math tools ~ worksheet name: - bc learning...

BCLN PHYSICS 11 - Rev. Sept/2012

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Math Tools ~ Worksheet Name: ________________________

Instructions: Using a pencil, answer the following questions. The Pre-Reading is marked, based on effort, completeness, and neatness (not accuracy). The rest of the assignment is marked, based on effort, completeness, neatness, and accuracy. Do your best!

Pre-Unit Thoughts:

Before starting this unit, what do you think is the main way(s) that physicists and engineers use math? Measurements: 1. Do an Internet or book search and find something in your universe that is represented by a

REALLY small number. a) What is it that is being described? b) Show the value in scientific notation: ____________________ c) Show the value in regular notation: ____________________

2. Do an Internet or book search and find something in your universe that is represented by a

REALLY large number. a) What is it that is being described? b) Show the value in scientific notation: ____________________ c) Show the value in regular notation: ____________________


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3. Convert the following to scientific notation in standard form.

a) 34674 ________________

b) .000235 ________________

c) -2300000 ________________

d) -.0000150 ________________

e) 0.00750 ________________

4. Round the following to the number of figures shown and convert to scientific notation in standard form

a) 634000 round to 2 sig figs ________________

b) .0345 round to 2 sig figs ________________

c) 298.76 round to 1 sig figs _________________

5. Indicate the number of significant figures in the number given

a) 120000 __________ b) 32100.0 __________ c) .00123 __________ d) 0.20040 __________ e) 730.01 __________ f) 0.0300 __________ g) 7.590 x 103 __________ h) 9 x 10-4 __________

6. Physics students often get confused between the terms "scientific notation" and "significant

figures." Figure out a way that will ensure you don't get confused between the two. Describe your method below.


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7. Suppose that three people were told to determine the length of a piece of wood and were given a tape measure whose smallest markings were at 0.1 centimeter intervals.

They report the following values:

Person Value measured for length 1 11.6 cm 2 11.6283476 cm 3 11.63 cm

Who is documenting this measurement correctly? The correct question is "who recognizes the questionable digit and documented accordingly?" Justify your answer.


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8. Evaluate the following and use the correct number of significant figures in your answer (Show all work)

a. 12.4 x 3.4560

__________

b) 33560000000 0000001224 5

×..

__________

c) ( )( )−125 3234

. ..

__________ d) 9.02 + 4.5784 + 6.2

__________ e) 2301 + 834.12 + 9.0

__________ g) 9.81 x (3.7)2

__________

9. Summarize the difference between the rules for significant figures when adding/subtracting and when multiplying/dividing?


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10. Solve for x in the following equations (show all work):

a. 2 = 5 + x ans. -3

__________

b. 19 = 2x + 7 ans. 6

__________

c. 3 – 5x = 14 ans. -2.2

__________

d. 2

5 x= ans. 10

__________

11. Rearrange the equation, solving for the variable shown (show all work).

a) E mghp = solve for m

__________

b) E mvk =12

2 solve for m

__________


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c) vd dt t

f i

f i

=−

− solve for ti

__________

d) d v t ati= +12

2 solve for vi

__________ e) vf

2 = vi2 + 2ad solve for vi

__________

f) tvv

d fi

+=

2 solve for vi

__________

g) E mvk =12

2 solve for v

__________


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12. Solve the following triangles using SOHCAHTOA and Pythagoras. Show all work.

a) In the figure below, the 4 meter ladder is making a 60 degree angle with the ground. How high does the ladder reach? How far is the base of the ladder from the wall?

h = ____________

b = ____________

b) In the figure below, the 4 meter is reaches only 1.5 meters up the wall. How far is the base of the ladder from the wall? What is the angle the ladder makes with the ground?

b = ____________

= ____________ c) Solve for x, y, and A.

x = ____________

y = ____________

A = ____________ d) Solve for x, y, and A.

R = ____________

= ____________


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13. Unit conversions (show all work – lay out in brackets, same as lesson examples)

a. 34 km into meters

__________ b. 1 day into seconds

__________ c. 12 hours into seconds

__________ d. 100 km/hr into m/s

__________

e. 40 km/hr into m/s

__________ f. 12 m/s into km/hr

__________ g. 200 g into kg

__________ h. 10 kg into grams

__________


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9. Find the slope and y-intercept of the following lines, then answer with the resulting equation of the line in y=mx + b format. Show work for slope calculation.

a)

_________________

b)

_________________

c)

_________________


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Dimensional Analysis – Verifying a Formula: 1. We can only add and subtract numbers in Physics if they have the same units. For example I can add

5.0m to 12m to get 17m but I cannot add 5.0m to 10m/s. You cannot add a velocity (10m/s) to a distance (5m) and get anything meaningful. Use dimensional analysis to ensure that the kinematic equations shown below adhere to this rule. (Note: it does not matter at this stage if you understand the physics behind the equations). The units for each variable are given. The first one is done for you.

Variable Units d m vi m/s vf m/s a m/s2 t s

a. vf = vi + at

vf = vi + at Step 1: replace each variable with units only [m/s] = [m/s] + [m/s2][s] Step 2: cancel and simplify where possible [m/s] = [m/s] + [m/s2][s] Step 3: compare resulting terms (same?) [m/s] = [m/s] + [m/s] Conclusion: Since each term has the units of m/s, the equation is likely valid.

b. v = dt

conclusion: valid / invalid (circle one)

c. d = vt


d. d = vit + ½at2 (remember that the ½ doesn’t have a unit so isn’t considered)


math tools ~ worksheet name: - bc learning...

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