Chapter 10: Mathematics

Question 1

MCAT Mastery mathematics page 360 question 1

Answer 1

Question 2

MCAT Mastery mathematics page 360 question 2

Answer 2

Question 3

MCAT Mastery mathematics page 360 question 3

Answer 3

Question 4

MCAT Mastery mathematics page 360 question 4

Answer 4

Question 5

MCAT Mastery mathematics page 360 question 5

Answer 5

Question 6

MCAT Mastery mathematics page 360 question 6

Answer 6

Question 7

MCAT Mastery mathematics page 360 question 7

Answer 7

Question 8

MCAT Mastery mathematics page 360 question 8

Answer 8

Question 9

MCAT Mastery mathematics page 360 question 9

Answer 9

Question 10

MCAT Mastery mathematics page 361 question 10

Answer 10

Question 11

MCAT Mastery mathematics page 360 question 11

Answer 11

Question 12

MCAT Mastery mathematics page 360 question 12

Answer 12

Question 13

MCAT Mastery mathematics page 360 question 13

Answer 13

Question 14

MCAT Mastery mathematics page 360 question 14

Answer 14

Question 15

MCAT Mastery mathematics page 360 question 15

Answer 15

Question 16

When making an estimate for division, which way do we adjust each number (numerator and denominator)? Example?

Answer 16

We make a proportional adjustment in the same direction (in multiplication we lower one and try to increase the other)

Question 17

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?

Answer 17

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.

Question 18

MCAT concept check arithmetic and sig fig 1.1 page 367

Answer 18

Question 19

MCAT concept check arithmetic and sig fig 1.1 page 367 question 2

Answer 19

Question 20

MCAT concept check arithmetic and sig fig 1.1 page 367 question 3

Answer 20

Question 21

Table of common exponential and logarithmic equations on the MCAT

Answer 21

Question 22

What is any number to the zeroth power

Answer 22

Any number raised to the zeroth power is 1.

Question 23

If the base and exponent are the same, can we add them together?

Answer 23

Question 24

What are the rules for multiplication and division of number with exponents?

Answer 24

Question 25

What is the rule for a number that is raised to an exponent that is also raised to another exponent?

Answer 25

Question 26

What is the rule for a fraction raised to an exponent?

Answer 26

Question 27

How do we represent negative exponents as a fraction?

Answer 27

Question 28

When adding, subtracting, multiplying, or dividing numbers with exponents, what must be true about their bases?

Answer 28

Question 29

What is the convention for a number raised to a fractional exponent?

Answer 29

Question 30

Table of square values of integers from 1-20

Answer 30

Question 31

Solve 180^(1/2)

Answer 31

Question 32

Solve this:

Answer 32

Question 33

What is the approximate value of sqrt(2) and sqrt(3)?

Answer 33

Question 34

The rules for logarithms follow the same trend for exponents because they are inverse functions. What are the rules for logarithms?

Answer 34

Question 35

Derive the Henderson Hasselbalch from the expression for Ka

Answer 35

This is a good one.

Question 36

How do we convert between natural logarithms and common logarithms?

Answer 36

Question 37

What is the quantity of Euler’s number?

Answer 37

2.718

Question 38

How do we estimate logarithms using scientific notation?

Answer 38

Question 39

What is a good approximation for this:

Answer 39

Question 40

Approximate this:

Answer 40

Question 41

Approximate what is in the image. Why does that look familiar?

Answer 41

Estimating logarithms is used in calculations of pH. We work with negative logarithms and a negative exponent in the case of pH.

Question 42

MCAT concept check 10.2 exponents and logarithms page 372 question 1

Answer 42

Question 43

MCAT concept check 10.2 exponents and logarithms page 372 question 2

Answer 43

Question 44

MCAT concept check 10.2 exponents and logarithms page 372 question 3

Answer 44

Question 45

What are sin and cos of 0, 30, 45, 60, 90°?

Answer 45

Question 46

What is sin cos and tan of 0, 30, 45, 60, and 90°?

Answer 46

Question 47

MCAT concept check trigonometry 3.1 page 375 question 1

Answer 47

Question 48

MCAT concept check trigonometry 3.1 page 375 question 2 Also, what is sin cos tan of 0,30,45,60,90°?

Answer 48

SOH CAH TOA

Question 49

Why is tan of 90° undefined?

Answer 49

Because it involves dividing by 0. Tan being sin/cos, and cos(90°) is 0.

Question 50

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.

Answer 50

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.

Question 51

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°?

Answer 51

Question 52

What is a direct relationship, what is an inverse relationship?

Answer 52

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.

Question 53

Table of metric prefixes and factors

Answer 53

Question 54

Convert 6 hours to minutes. To seconds.

Answer 54

Question 55

Conversion example page 378

Answer 55

This was a good exercise in unit conversion and estimation.

Question 56

What are the conversations between F, C, and K.

Answer 56

Question 57

What is normal body temp in F and C? What is a fever designated as? Hypothermia?

Answer 57

Question 58

What is dimensional analysis? How is it helpful?

Answer 58

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:

Question 59

Example proportion of blood volume in left ventricle with each contraction. Page 379.

Answer 59

Question 60

Solve the following equation using substitution.

Answer 60

Question 61

Solve the following equation by setting the equations equal.

Answer 61

Question 62

Solve the following equation by using elimination

Answer 62

Question 63

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?

Answer 63

Conversion between metric prefixes is accomplished by multiplication or division by the appropriate power of 10.

Question 64

MCAT concept check problem solving 10.4 page 381 question 2

Answer 64

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.

Question 65

MCAT concept check problem solving 10.4 page 381 question 3

Answer 65

Question 66

Relevant equations and relationships for chapter 10 mathematics.

Answer 66