UMN CoP Prerequisite Knowledge Check: Calculus

Which temperature scale is used in theoretical expressions with T?

Kelvin

Boiling point of water?

373.15 K, 100°C, 212°F

Freezing point of water?

273.15 K, 0°C, 32°F

Absolute zero?

0 K, -273.15°C, -459.67°F

Celsius to Kelvin?

K = 273.15 + °C

Kelvin to Celsius?

°C = K - 273.15°

Celsius to Fahrenheit?

°F = (°C × 9/5) + 32

°F = (°C × 1.8) + 32

Fahrenheit to Celsius?

°C = (°F - 32) × 5/9

°C = (°F - 32) × 0.56

Rectal temperature is (>, =, OR <) oral temperature?

Rectal > oral, by about 1°F.

Oral temperature is (>, =, OR <) axillary temperature?

Oral > axillary, by about 1°F.

Normal body temperature?

98.6°F, 37.0°C

Oral temperature?

39.6°C, 103.3°F

Which metric units are used to measure length (like width, distance, thickness, girth)?

Millimeter (mm), centimeter (cm), meter (m), kilometer (km)

10mm = __?__ cm; 100cm = __?__ m; 1km = __?__ m

1; 1; 1,000

Which metric units are used to measure mass?

Milligram (mg), gram (g), kilogram (kg)

1,000mg = __?__ g; 1kg = __?__ g

1; 1,000

Which metric units are used to measure volume?

Milliliter (mL), cubic centimeter (cm³), liter (L), cubic meter (m)

1,000mL = __?__ L; 1cm³ = __?__ mL; 1,000L = __?__ m³

1; 1; 1

kilo-: symbol / factor / numerically / meaning

k / 10³ / 1,000 / thousand

deci-: symbol / factor / numerically / meaning

d / 10^-1 / 0.1 / tenth

centi-: symbol / factor / numerically / meaning

c / 10^-2 / 0.01 / hundredth

milli-: symbol / factor / numerically / meaning

m / 10^-3 / 0.001 / thousandth

micro-: symbol / factor / numerically / meaning

μ / 10^-6 / 0.000001 / millionth

nano-: symbol / factor / numerically / meaning

n / 10^-9 / 0.000000001 / billionth

pico-: symbol / factor / numerically / meaning

p / 10^-12 / 0.000000000001 / trillionth

1 fl. oz. = __?__ mL

29.6

1 gal = __?__ L

3.8

1 pint = __?__ fl. oz. = __?__ mL

16, 473

1 teaspoonful = __?__ mL

5

1 tablespoonful = __?__ mL

15

1 in = __?__ cm

2.54

1 oz = __?__ g

28.4

2.2 lb = __?__ kg

1

1 mL = __?__ cm³

1

1 mL of water ≈ __?__ g; 1 L of water ≈ __?__ kg

1; 1

Molar concentration (M) = ?

Amount in moles (mol) / volume of solution in liters (L)

1 M = 1 mol/L

1 mM = 1 mmol/L

1 μM = 1 μmol/L

1 nM = 1 nmol/L

A mole is the __?__ of a substance in grams.

molecular weight

Convert 5% (w/v) dextrose (MW = 180) to molar concentration.

5% (w/v) = 5 g/100 mL = 50 g/1,000 mL = 50 g/L

50 g/L × (1 mol/180 g) = 0.278 mol/L = 0.278 M

5 lb, 9 oz = __?__ g

5 lb × (16 oz/1 lb) = 80 oz + 9 oz = 89 oz

89 oz × (28.4 g/1 oz) = 2,528 g

1.6 ng/mL = __?__ mg/L

1.6 ng/mL × (1 μg/1000 ng) × (1 mg/1,000 μg) × (1,000 mL/1 L) = 0.0016 mg/L

a × a × a = ?

a³

a² × a³ = ?

a²⁺³ = a⁵

(a²)³ = ?

a² × a² × a² = a⁶

(a/b)³ = ?

a³/b³

a⁵/a² = ?

a^5-2 = a³

a⁵/a⁴ = ?

a^5-4 = a¹ = a

a²/a⁴ = ?

a^2-4 = a^-2 = 1/a²

a²/a² = ?

a^2-2 = a⁰ = 1

a^1/2 = ?

√a

a^1/2 × a^1/2 = ?

a^1/2 + a^1/2 = a¹ = a

a^2/3 = ?

(a²)^1/3 = ∛a²

logab = ?

loga + logb

log(a/b) = ?

loga - logb

log₁₀1 = ?

0 because 10⁰ = 1.

log_e1 = ?

0 because e⁰ = 1.

log1 = ?

0

log(1/a) = ?

log1 - loga = -loga

loga² = ?

loga + loga = 2loga

log√a = ?

loga^1/2 = (1/2)loga

loga^-2 = ?

-2loga = 2log(1/a)

log₁₀1,000 = ?

3 because 10³ = 1,000.

The exponent 3 is the logarithm of 1,000.

1,000 is the antilogarithm of 3.

log10³ = ?

3log10 = 3

e^lnx = ?

x

ln(e^x) = ?

x

ln(e^1/x) = ?

1/x

10^log2+logx = ?

10^log2x = 2x

10(x+logx) = ?

x10^x

What do the dependent and independent variables represent?

y is the dependent variable and x is the independent variable.

Changes in y result from changes in x.

If x changes, how does y change in y = kx?

y changes by a constant factor; the ratio y/x stays the same.

How do you find the slope of a best-fit line?

Choose two points on the best-fit line, not the raw data points. Then calculate the slope between those two points.

This is more accurate when the data are variable.