133 terms

11^2

121

12^2

144

13^2

169

14^2

196

15^2

225

25^2

625

2^6

64

2^7

128

2^8

256

2^10

1024

1/6

.166

1/8

.125

1/12

.083

1/9

.11

1/11

.09

Divisibility Rule for 3

If the sum of the digits is a multiple of 3

Divisibility Rule for 4

Last two digits are divisible by 4

First 15 Prime Numbers

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47

Dividing by a negative exponent..

makes a number larger

Multiplying by a negative exponent...

makes a number smaller

2^9

512

When cross multiplying put the answer by the

Numerator (top number)

6 division rule

Divisible by both 2 and 3

Reciprocal

Product of the two fractions equals 1

If you increase a numerator

The number increases

Compound Interesr

P(1 + r/n)^nt

Rate Time Work equation

Rate*Time=work

30-60-90 proportions

X:X*root(3):2x (opposite 30, opposite 60, hypotenuse)

Circumference to diameter

C = 2(pi)r

Is neither singular or plural

Singular

Proper use of correlate

Correlates with

1/50

.02

1/25

.04

1/20

.05

3/8

.375

5/8

.625

5/6

.833

7/8

.875

Root 2

1.4

Last digit short cut

Multiply the digits of relevant numbers

16^2

256

Root 3

1.7

Root 5

2.25

4^3

64

5^3

125

X^2 - Y^2

(X + Y)(X - Y)

X^2 + 2xy + Y^2

(X + Y)^2

X^2 - 2xy + Y^2

(X - Y)^2

XY > O implies

XY are both positive or both negative

XY < O implies

X and Y are different signs

X^2 - X < 0

0 < x < 1

Quadratic

X = -b +/- root(b^2 - 4ac) / 2a

Proportion

X / Y

Inverse Proportion

XY

Exponential groeth

Y = Y*k^t

Simple interest

P(1 + rt/100)

45 45 90 ratio

X:X:Xroot(2)

Rhombus

Opposite angles equal all sides equal

Parallelogram

Opposite sides and angles equal

Trapezoid

One pair of opposite sides parallel

Angles of shape

(N-2)*180

Trapezoid Area

(B1 + B2) * H / 2

Area of Rhombus

Diagonal1*diaganol2/2

Triangle inequality law

Sum of any two sides are bigger than the third, third must also be bigger than the difference of the two

Common triangle combos

3-4-5 (6-8-10, 9-12-15, 12-16-20)

5-12-13 (10-24-26)

8-15-17

5-12-13 (10-24-26)

8-15-17

Diagonal equation square

D = s*root(2)

Cube diagonal equation

D = s*root(3)

17^2

289

Arc length

Angle/360**d**pi

Inscribed angle vs. arc

.5 *arc angle

Cylinder surface area

2*pi*r^2 + 2**pi****pi***r^2 + 2*pi*r*h

Volume of a cylinder

Pi**r^2**h

How to arrange group of n objects without restrictions

N!

How to handle a group of n size with m and omembers the same

N!/M!*O!

P(a) + p(not a)

Equals 1

Divisibility rule 8

Divisible by 2 3 times or last 3 digits divisible by 8

Divisibility 9

Sum of digits are divisible by 9

Factor foundation rule

If b is a factor of a and c is a factor of b, then c is also a factor of a

Dividend remainder equation

A/B = multiple + remainder/B

Sum of two odds vs mult of two odds

Even and odd

Standard deviation

Root of the sum of the difference between the items of the set and the mean squared divided by the number of elements

GCF

Product of overlapping primes

LCF

Product of all primes in diagram

GCM of m and n x LCF of m and n

Equals m x n

How do you determine prime factor length?

Adding up exponents

How many factors do perfect squares have

Odd number

Prime factorization of a perfect square contains..

Only even powers

How do you determine any higher level perfect number

Factors are divisible by the level of perfect it is (perfect cubes, 3, etc)

For evenly spaced sets mean and median are

Equal, the average of the first and last number

Sum of a set of consecutive integers equals

Average time number of items

The product of k consecutive integers is divisible by

K!

A sum of k integers if k is odd is

A multiple of k

A sum of k integers if k is even is

Not a multiple of k

Exterior angle equals

Sum of non-adjacent angles

What type of quadrilateral has the largest area with a given perimeter

Square

Mid point between A(x,y) and B(x,y)

X + X / 2, Y + Y/2

If you add or subtract a non multiple of n to a multiple of n

The result is not a multiple of n

Mode is

Observation that shows up most

Neither nor verb agreement

Agrees with the closest subject

Collective nouns are

Considered singular

The boy, along with his friends, - is?

Singular

Can THAT modify people

No, use who or whom

We had an arrangement WHERE or IN WHICH

IN WHICH

Terminating decimal must include

2^x or 5^x or both

Can a perfect square be expressed as the product of an even number of positive prime factors

Yes 5x5

If x > O then

|x| = x

If x < 0 then

|x| = -x

When testing inequalities with powers remember

Test fractions and negatives

Think of one combinatorial problem where order matters and one where it does not. What do you divide by if it does not?

The factorial number of choices

For a definitional sentence use what tense

Simple present not present progressive

What tense should be used to indicate future action

Simple future (will x) not present progressive (is xing)

Present perfect is

An action that happened in the past and continues to today (can also have an impact currently)

Use Past Perfect when

You need to clarify the timing between two past events, not when one event is obvious or continued effect in the past

What are the pairs of tenses for reporting

Present + future and past + conditional

Command verbs that take the infinitive

Advise, allow, forbid, persuade, want

Command verbs that take either infinitives or command subjunctives

Ask, beg, order, prefer, urge, require

Past progressive can be used for

Background state of affairs "he was wearing a helmet, so he did not get hurt"

Present tense of subjunctive

Looks like past simple (swallowed, ate, etc)

Is 0 positive or negatice

Neither

Comparison signals

As, as blank as, as much as, as little as, more than, less than, different than, in contrast to, the same as

Like must be followed by

Nouns pronouns or noun phrases not a clause

As can be followed by

Either a noun alone or a clause

Comparisons must be

Structurally similar in terms of grammar

When is 1/x > 1/y

When x and y are positive and x < y

When is 1/x < 1/y

When x is negative and y is positive and x < y

If both sides are negative, what should you do when you square an inequality

Flip it

If both sides are positicd, what should you do when you square an inequality

Nothing

Can you square an inequality with one side positive and the other negative

No

Can less be used with countable items

No, use few instead (except for units which take less I.e dollars)

How many things can between modify

2 for 3 use among

Which is singular "a number of" or "the number of"

The number ofp

When finding the length of an arc from an angle you use an angle from x

Center of the circle, which is 2x an angle from the circumference

Ratio of sides and areas for similar triangles

A:B and a^2:b^2