Quantitative Reasoning

log_x (a) + log_x (b) = ?

log_x(ab)

log_x (a) - log_x (b) = ?

log_x(a/b)

log_x (a²) = ?

2 log_x (a)

What is a prime number?

A whole number which is greater than one and that is only divisible by one and itself

What happens when you multiply both sides of an inequality by a negative number?

It switches directions of the inequality

How do you find the discriminant?

B²-4ac

What does solving for the discriminant do for you?

It is used to find how many roots a quadratic function has.

Equation of a straight line?

y=mx+b

Slope is???

M > 0 uphill

M < 0 downhill

What is the y-intercept?

The value of y at x=0

How to sovle for slope given two points?

(y₂ - y₁) / (x₂ - x₁)

When are two lines parallel?

When they have the same slope but different y-intercepts

Where are two lines perpendicular?

When their slopes are the negative reciprocals of each other

What determines the direction of a parabola in the equation ax² + bx + c ?

a

If a > 0

concave up

If a < 0?

Concave down

If |a| is large?

Narrow parabola

If |a| is small?

Wide parabola

What is the y-intercept of the quadratic equation? ax² + bx + c

c

How do you find the vertex of a parabola?

-b/2a

In cubic functions ax³ + bx² + cx + d, what is the y-intercept?

d

Graph of a cubic function

f (x) = x^1/n = ⁿ√

fractional power

If n is odd then?

s or z shaped

If n is even then?

Half parabola rotated 90 degrees

What is the general form of a square root function?

f(x) = a √x-h +k

What is h equal to in the function f(x) = a √x-h +k?

h is equal to the x-coordinate of the endpoint

What is k equal to in the function f(x) = a √x-h +k?

K is equal to the y-coordinate of the endpoint

What is the domain of the function f(x) = a √x-h +k?

x ≥ h

What is the cube root function?

f(x) = a ∛x-h + k

What is the location of the inflection point for f(x) = a ∛x-h + k

(h,k)

Cube root function

Square root function

What is the general form of the reciporacal function?

f(x) = a/x-h + k

What does x = h mean in the function f(x) = a/x-h + k ?

Vertical asymptote

What does x = k mean in the function f(x) = a/x-h + k ?

Horizontal asymptote

Reciprocal function

What are strict inequalities?

< OR >

What are non-strict inequalities?

≤ or ≥

What is the general form of an absolute value function?

f(x) = a |x-h| + k

What is the slope of two lines in a absolute value function?

+ or - a

What is h of an absolute value function?

H = x-coordinate of the vertex

What is k of an absolute value function?

K = y-coordinate of the vertex

In strict inequalities, the boundary is?

Excluded - - - - - -

In non strict inequalities, the boundary is?

Included —————-

What is the distance formula?

The distance formula is just the….

pythagorean theorem

What is the midpoint formula?

If order does NOT matter what formula do you use?

Combination formula

If order DOES matter, what formula do you use?

Permutation formula

A normal die has six equal sides numbered 1-6. The probablility of rolling any given number is…. ?

1/6

How many cards are in a standard deck of cards?

52 cards

How many cards in a standard deck of cards has red card / black cards?

26 red cards and 26 black cards

How many suits are there in a deck of cards? And how many cards per suit?

4 suits

13 cards per suit

How many jacks, queens, and kings in a deck of cards?

4, 4, 4

Which suits in a deck are black?

clubs and spades

Which suits in a deck are red?

hearts and diamonds

For letter problems like; “how many different letter combinations…”

If no repeating letters = ….?
If the word has repeating letters, ……?

(# of letters) !

apply the above and then divide by the factorial of the number of repeats

If a probability question says AND then you?

Multiply

If a probablility question says OR then you?

Add

For at least one probabilities that are for dependent events;

P (at least one) = 1-P (none)

For at least one probabilities that are for independent events;

P (at least one) = 1 - P [P(none)]^{# of trials}

Union U means?

Combining all data points except duplicate values

Intersections ∩ means?

Shared values between data sets

Includes only data points that exist in both data sets

What is the standard deviation formula?

In a normal distribution, _________ of the data fall within 1 stdv of the mean. ____________ of the data fall within 2 stdv of the mean, and _________ of the data within 3 stdv of the mean.

68%

95%

99.7%

What is z-score?

How far away a data point is away from the mean in terms of standard deviation

negative is below the mean

positive is above the mean

What is the distance formula?

(rate) (time) = distance

What is the average speed formula?

total distance / total time

What is the compound interest formula?

What is the concentration increase formula?

C₁V₁ + C₂V₂ = C_fV_f

What is the dilution formula?

C₁V₁ = (W + V₁) C_Total

What two formula’s do you need for flight path questions?

Vertex formula and horizontal velocity

What is the area of a circle?

Circumference of a circle?

Perimeter of a square?

P = 4s

Area of a square?

s²

Area of a rectangle?

A = lw

Perimeter of a rectangle?

P = 2l + 2wa

Area of a triangle?

A = 1/2bh

Pythagorean theorem?

a² + b² = c²

The three interior angles of any triangle sum to?

180 degrees

Complementary angles

Two angles sum to 90 degrees

Supplementary angles

Two angles sum to 180 degrees