Math practice questions and math explained at end

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Last updated 12:38 AM on 7/18/26
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100 Terms

1
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calculate the necessary MU to deliver 200 cGy at a depth of 6 cm, at 100 cm SSD, for a single field, with a field size of 8 cm x 8 cm with an output of 0.985 and the following factors:

Depth=4 ,8X* TMR = 0.998, PDD= 0.913

Depth=5 ,8X* TMR = 0.923, PDD= 0.816

Depth=6 ,8X* TMR = 0.894, PDD= 0.797

Depth=7 ,8X* TMR = 0.815, PDD= 0.722

225MU

3 multiple choice options

2
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180 cGy is to be treated to a depth of 8 cm where the PDD is 84.2. What is the dose at 10 cm if the PDD is 80.2?

171 cgy

3 multiple choice options

3
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If 225 cGy is delivered to a depth of 7 cm with a PDD of 68%, what is the dose delivered to dmax?

331 cgy

3 multiple choice options

4
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A patient is to be treated using a three-field prone pelvis SAD plan. The lateral fields use wedges. How many MU will each lateral field receive if the prescribed dose is 180 cGy per fraction, and if the fields are weighted equally and have a wedge factor of 0.74, output of 0.90 cGy/MU, and TMR of 0.812?

111MU

3 multiple choice options

5
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Two abutting PA fields are to be matched at a depth of 5 cm. The beam energy used is 10 MV. The field collimator lengths are 20 cm and 24 cm and both are treated using 100 SSD. Calculate the skin gap.

1.1 cm

3 multiple choice options

6
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What collimator rotation is needed for a CSI treatment with a spinal field length of 20 cm that is treated at 100 SSD?

6 degrees

3 multiple choice options

7
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If the dose rate is 250 cGy/min at 100 cm from the source, what is the dose rate at 250 cm from the source?

40 cGy/min

3 multiple choice options

8
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A port film is taken at 140 cm from the source, The irradiated field measures 12 cm x 12 cm on the imager. What does this field size measure at isocenter?

8.6 cm x 8.6 cm

3 multiple choice options

9
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What is the MU setting requires to treat a 9MeV electron field that delivers 180 cgy per fraction at the 90% isodose line? The output with the cone insert is 1.01 cgy/MU

198 MU

3 multiple choice options

10
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A gold seed permanent implant was placed on Sunday and started with an activity of 150 mCi. What is the activity of this seed 5 days later if the half-life is 2.7 days?

42 mCi

3 multiple choice options

11
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A patient is treated AP/PA to midplane. At 100 SAD isocenter, the field size measures 15 x 7 cm. What is the field size at the skin surface if the patient's separation is 24 cm?

13 cm x 6 cm

3 multiple choice options

12
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Which would be used to calculate MU for a 12 cm x 9 cm rectangular field

Look at chart on page 79

86.2

13
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The maximum field size at 100 SAD is 40 cm x 40 cm. What SSD is needed to achieve a field size of 55 cm x 25 cm?

138 SSD

3 multiple choice options

14
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The treatment is prescribed to deliver per fraction. This treatment not require a block or tray. However, the pc3tient was accidentally treated With a tray in place. This tray has a tray factor of 0.910. What is the actual dose that the patient recieved?

164 cgy

3 multiple choice options

15
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A conventional simulation was to simulate a patient. A radiopaque marker was placed on the table which is at a distance of 110 SSD. The marker measures 8 mm on the image detector that is 130 cm from the source. What is the actual size of the marker?

6.8 mm

3 multiple choice options

16
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A seed appears on an image measuring 15 mm. The actual seed is 9 mm. What is the magnification factor if the source to image receptor distance is 115 cm?

1.7

3 multiple choice options

17
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18
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19
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The calculated MU to deliver 180 cGy is 210 MU. If all factors remain the same, what is the MU needed to deliver 150 cGy?

175 MU

3 multiple choice options

20
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The patient's treatment was planned to receive 180 cGy at a distance of 100 SSD. The patient was mistakenly treated at 95 SSD due to an uncalibrated ODI. What dose did the patient actually receive?

199 cGy

3 multiple choice options

21
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What is the equivalent square of a rectangle that measures 30 cm x 12 cm?

17 cm x 17cm

3 multiple choice options

22
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A patient is prescribed 3000 cGy with a total of 10 fractions for an AP/PA lung field weighted 2:1 respectively. How many cGy the AP field receive in one fraction

200 cgy

3 multiple choice options

23
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Calculate the necessary couch rotation needed for a CSI treatment with the following parameters:

brain field length = 12 cm

brain SAD = 100

spine field length = 30 cm

spine SSD = 100

3.4 degrees

3 multiple choice options

24
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A treatment plan was created to treat a total of 281 MU. The radiation oncologist decides to add a wedge to the plan. What will be the new MU if the wedge factor is 0.82?

