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Math Flashcards

1
Q

What is 2 squared?

A

4

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2
Q

What is 3 squared?

A

9

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3
Q

What is 4 squared?

A

16

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4
Q

What is 5 squared?

A

25

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5
Q

What is 6 squared?

A

36

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6
Q

What is 7 squared?

A

49

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7
Q

What is 8 squared?

A

64

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8
Q

What is 9 squared?

A

81

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9
Q

What is 10 squared?

A

100

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10
Q

What is 11 squared?

A

121

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11
Q

What is 12 squared?

A

144

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12
Q

What is 13 squared?

A

169

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13
Q

What is 14 squared?

A

196

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14
Q

What is 15 squared?

A

225

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15
Q

What is 1 cubed?

A

1

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16
Q

What is 2 cubed?

A

8

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17
Q

What is 3 cubed?

A

27

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18
Q

What is 4 cubed?

A

64

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19
Q

What is 5 cubed?

A

125

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20
Q

What is 6 cubed?

A

216

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21
Q

What is the trick when figuring out the number of zeros when taking a square root in the answer?

ex. square root of (0.00000025)

A

CUT THE ZEROS IN HALF!!!!

0.0005

If you square (0.006) = 0.000036

DOUBLE THE ZERO’S

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22
Q

In a fractions problem (say 1/3 and 1/4) what is the best picking number that you could choose?

A

Least common denominator

ie. 3 x 4 = 12 would be the best choice for this problem

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23
Q

What is the conversion of feet to miles?

A

5280 feet / mile

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24
Q

Explain the communtative laws of addition and multiplication

A

a + b = b + a

a x b = b x a

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25
Q

Explain the associative law of addition and multiplication

A

(a + b) + c = a + (b + c)

(a x b) x c = a x (b x c)

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26
Q

Explain the distributive law

A

a (b + c) = ab + ac

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27
Q

What is the order of operation and how is it easy to remember?

A

Please _E_xcuse _M_y _D_ear _A_unt _S_ally

Parentheses

Exponents

Multiplication

Division (together from L to R)

Addition

Subtraction (together from L to R)

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28
Q

How do you multiply fractions?

A

num x num

den x den

3/4 x 9/7 = 27/28

29
Q

How do you divide fractions?

A

1/5 / 4/11 = 1/5 x 11/4 = 11/20

flip the bottom fraction then multiply

30
Q

How do you add fractions?

A

need to have the same denominator, then add

31
Q

How do you add and subtract mixed numbers?

A

subtract or add the integer out front, then add or subtract the fractions

if the fraction would be a negative number, take from the integer prior to adding or subtracting

ex. 4 5/8 - 2 7/8
fraction: 13/8 - 7/8 = 6/8 = 3/4

Integer: 3 - 2 = 1

Answer = 1 3/4

32
Q

Explain a ratio

A

part / part that add up to the whole

33
Q

what is the fraction for 0.0001

A

1 / 10,000

34
Q

what is the fraction for 0.111

A

111 / 1000

35
Q

Change 0.564 into a fraction

A

564 / 1000 (divide by 4) = 141 / 250

36
Q

Explain the division of decimals

A

It’s easiest to discuss division of decimals if expressed in fraction form

ex. 4.15 divided by 32.2 = 4.15 / 32.2

step 1: make both, numerator and denominator whole numbers

4.15 / 32.2 x 100 = 415 / 3220 = 0.12

37
Q

Explain the process of multiplying two expressions in scientific notation.

ex. (1.1 x 10^6) (5 x 10^17) = ?

A

Simply multiply the coefficients and add the exponents to find answer

(1. 1 x 10^6) (5 x 10^17)
1. 1 x 5 = 5.5

10^(6+17) = 10^(13)

answer = 5.5 x 10^(13)

38
Q

Explain the process of dividing two expressions in scientific notation.

ex. (6.2 x 10^5) / (2.0 x 10^-7)

A

Simply divide the coefficients and subtract the exponents

(6. 2 x 10^5) / (2.0 x 10^-7)
6. 2 / 2 = 3.1

10^(5 - -7) = 10^12

answer = 3.1 x 10^12

39
Q

Explain when a number is in scientific notiation and raised to an exponent

ex. (6.0 x 104)2

A

the coefficient is raised to that exponent, and the original exponent is multiplied by that exponent

