Chapter 1: Basic Math Review

Question 1

Physical quantities are expressed with _______ and _____

Answer 1

Numbers / Units

Question 2

What is the abbreviation for “Mega”?

Answer 2

M

Question 3

What is the abbreviation for Kilo?

Answer 3

k

Question 4

What is the abbreviation for Centi?

Answer 4

c

Question 5

What is the abbreviation for milli

Answer 5

m

Question 6

What is the abbreviation for micro

Answer 6

mu

Question 7

What is the abbreviation for nano?

Answer 7

n

Question 8

What is the value of M?

Answer 8

Million / 10^6

Question 9

What is the value of k?

Answer 9

1,000 / 10^3

Question 10

What is the value of centi?

Answer 10

0.01 / 10^-2

Question 11

What is the value of milli?

Answer 11

0.001 / 10^-3

Question 12

What is the value of micro?

Answer 12

10^-6

Question 13

What is the value of nano?

Answer 13

10^-9

Question 14

What is the method for converting units?

Answer 14

Multiply by 1 and ensure old units are canceled away

Question 15

What does SOH-CAH-TOA stand for?

Answer 15

Sin = opp/hyp
Cos = adj/hyp
Toa = opp/adj

Question 16

Define vector

Answer 16

A quantity with a direction and a strength (magnitude)

Question 17

T/F: The magnitude of a vector is always a positive number.

Answer 17

True

Question 18

What is the difference between distance and displacement?

Answer 18

Distance is the total amount travleded while displacement is the amount moved from start to finish.

Ex: A swimmer swim laps of a 50ft pool. They swim 6 times. Their distance is (50x6) but their displacement is 0.

Question 19

How many significant figures does 2.0 have?

Answer 19

2

Question 20

How many significant figures does 2.02 have?

Answer 20

3

Question 21

How many significant figures does 2.020 have?

Answer 21

4 (any 0 past a decimal point is significant)

Question 22

How many significant figures does 0.202 have?

Answer 22

3. (Leading 0’s are never significant)

Question 23

How many significant figures does 202ō

Answer 23

4 (A line above the last number means that number is measured and therefore significant)

Question 24

How many signifiant figures does 20ō0 have?

Answer 24

3 (since the 0 with a line above it is the last measured number, the 0 after it is considered “rounding” and therefore NOT significant)

Question 25

How many significant figures is 2020?

Answer 25

3 for sure, but maybe 4. It is inconclusive since we do not know what is and is not measured.

Question 26

Evaluate 5.113 + 4.90 and give proper sig. figs

Answer 26

10.01.

We have 4 sig. figs. because when +/- cut off at the decimal point in the same position. (So since 4.90 is the lower value, but has 2 decimal places, our final answer must have 2 decimal places)

Question 27

What is meant by “polar” form?

Answer 27

Instead of x,y coordinates you would say “28 North of east” to represent the direction.

Question 28

How many sig. figs. is 3000?

Answer 28

1, trailing 0’s NOT behind a decimal are not significant

Question 29

How many sig. figs. is 0.009?

Answer 29

1, leading zeros, even after a decimal are not significant

Question 30

How many sig. figs is 4.050?

Answer 30

4

Question 31

How many sig. figs is 2300

Answer 31

2, trailing 0’s are not significant

Question 32

Consider this formula: z = y /x

If Z = 4.0, and y = 6.0, what is the value of x? Express your answer to the tenths place

Answer 32

X = 1.5

Explanation:
1.) Assess what you know
z = 4.0
y = 6.0
2) Rearrange the equation
2a) z = y / x
i) Multiply both sides by x
2b) zx = y
ii) divide both sides by z
2c) x = y/z
3) Plug in the numbers
3a) x = 6.0 / 4.0
3b) x = 1.5

Question 33

The expression a-(b+c) is equal to which quantities

1. a - b - c
2. (a-b)+c
3. a - b + c

Answer 33

1. a - b - c

Explanation:

a - (b+c)
a - (bc)
distribute the - sign
a - b - c

Question 34

Rearrange the equation to isolate a

(a + b/c)(d-e) = f

Answer 34

a = f/(d-e) - b/c

explanation:
(a + b/c)(d-e) = f
-Divide (d-e)
(a+ b/c) = f / (d-e)
-Subtract b/c
a = f/(d-e) - b/c

Question 35

Solve for x

625 = 5x^3

Express the answer to the hundredth place

Answer 35

x = 5

Explanation
625 = 5x^3
-divide both sides by 5
125 = x^3
-take the cube root of both sides
x = 5

Question 36

A certain line is defined by the equation

y = 5x-8 / 2

What is the slope? (Hint: y=mx+b)

Answer 36

m = 5/2

Explanation:
y = mx+b
y = 5x +b
5 = m
Slope = rise / run
5 /2

Question 37

A certain line is defined by the equation

y = 5x-8 / 2

What is the y-intercept of the line? (Hint: y=mx+b)

Answer 37

b = -4

Explanation:
y = 5x - 8
y = mx + b
b = -8
-8 /2 = -4

Question 38

What is the scientific notation of 673.5?

Answer 38

6.735 x 10^2

Question 39

What is the scientific notation of 0.034?

Answer 39

3.4 x 10^-2