343 MU

3 multiple choice options

25
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Calculate the therapeutic ratio given a lethal dose of 5000 cGy and normal tissue tolerance of 6000 cGy?

1.2

3 multiple choice options

26
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A plan is intended to treat 180 cGy with 210 Mu. A tray was accidentally left in place during treatment What dose did the patient actually receive if the tray factor is 0.96?

173 cgy

3 multiple choice options

27
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After looking over an electron plan, the radiation oncologist decides to treat the patient with 200 cGy per fraction using 9 MeV and to the 80% isodose line. Calculate the MU needed given a cone factor of 0.78 and PDD of 0.963.

333 MU

3 multiple choice options

28
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Parallel opposed lateral brain fields are equally weighted to deliver 300 cGy to midplane. Calculate the MU p« field given a TMR of 0.895.

168 MU

3 multiple choice options

29
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If the field size measures 8 cm x 8 an on the patienEs skin at 75 SSD, what is the field size at isocenter 100 SAD?

10.7 cm x 10.7 CM

3 multiple choice options

30
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A treatment plan calls for the patient to be setup at 100 SSD. However, the Patient is accidentally treated at 109 SSD. What is the dose error?

16% underdose

3 multiple choice options

31
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The patient's original treatment plan was to midplane for an AP/PA spine treatment. However, the radiation oncologist decided to make a 3 Cm anterior isocenter shift. What is the new SSD if the patient's separation is 30 cm?

88cm

3 multiple choice options

32
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Determine the appropriate wedge angle given a hinge angle of 90 degrees.

45 degrees

3 multiple choice options

33
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Which hinge angle below requires a 15-degree wedge to reduce the hot spot?

150

3 multiple choice options

34
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A counter-clockwise arc therapy treatment will be delivering 80 MI.-J. The gantry has a speed of 0.8 degrees/MU. If the gantry is starting at 20 degrees, determine the stop angle.

316 degrees

3 multiple choice options

35
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Calculate the estimated error if a patient was intended to be treated at 100 SSD, but was accidentally treated at midplane with a separation of 28 cm.

35 % overdose

3 multiple choice options

36
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A PA field with an SSD setup measures 40 cm x 14 cm at 100 SSD. However, an area measuring 44 cm x 14 cm must be covered, Calculate the extended SSD required to ensure the entire field is encompassed,

110 SSD

3 multiple choice options

37
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Two adjacent PA fields are treated at a depth of 4 cm. The beam energy used is 10 MV. One field is 20 cm x 10 cm and is treated to 100 SSD. The other field is 40 cm x 12 cm and is treated to 110 SSD. Calculate the skin gap.

1.2 cm

3 multiple choice options

38
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A source has a half-life of 30 days. What is the activity after 20 days if the initial activity is 3.2 mCi?

2.0 mCi

39
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A patient is prescribed a dose of 6000 cGy to a single field over 30 fractions. The daily fractionated dose is 200 cGy and is intended to be treated at 90 SSD. What is the patient's total dose if the patient was accidentally treated at 80 SSD daily?

7594cGy

3 multiple choice options

40
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Calculate the equivalent square of a rectangle that measures 8 cm x 15 cm?

10.4 cm x 10.4 cm

3 multiple choice options

41
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Calculate the therapeutic ratio given a normal tissue tolerance of 10 Gy and lethal tumor dose of 7 Gy?

1.4

3 multiple choice options

42
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Calculate the extended SSD required to achieve a field size of 54 x 54 cm if the maximum field size is 40 x 40 cm at 100 SSD.

135 SSD

3 multiple choice options

43
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Calculate the average life for a radioaaive source that has a half-life of 30 years.

43 years

3 multiple choice options

44
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Calculate the approximate equivalent square of a field measuring 23 x 31 cm that has two blocked areas each measuring 5 x 8 cm.

25cm X 25cm

3 multiple choice options

45
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Atreatment plan delivers 210 MU per fraction. The right and left laterals are weighted 3:1 respectively. Calculate the left lateral MU received in one

53 MU

3 multiple choice options

46
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The field size measures 12 cm x 12 cm at isocenter, which is at a depth of 12 cm within the patient. Calculate the field size as it appears on the patient's skin surface

10.6cm x 10.6 cm

3 multiple choice options

47
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Calculate the output for a TBI treatment at 450 cm given the output is 1.0 Cgy per mu at 100cm?

