Chapter 10: Mathematics Flashcards
MCAT Mastery mathematics page 360 question 1
MCAT Mastery mathematics page 360 question 2
MCAT Mastery mathematics page 360 question 3
MCAT Mastery mathematics page 360 question 4
MCAT Mastery mathematics page 360 question 5
MCAT Mastery mathematics page 360 question 6
MCAT Mastery mathematics page 360 question 7
MCAT Mastery mathematics page 360 question 8
MCAT Mastery mathematics page 360 question 9
MCAT Mastery mathematics page 361 question 10
MCAT Mastery mathematics page 360 question 11
MCAT Mastery mathematics page 360 question 12
MCAT Mastery mathematics page 360 question 13
MCAT Mastery mathematics page 360 question 14
MCAT Mastery mathematics page 360 question 15
When making an estimate for division, which way do we adjust each number (numerator and denominator)? Example?
We make a proportional adjustment in the same direction (in multiplication we lower one and try to increase the other)
When making an estimate for multiplication, what should we do if we need to adjust both numbers? Why do we need to keep track of adjustments?
If one number is rounded up, it is best to round the other number down slightly to compensate.
Keep track of adjustments and how they impact your final answer.
MCAT concept check arithmetic and sig fig 1.1 page 367
MCAT concept check arithmetic and sig fig 1.1 page 367 question 2
MCAT concept check arithmetic and sig fig 1.1 page 367 question 3
Table of common exponential and logarithmic equations on the MCAT
What is any number to the zeroth power
Any number raised to the zeroth power is 1.
If the base and exponent are the same, can we add them together?
What are the rules for multiplication and division of number with exponents?
What is the rule for a number that is raised to an exponent that is also raised to another exponent?
What is the rule for a fraction raised to an exponent?
How do we represent negative exponents as a fraction?
When adding, subtracting, multiplying, or dividing numbers with exponents, what must be true about their bases?
What is the convention for a number raised to a fractional exponent?
Table of square values of integers from 1-20
Solve 180^(1/2)
Solve this:
What is the approximate value of sqrt(2) and sqrt(3)?
The rules for logarithms follow the same trend for exponents because they are inverse functions. What are the rules for logarithms?
Derive the Henderson Hasselbalch from the expression for Ka
This is a good one.
How do we convert between natural logarithms and common logarithms?
What is the quantity of Euler’s number?
2.718
How do we estimate logarithms using scientific notation?
What is a good approximation for this:
Approximate this:
Approximate what is in the image. Why does that look familiar?
Estimating logarithms is used in calculations of pH. We work with negative logarithms and a negative exponent in the case of pH.
MCAT concept check 10.2 exponents and logarithms page 372 question 1
MCAT concept check 10.2 exponents and logarithms page 372 question 2
MCAT concept check 10.2 exponents and logarithms page 372 question 3
What are sin and cos of 0, 30, 45, 60, 90°?
What is sin cos and tan of 0, 30, 45, 60, and 90°?
MCAT concept check trigonometry 3.1 page 375 question 1
MCAT concept check trigonometry 3.1 page 375 question 2
Also, what is sin cos tan of 0,30,45,60,90°?
SOH CAH TOA
Why is tan of 90° undefined?
Because it involves dividing by 0. Tan being sin/cos, and cos(90°) is 0.
MCAT concept check trigonometry 3.1 page 375 question 3
True or false. Only angles in right triangles have characteristic values of the trigonometric functions.
False. Even though calculating the values of sine, cosine, and tangent, is more complicated in a triangle that does not contain a right angle, all possible angles do you still have characteristic trigonometric values.
MCAT concept check trigonometry 3.1 page 375 question 4
At what angle between 0° and 180° does each trigonometric function have a value of 1?
Also. What is sin, cos, and tan, of 0, 30, 45, 60, 90°?
What is a direct relationship, what is an inverse relationship?
Indirect relationships, increasing one variable proportionately increases the other: as one decreases the other decreases by the same proportion.
In inverse relationships, any increase in one variable is associated with a proportional decrease in the other.
Table of metric prefixes and factors
Convert 6 hours to minutes. To seconds.
Conversion example page 378
This was a good exercise in unit conversion and estimation.
What are the conversations between F, C, and K.
What is normal body temp in F and C? What is a fever designated as? Hypothermia?
What is dimensional analysis? How is it helpful?
Dimensional analysis is the analysis of a relationship utilizing the units given and desired as the units of the calculated answer must match the units of the answer choices on the MCAT.
Consider given quantity of N/C, and the other in volts. The answer choice for the question are in meters. Even without tempering that E=Vd, we can divide the voltage by the electric field to get meters:
Example proportion of blood volume in left ventricle with each contraction. Page 379.
Solve the following equation using substitution.
Solve the following equation by setting the equations equal.
Solve the following equation by using elimination
MCAT concept check problem solving 10.4 page 381 question 1
how are conversions between metric prefixes accomplished? How would a distance be converted from millimeters to kilometers?
Conversion between metric prefixes is accomplished by multiplication or division by the appropriate power of 10.
MCAT concept check problem solving 10.4 page 381 question 2
In direct relationships, as one quantity increases, the other also increases in proportion.
In inverse relationships, as one quantity increases, the other decreases in proportion.
MCAT concept check problem solving 10.4 page 381 question 3
Relevant equations and relationships for chapter 10 mathematics.
