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For the final, you may prepare one side of an 8 ½” by 11” sheet with equations, constants, and anything else you think you may need for the exam. You will turn this in with your final. It would be to your advantage to prepare your card yourself, so that you know where everything is, and what everything means. At a minimum, your card should contain all of the equations that we have used this year, as I WILL NOT BE PROVIDING THESE FOR YOU. A review of the topics is below.

Math and Measurement (Chapter 2) Identify what digits in a reported measurement are significant. Add/subtract, and multiply/divide significant figures according to the prescribed rules. Use dimensional analysis to convert from one unit to another. Distinguish between accuracy and precision. Use graduated instruments to measure quantities. Create graphs to demonstrate the relationship amongst variables. Draw lines of best-fit on a graph, and calculate the slope of best-fit lines to analyze data.

Motion in One Dimension (Chapters 3 and 4) Describe motion in terms of frame of reference, displacement, time, and velocity. Define and distinguish between distance and displacement, between speed and velocity. Define acceleration and recognize situations in which acceleration exists. Distinguish between instantaneous speeds, velocities, and accelerations, and average speeds, velocities, and accelerations. Calculate average speeds, velocities and accelerations. Construct and interpret graphs of position vs. time, velocity vs. time and acceleration vs. time. Apply kinematic equations to calculate distance, time, initial or final velocities under conditions of constant acceleration. Given the initial velocity and acceleration of an object, predict the resulting motion (see page 51). Recognize the value of g, the acceleration due to gravity on Earth (near sea level).

Vectors and Projectiles (Chapter 6) Recognize which quantities we’ve discussed are scalar and which are vector. Add and subtract vectors using graphical methods. Break vectors into vector components. Add and subtract vectors mathematically including vectors that are not parallel nor perpendicular to each other. Resolve the weight of an object on an incline into components that are parallel and perpendicular to the incline. Recognize examples of projectile motion. Describe the changes in the horizontal and vertical components of a projectile’s velocity. Resolve projectile vectors into their components and apply kinematic equations to solve problems.

Forces and Newton’s Laws (Chapter 5) Explain how unbalanced forces affect the motion of an object. Interpret and construct free-body diagrams. State each of Newton’s three Laws of Motion. Explain the relationship between the motion of an object and the net force acting on it (Newton’s Second). Use free-body diagrams to determine the net force on an object. Calculate static and kinetic friction forces. Define equilibrium, and recognize situations in which an object or system of objects is in equilibrium. Identify action-reaction pairs, and realize the impact of Newton’s oft-misunderstood Third Law. Explain the difference between mass and weight, and recognize appropriate units for both. Find the direction and magnitude of normal forces and for goodness sake, recognize that the normal force is not necessarily equal to the weight of an object!

Math and Measurement

SIGNIFICANT FIGURES:

What’s Significant? Don’t Forget the Rules – look them up if you have to. Answer the following with “always”, “sometimes”, or “never”:

• Non-zero digits are ________________ significant.

• Zeros between two significant digits are __________________ significant. (I like to call these “sandwich zeros”)

• Leading zeros, (zeros to the left of the first non-zero digit) are ____________________ significant.

• Trailing zeros, (zeros to the right of the last non-zero digit) are ____________________ significant if they are in a number with a decimal point.

1. Give the correct number of significant figures in the following measurements,

a) 7.0890

b) 0.00520

c) 6200

d) 1.20000500

e) 100,001

Addition and Subtraction: When adding or subtracting significant figures, remember that your calculated value cannot be more precise than the least precise quantity used in the calculation – that least precise quantity has the fewest digits to the right of the decimal point.

Multiplication and Division: When multiplying or dividing significant figures, remember that the number of significant figures in your final calculated value will the same as the quantity with the fewest number of significant figures.

2. Use the rules above to complete the following operations; express your answer using the correct number of significant figures – it may be necessary to convert quantities so that they have the same units.

(a) 0.0025 cm + 1.24 cm + 0.45 cm =

(b) 2.367 mm × 1.52 mm =

(c) 2.67 x 10-3 kg – 9.5 x 10-4 kg + 47.3 kg =

(d) 7 x 105 kg /2.4 x 107 L =

(e) 0.006 m + 0.03 cm =

METRIC SYSTEM: The international science community uses the SI measurement system.

3. What is the factor denoted by the following metric prefixes (note, you must REMEMBER the ones in bold)?

milli- (m)____________ 2015 milliamperes is ____________ amperes

centi- (c)____________ 5200 cm3 is ____________ m3

kilo- (k)____________ 15 kilocalories is _______ calories

4. Arrange the following prefixes from largest to smallest:

deci-, kilo-, deka-, milli- hecto-, centi-

SCIENTIFIC NOTATION: When reporting numbers in proper scientific notation, the base number n must be ≥1 and ................
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