Formulas

Question 1

Group formula

Answer 1

Total = [Group 1] + [Group 2] − [Both] + [Neither]

Question 2

Arithmetic sequence

Answer 2

an = a₁ + (n - 1)(d)

d= the common difference between the numbers

Question 3

Geometric sequence

Answer 3

a_n = a₁(r)^{(n -1)}

r = the common ration of dividing the second by the first and the forth by the third and successively.

Question 4

The sum of the first n positive integers is

Answer 4

n (n + 1)/2. For example, 1 + 2 + 3 + … + 17 = 17(18)/2 = 153.

Question 5

parallelogram

Answer 5

p= 2a + 2b or p = 2(a + b)

A = bh

Question 6

triangle

Answer 6

P = a + b + cA = bh/2 A = 1/2bh

Question 7

rombus

Answer 7

p = 4a A = ah

Question 8

trapezoid

Answer 8

p = b1 + b2 + x + y A = [(b1 + b2)h] / 2

Question 9

The sum of the first n odd numbers

Answer 9

The sum of the first n odd numbers is n². For example, 1 + 3 + 5 + 7 + 9 = 5² = 25

Question 10

polygones sum of angles

Answer 10

In any regular polygon the measure of each interior angles is (n - 2) * 180/n and the measure of each exterior angle is 360/n.

Question 11

if the area of an equilateral triangle has side x

Answer 11

then A = [s²⁽V3)]\4 then it has height (V3)/2

Question 12

simple interest

Answer 12

A = P(1 + rt)

Question 13

The average of any sequence of elements

Answer 13

is either

• the middle number (if the number of elements is odd);
• or, the average of the middle two numbers (if the number of elements is even).

Question 14

point-slope formula

Answer 14

y − y0 = m (x − x0).

Question 15

cube

Answer 15

SA = 6a^2 V = a^3

Question 16

rectangular solid

Answer 16

SA = 2(lw+lh+wh)
SA = h(base perimeter) + 2(area of the base)

V = lwh

V = h(area of the base)

Question 17

prism in general

Answer 17

SA = h(perimeter of the base) + 2(area of the base)

V = h(area of the base)

Question 18

cylinder

Answer 18

SA = 2TTr(h + r)

V = h(r²TT)

Question 19

sphere

Answer 19

SA = 4IIr²

V = (4/3)IIr³

Question 20

length of an arc

Answer 20

(x/360)2IIr

Question 21

area by and ark and 2 radii

Answer 21

(x/360)TTr²

Question 22

coodinate geometry - distance between two points

Answer 22

d = V(X₂ - X₁)² + (Y₂ - Y₁)²

Question 23

compound interest

Answer 23

Final balance = (principal) x {1 + (interest rate/C)}^time(C)

C= number of times compounded annually

Question 24

Combined work problem formula

Answer 24

1/r + 1/s = 1/t

KW(517)

Question 25

Mixed solutions balancing formula

Answer 25

(amount of weaker solution) X (% difference between the weaker solution and the desired solution) = (amount of stronger solution) X (% difference between the stronger solution and the desired solution)

Question 26

1. For a given perimeter, the rectangle with the largest area is a:
2. For a given area, the rectangle with the smallest perimeter is a:

Answer 26

1. square
2. square

Question 27

Joining the midpoints of the four sides of any quadrilateral creates a parallelogram whose area is

Answer 27

one-half the area of the original quadrilateral.

Question 28

Let a, b, and c be the sides of ΔABC, with a ≤ b ≤ c.

1. If ΔABC is a right triangle:
2. if a² + b² = c²:

Answer 28

1. a² + b² = c²
2. ΔABC is a right triangle.

Question 29

Let a, b, and c be the sides of ΔABC, with a ≤ b ≤ c.

• a² + b² < c² if and only if angle C is:

Answer 29

obtuse. ΔABC is an obtuse triangle

Question 30

Any triangle, such as ΔCOD formed by connecting the endpoints of two radii to the center O is a:

Answer 30

isosceles triangle

Question 31

The distance, d, between two points, A( X_{<span>1</span>}, Y₁) and B( X₂, Y₂) can be calculated using the distance formula:

Answer 31

d = V(X₂ - X₁)²+ (Y2- Y1)²

Question 32

If P( x₁, y₁) and Q( x₂, y₂) are any two points, then the midpoint, M, of segment PQ is the point whose coordinates are:

Answer 32

(X₁ + X₂/2), (Y₁ + Y₂/2)

Question 33

• If two nonvertical lines are parallel, their slopes are:
• If two nonvertical lines are perpendicular, the product of their slopes is:
• OR if two nonvertical lines are perpendicular, the slope of one is the:

Answer 33

• equal
• − 1
• negative reciprocal of the slope of the other.

Question 34

• For any real number a: x = a is the equation of the vertical line that crosses the x-axis at:
• For any real number b: y = b is the equation of the horizontal line that crosses the y-axis at:
• For any real numbers b and m: y = mx + b is the equation of the line that crosses the y-axis at:

Answer 34

• (a, 0)
• (0, b)
• (0, b) and whose slope is m

Question 35

To count how many integers there are between two integers, follow these rules:

• If exactly one of the endpoints is included:
• If both endpoints are included:
• If neither endpoint is included:

Answer 35

• subtract
• subtract and add 1
• subtract and subtract 1 more

Question 36

If two jobs need to be completed and there are m ways to do the first job and n ways to do the second job, then there are:

Answer 36

m × n ways to do one job followed by the other. This principle can be extended to any number of jobs

Question 37

If an experiment is done two (or more) times, the probability that first one event will occur and then a second event will occur is the:

Answer 37

product of the probabilities

Question 38

Probability Formulas

When A and B are independent P(A and B) =

When A and B are not independent or it is not specified P(A and B) =

Answer 38

P(A)*P(B)

P(A)*P(B) - P(A|B)

P(B)*P(A) - P(B|A)

Question 39

Probability Formulas A or B

When A and B are mutually exclusive P(A and B) =

When A and B are not mutually exclussive or it is not specified P(A and B) =

Answer 39

P(A) + P(B)

P(A) + P(B) - P(A + B)

Question 40

If elements of the factorias are not unique

Answer 40

11! / 4!4!2!

The denominator is the number of times the non-unique elements appears.