0.05 cGy/MU

3 multiple choice options

48
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Determine the gantry speed if a gantry rotates from 275 to 145 in a clockwise direction and delivers 321 MU?

0.7 degrees/MU

3 multiple choice options

49
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Calculate the collimator rotation required for a lateral brain field of a CSI treatment with the following parameters: brain field length = 14 an brain SAD = 100 spine field length = 22 cm spine SSD = 110

5.7 degrees

3 multiple choice options

50
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A radioactive source has a half-life of 2.5 days. How many days will it take to reduce the source to about 3% of its original value?

12.5 days

3 multiple choice options

51
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What is the acronym to remember unit or metric conversions

KHDBDCM

King, Henry, died, by drinking, chocolate milk

52
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King = kilo = 1,000

Henry= Hecto = 100

Died = deka = 10

By = base = 1

Drinking= Deci = 0.1

Chocolate= centi = 0.01

Milk = milli = 0.001

This is a helpful hint for....

conversion

53
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Convert 5 cgy to 5 GY

0.05 GY

Starts with Centi, goes to the base so you slide decimal over 2 with zeros.

54
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The inverse square law accounts for the

change in quality of radiation as distance changes

55
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What is inverse square formula?

I1 / I2 = ( D2/ D1) ^2

56
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IF the dose rate is 400 mR/ hr at 3 meters from the source, what is the dose rate at 2 meters from the source?

Pick the correct answer and correct steps

400/ X = (2/3)^2

400/ 0.444 = X

X= 900 mR/ hr

3 multiple choice options

57
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What is the equation for inverse square factor?

(SSD1/ SSD2) ^2

58
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inverse square factor is used to calculate

Dose error- Overdose or underdose

59
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If SSD is further then the original then it will be an

underdose

3 multiple choice options

60
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If SSD is closer then the original then it will be an

overdose

3 multiple choice options

61
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A treatment plan is set to treat the patient at 110 SSD. However, the patient is accidentally treated to 100 SSD. What is the dose error?

(110/100) ^2

110/100 = 1.1

1.1 ^2 = 1.21 or 121 %

121% indicates an overdose, however the percent of overdose the patient received is 121-100

21 % overdose = answer

1 multiple choice option

62
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When are direct proportions used?

when trying to find a new field size at different distance or SSD

63
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There is a(n) ________ relationship between the field size and distance

direct

3 multiple choice options

64
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What is the direct proportions formula?

( FS1 / SSD1) = (FS2 / SSD2)

65
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IF the field size at isocenter is 12 X 12cm, what is the field size at 91 SSD if the linear accelerator is calibrated to 100 SAD?

( FS1 / SSD1) = (FS2 / SSD2)

( 12 / 100) = (X / 91)

.12 = X / 91

.12 (90) = X

X = 10.9

The field size needed is 10.9 X 10.9

66
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PDD is a ratio that compares the

absorbed dose at a specified depth to the absorbed dose at a reference depth (dmax)

67
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PDD is utilized for ___ MU calculations

SSD

68
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What 4 things effect PDD

energy, depth, field size, SSD

69
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Different types of tissue have different densities which may affect the attenuation scatter which can then impact ____

Examples: lung, bone, water

PDD

70
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What is the PDD equation at central axis

( Dose A / PDD a) = (Dose B / PDD b)

71
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For a 6MV beam the dose at a depth of 6cm is 200cgy with a PDD of 0.892. What is the dose at dmax?

( Dose A / PDD a) = (Dose B / PDD b)

We get 1 from knowing PDD at dmax is 1

( 200 / 0.892) = (X / 1)

200/ 0.892 = 224.215

224.215/ 1 = 224 cGy

Answer= 224 cGy

1 multiple choice option

72
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What is the Mayneord F factor used for?

Correction factor for SSDs different than 100 cm

73
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What is the Mayneord F factor equation

[(ssd2 + dmax) / (ssd1 + dmax)] multiplied by

[(ssd2 +depth) /(ssd1 + depth)]

74
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magnification occurs on imaging due to

beam divergence

75
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What is the magnification factor formula?

image size ÷ object size

OR

SID ÷ SOD

76
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What does SID in magnification formula mean

source to image detector distance

77
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What does SOD in magnification formula mean

Source to object distance

78
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What is the actual size of the fiducial marker in the patient at a distance from the source of 88cm when they appear 4mm in width on an image that is taken 120cm from the source?

mag factor = SID ÷ SOD

mag factor= 120 / 88

mag factor = 1.36

mag = image size ÷ object size

1.36 = 4mm / X

4mm/ 1.36 = X

X = object size= 2.9 mm

79
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Skin gaps may need to be used for larger treatment fields to avoid

hot or cold spots

80
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What is the gap calc formula?

