MCAT Math

Question 1

What does standard deviation measure?

Answer 1

Standard deviation measures how spread out a data set it.

68. 2% of data points lie within ONE standard deviation of the mean.
69. 4% of data points like within TWO standard deviations of the mean.
70. 6% of data points like within THREE standard deviations of the mean.

Question 2

N^x x N^y =

Answer 2

N^(x+y)

Question 3

N⁰ =

Answer 3

1

This is true for any number except 0.

0⁰ is undefined.

Question 4

M^x x N^x =

Answer 4

(M x N)^x

Question 5

N^x / N^y =

Answer 5

N^(x-y)

Question 6

(N/M)^x =

Answer 6

N^x / M^x

Question 7

(N^X)^Y =

Answer 7

N^{(X x Y)}

Question 8

N^(1/2) =

Answer 8

sqrt(N)

Question 9

N^(-x) =

Answer 9

1 / N^x

Question 10

sqrt(2) =

sqrt(3) =

Answer 10

sqrt(2) = 1.4

sqrt(3) = 1.7

Question 11

3.4 x 10^-5 + 9.1 x 10^-6 =

Answer 11

34 x 10^-6 + 9.1 x 10^-6 =

To add or subtract in scientific notation, adjust to get the same exponent. Then add the coefficients and do not change exponent.

43. 1 x 10^-6 =
44. 31 x 10^-5

Question 12

(2 x 10^-3) x (7 x 10^-5) =

Answer 12

2 x 7 x 10^-3 x 10^-5 =

14 x 10^-8 =

1.4 x 10^-7

Question 13

(6 x 10⁸) / (1.5 x 10³) =

Answer 13

(6 / 1.5) x (10⁸ / 10³) =

4 x 10⁵

Question 14

V₁ / T₁ = V₂ / T₂

is what kind of relationship

Answer 14

Direct relationship. As one variable increases, the other increases as well.

This is Charles’s Law, which states that temperature and volume of a gas are directly related.

Question 15

P₁V₁ = P₂V₂

What type of relationship is this?

Answer 15

Inverse relationship. As one variable increases, the other goes down.

This is Boyle’s Law. Pressure and Valume of a gas are inversely related.

Question 16

Express 10^A = B as a logarithm

Answer 16

log₁₀B = A

Question 17

log_X1 =

Answer 17

log_X1 = 0

Question 18

log_XX =

Answer 18

log_XX = 1

Question 19

log (N x M) =

Answer 19

log (N x M) = log N + log M

Question 20

log (N / M) =

Answer 20

log (N / M) = log N - log M

Question 21

log (N^M) =

Answer 21

log (N^M) = M x log N

Question 22

• log N =

Answer 22

• log N = log (1 / N)

Question 23

What is the shortcut for solving for pH?

What is the pH of a solution whose [H⁺] = 4 x 10^-8?

Answer 23

pH = - log [H⁺] = - log [A x 10^-B] = B - log A

pH = - log [H⁺] = - log [4 x 10^-8] = 8 - log 4 =~ 7.5

log 2 thru log 9 can be approximated to 0.5 for MCAT estimation.

log 1 = 0

log 10 = 1

Question 24

What are the SI base units?

Answer 24

meter (m)

kilogram (kg)

second (s)

ampere (A)

kelvin (K)

mole (mol)

candela (cd)