Math Shortcuts

Question 1

two digit number divided by 99

Answer 1

becomes a decimal with that two digit number repeating. For instance –> 49/100 = 0.494949….

Question 2

FDP: Scientific Notation

Answer 2

Question 3

FDP: Compensating Decimals

Answer 3

Question 4

FDP: Solution Less Traveled

Answer 4

Question 5

Quadratic Formula

Answer 5

Question 6

The discriminant (b^2 - 4ac) which is under the radical in the quadratic formula can tell you how many solutions.

Answer 6

b^2 - 4ac > 0 –> 2 solutions
b^2 - 4ac = 0 –> 1 solutions
b^2 - 4ac = 0 –> 0 solutions

Question 7

Conjugate of square root expression involving addition or subtraction

Answer 7

Question 8

multiply by a negative number in an inequality

Answer 8

flip the sign

Question 9

On test cases, when I see |x|, I will try

Answer 9

absolute value: + and -

Question 10

On test cases, when I see x^2, I will try

Answer 10

exponents: 0, 1, and fractions

Question 11

On smart numbers, I will avoid…

Answer 11

0 and 1 and usually #s that appear in the problem

Question 12

On smart numbers when choosing 2 variables, I will…

Answer 12

pick two differen tnumbers

Question 13

decimal raised to exponent = how many decimal places?

Answer 13

of decimals * exponent

Question 14

decimals for a root = how many decimal places

Answer 14

of decimals / root
=# of decimals * (1/root)

Question 15

What is the pattern if the denominator is a number equal to a power of 10 - 1 (eg 9, 99, 999, etc)

Answer 15

then the numerator is repeating

Question 16

How to check if a number will terminate?

Answer 16

The denominator only has 2 and 5 as prime factors once fraction is in smallest form

Question 17

Digit Place Value questions

example two digit number -A -> how to represent this

Answer 17

A = 10x + y

Question 18

Find units digit or a remainder after division of 10

Answer 18

you can pay attention to only the digits

Question 19

x^2 - y^2

Answer 19

(x+y)(x-y)

Question 20

x^2 + 2xy + y^2

Answer 20

(x+y)(x+y) = (x+ y)^2

Question 21

x^2 - 2xy - y^2

Answer 21

(x-y)(x-y) = (x+ y)^2

Question 22

inequality statement –> what is the implication?

xy>0

Answer 22

x and y are both positive or negative

Question 23

inequality statement –> what is the implication?

xy < 0

Answer 23

one positive, one negative

Question 24

inequality statement –> what is the implication?

x^2 - x < 0
x^2 < x

Answer 24

0 < x < 1

Question 25

When combining inequalities can yo subtract?

Answer 25

NO

Question 26

direct proportions > what to use?

Answer 26

ratios

Question 27

indirect proportions > what to use?

Answer 27

products

Question 28

Reciprocals of Inequalities

Answer 28

Only flip the inequality if both are the same sign. If you do not know the sign, then you cannot take reciprocals

Question 29

squaring inequalities if both sides are known to be negative then

Answer 29

then flip the inequality sign. if this is not known you can't do this

Question 30

squaring inequalities if both sides are known to be positive then

Answer 30

do not flip the sign

Question 31

squaring inequalities if one is positive and one is negative then

Answer 31

likely choose another technique besides squaring

Question 32

squaring inequalities if sign is unknown then

Answer 32

you cannot square

Question 33

Compound interest formula

Answer 33

Question 34

Rate -> how to express

Answer 34

ALWAYS distance over time use one unit of time

Question 35

If object moves the same distance twice at different rates, what's the average weighted towards?

Answer 35

weighted towards slower!!

Question 36

For evenly spaced sets what is the relation between the mean and median?

Answer 36

they are equal

Question 37

For evenly spaced sets the median equals to

Answer 37

(first+ last)/2

Question 38

Products of x consecutive integers is always divisible by what?

Answer 38

x!

Question 39

Sums of consecutive integers

Answer 39

Odd: the sum is always a multiple of the number of items (sum = average * # of items) Even: the sum of all the items is NEVER multiple of then number of items. b

Question 40

Counting integers formula

Answer 40

last - first +1

Question 41

Is the average of n consecutive integers an integer?

Answer 41

Yes if n is odd No, if n is even

Question 42

Composites

Answer 42

three or more factors (not 1 or prime)

Question 43

factor foundation rule

Answer 43

if a is a factor of b, and b is a factor of c, then a is a factor of c

Question 44

x and y are both a multiple of r. Is x + y a multiple of r?

Answer 44

Yes! And so would ax + by

Question 45

What prime number is not odd?

Answer 45

2

Question 46

If the sum of two prime numbers is odd, what must be one of the primes?

Answer 46

2

Question 47

If the sum of two prime numbers is even, what must not be one of the primes?

Answer 47

2

Question 48

Prime

Answer 48

only 2 factors > therefore 1 is not prime

Question 49

even * even

Answer 49

even

Question 50

even * odd

Answer 50

even

Question 51

odd * odd

Answer 51

odd

Question 52

even +/- even

Answer 52

even

Question 53

odd +/- odd

Answer 53

even

Question 54

odd +/- even

Answer 54

odd

Question 55

4!

Answer 55

24

Question 56

5!

Answer 56

120

Question 57

6!

Answer 57

720

Question 58

arranging group of n without restrictions

Answer 58

n!

Question 59

if you add(or subtract) a multiple of N to a non multiple of N, is the result a multiple of N

Answer 59

NO

Question 60

if you add (or subtract) two non multiples of N, is the answer a multiple of N

Answer 60

maybe

Question 61

if a number has a prime factorization of a^x*b^y*c^z, what is the total number of factors?

Answer 61

(x+1)*(y+1)*(z+1)

Question 62

perfect square

Answer 62

squares of other integers (25,4,9)

Question 63

what does it mean if a number has an odd number of total factors

Answer 63

it is a perfect it must be a perfect square, cube, etc Otherwise it would be a pair!!

Question 64

What does it mean if a number's prime factorization contains any odds?

Answer 64

It is not a perfect square!

Question 65

remainder formula

Answer 65

dividend = quotient * divisor + remainder