[ (L1 / 2) x ( d/ SSD1)] +

[ (L2 / 2) x ( d/ SSD2)]

81
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Two posterior spine fields are required to treat a patient. Each field is treated with 6 MV and to a depth of 6cm. One field measure 20cm x 6cm at 100 SSD. The other field measures 30cm x 6cm at 100 SSd. What is the required gap needed?

Gap = [ (L1 / 2) x ( d/ SSD1)] +

[ (L2 / 2) x ( d/ SSD2)]

Gap = [ (20/ 2) x ( 6/ 100)] +

[ (30 / 2) x ( 6/ 100)]

Gap = (0.6) + (0.9)

Gap = 1.5 cm

82
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Some treatments require collimator and couch rotations that coincide with beam angles and divergence to avoid

hot spots or overdose to certain areas

83
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Using collimator and couch rotations to avoid hot spots or overdose is commonly used for ____________ is CSI irradiation treatments

brain and spine

84
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For the lateral brain fields of CSI treatments the collimator roatation will need to be calculated to align with, or match the

divergence of the length of the spine field

85
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What is the fomrula for collimator/ couch rotations

Tan^-1 [ (1/2) ( L1 / SSD1) ]

2 multiple choice options

86
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A craniospinal plan is using 100cm SSD for all spinal fields. The brain field length is 14cm. The spine field length is 35cm. In order to avoid overlap, what is the necessary collimator rotation for the brain field?

Tan^-1 [ (1/2)( L1/SSD1) ]

Tan^-1 [ (1/2)( 35/100) ]

Tan^-1 [ (1/2)(.35)

tAN^-1 (0.175)

Final answer: 9.9- degree collimator rotation

1 multiple choice option

87
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What is the equation for equivalent square?

Eq square= 2 ( a x b) / a +b

2 multiple choice options

88
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What is the equivalent square of a rectangle measuring 12 cm X 18 cm ?

Eq square= 2 ( a x b) / a +b

Eq square= 2 ( 12 x 18) / 12 + 18

Eq Square = 14.4 x 14.4

2 multiple choice options

89
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What is formula for blocked equivalent square

Sq Root of: (area of open field) - (area of blocked field)

2 multiple choice options

90
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If a large rectangle measures 20cm x 16cm with a blocked field of 9cm x 7cm. What is the equivalent squared?

Sq Root of: (20x16) - (9x7)

Sq Root of: (320) - (63)

Sq Root of: 257

answer: 16cm x 16 cm

2 multiple choice options

91
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What is SSD MU equation?

prescribed dose / PDD (other given factors)

3 multiple choice options

92
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What is SAD MU equation?

prescribed dose / (output factor)(TMR)(tray factor)

93
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What terminology indicates SAD MU problems?

midplane and use of two fields (ex. AP/PA)

94
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calculate the MU needed to deliver 180cGy to two fields (AP and PA) delivered to midplane if the dose rate is 1.0 cGy/ MU, the TMR is 1.013, and the Scp is 1.021, and there are no beam modifiers used.

SAD MU= prescribed dose / (output factor)(TMR)(tray factor)

SAD MU= 180cGy / (1.0 cGy/MU)(1.013)(1.021)

SAD MU = 180cGy / (1.034)

SAD MU= 174

1 multiple choice option

95
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Calculate the daily MU needed for a single field SSD treatment that uses a tray with a tray factor of 0.95 and a PDD of 98.6%. The prescribed dose is 3000cGy for a total of 10 fractions.

SSD MU= prescribed dose / PDD (other given factors)

SSD MU= 300cGy / 0.986 (0.95)

SSD MU= 300cGy/ 0.937

SSD MU = 320

1 multiple choice option

96
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What is tray factor equation?

tray factor= dose with tray/ dose without tray

97
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what is the tray factor if the dose with the tray is 178 cGy and the dose without the tray is 180 cGy?

tray factor= dose with tray/ dose without tray

tray factor= 178/ 180

tray factor= 0.99

1 multiple choice option

98
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field weighting can be used to avoid

overdose to certain organs at risk

99
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What is the equation for gantry rotation

gantry speed = degrees/ MU

1 multiple choice option

100
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What is the gantry speed for an arc treatment rotating a total of 360 degrees and delivering 331 MU?

gantry speed = degrees/ MU

gantry speed = 360/331

gantry speed = 1.09 degrees/MU

1 multiple choice option