basket 97 out of 100 times

accurate precise not accurate not precise

c) the basketball hits the rim 54 times and randomly misses the rim 46 times

accurate precise not accurate not precise

60)

Velocity Data Collected by Three Different Students

Student A / Student B / Student C
Trial 1 / 1.54 m/s / 1.50 m/s / 1.70 m/s
Trial 2 / 1.60 m/s / 1.68 m/s / 1.69 m/s
Trial 3 / 1.57 m./s / 1.45 m/s / 1.71 m/s
Average / 1.57 m/s / 1.51 m/s / 1.70 m/s

The actual value of the car’s velocity was 1.59 m/s.

a) student A was

accurate not accurate precise not precise

b) student B was

accurate not accurate precise not precise

c) student C was

accurate not accurate precise not precise

The data shown below was captured during an electronics experiment.

Voltage (V)
±0.05V / Current (A)
±0.005A
0.1 / 0.99
0.2 / 1.85
0.3 / 2.86
0.4 / 3.75
0.5 / 4.48
0.6 / 4.85
0.7 / 5.98
0.8 / 6.26
0.9 / 7.43
1.0 / 7.58
1.1 / 8.39
1.2 / 9.17
1.3 / 9.52
1.4 / 9.89
1.5 / 10.15

Examine the graph below. Which variable is the independent variable? The dependent variable?

The error bars on the graph signify the ______(accuracy/precision) of each individual measurement.

Explain why there appear to be only error bars in the y-direction. Hint look carefully at the data

There are ______(#) distinct measurements in this data set.

Out of these data, ______(#) display a high degree of precision.

This reflects ______(%) of the entire data set.

Is the best fit function a line? How do you know for sure? (i.e., how do you know you are not looking at an extreme close up of part of a smooth curve?)

What are the units of the slope of the best-fit function?

Is this function a good fit to the data? How can you tell?

Measurement (variable) (unit) / Dimension / Measurement (variable) (unit) / Dimension
Distance (x) (meters) / [L] / Acceleration (a) (meters per second-squared) / [L] / [T]2
Time (t) (seconds) / [T] / Force (F) (Newtons) / [M] [L] / [T]2
Mass (m) (kilograms) / [M] / Energy (E) (Joules) / [M] [L]2 / [T]2
Speed (v) (meters per second) / [L] / [T]

Some of the variables in the chart above appear in the following equations, along with some numeric constants. In the mathematical statement below, substitute the appropriate dimensions and use algebra to prove the statement as being potentially true or false based only upon your analysis of the dimensions. You must show every algebraic step and you must conclude your work by indicating TRUE or FALSE.

a) b) v2 = 2ax

______

______

______

______

c) E = max d)

______

______

______

______

Solve the following equations for the variable indicated. These are real physical relationships that we will study this year.

F=ma, solve for a , solve for x , solve for t

E = ½mv2, solve for v , solve for l n1sinq1 = n2sinq2, solve for q1

V = IR, solve for I

V = BLv, use the previous equation and solve for I with this relationship

Explain some of the strengths of using the target analogy to describe the relationships and differences between accuracy and precision.

Explain some of the weaknesses of using the target analogy to describe the relationships and differences between accuracy and precision. Think specifically about experimental factors which could effect your outcomes that are not shown by the “target.”

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