(6.0 x 104)2​

62 = 36

(104)2 = 108

answer = 36 x 108

= 3.6 x 10<span>9</span>

40
Q

Explain adding or subtracting numbers expressed in scientific notation

ex. (3.7 x 10^4) + (1.5 x 10^3)

A

They must have the same exponent, when they do not, the appropriate conversion must be made first

(3.7 x 10^4) + (1.5 x 10^3)

(37 x 10^3) + (1.5 x 10^3)

= 38.5 x 10^3

= 3.85 x 10^4

41
Q

Explain how to turn a fraction into a percent

ex. 3/5 to percent = ?

A

3/5 = 3/5 x 100

= (3x100)/5 %

= 3 x 20 %

= 60%

42
Q

What is the conversion from fraction, decimal, percent:

3/4

A

3/4 = 0.75 = 75%

43
Q

What is the conversion from fraction, decimal, percent:

2/3

A

2/3 = 0.666 = 66 2/3%

44
Q

What is the conversion from fraction, decimal, percent:

1/3

A

1/3 = 0.333 = 33 1/3%

45
Q

What is the conversion from fraction, decimal, percent:

1/4

A

1/4 = 0.25 = 25%

46
Q

What is the conversion from fraction, decimal, percent:

1/5

A

1/ 5 = 0.2 = 20%

47
Q

What is the conversion from fraction, decimal, percent:

1/6

A

1/6 = 0.167 = 16.7%

48
Q

What is the conversion from fraction, decimal, percent:

1/7

A

1/7 = 0.143 = 14.8%

49
Q

What is the conversion from fraction, decimal, percent:

1/8

A

1/8 = 0.125 = 12.5%

50
Q

What is the conversion from fraction, decimal, percent:

1/9

A

1/9 = 0.111 = 11.1%

51
Q

What is the conversion from fraction, decimal, percent:

1/10

A

1/10 = 0.1 = 10%

52
Q

What is the conversion from fraction, decimal, percent:

1/20

A

1/20 = 0.05 = 5%

53
Q

What is the percent formula?

ex. if percent is 60% and part is 12, what is whole?

A

percent = part / whole

or

part = whole x percent

ex. 12 / 60% = 20 is whole

54
Q

Explain what the following means:

“What percent of …A… is(are) …B…?

A

A = whole number

B = part

B / A = %

55
Q

Explain the percent increase/decrease formula

A

% increase = (amount of increase) / (original #) x 100

% decrease = (amount of decrease) / (original #) x 100

New whole = original whole +/- amount change

56
Q

Ex. if a number increases from 50 to 70, what is the percent increase?

A

70 - 50 = 20

20 / 50 x 100 = 2 / 5 x 100

= (2 x 100) / 5

= 2 x 20 = 40%

57
Q

Explain if, x is n% greater than y

A

then x is (100 + n)% of Y

ex. if x is 10% greater than y, then x is 110% of y

58
Q

Explain if, x is n% less than y

A

then x is (100 - n)% of Y

ex. if x is 70% less than y, then x is 30% of y

59
Q

What is the formula for computing average

A

average = (sum of the terms) / (# of terms)

60
Q

Explain how you can use the average to find the sum

A

sum = (average) x (# of terms)

ex. if average = 50 of 10 numbers, the sum is ?

sum = 50 x 10 = 500 total sum

61
Q

Explain how you find a missing number?

ex. if the average is 7 of 4 numbers, the numbers are 3, 5, and 8, what is the fourth number?

A
  • To find the missing number when you’re given the average, use the sum
    ex. average = sum / total #

sum = avg x total # = 7 x 4 = 28

total of the three given numbers = 3, 5, 8 = 16

28 - 16 = 12 = fourth number

62
Q

Explain the basic logarithms property formula

A

Properties of logs are dependant on the Law of exponents

“The lagarithm of x to the base b”

logb(x) = c ; then bc = x

63
Q

What is:

log4(16) = c

log<span>10</span>(10000) = c

log25(5) = c

log5(x) = 3

logb(36) = 2

log10(100) = c

A

log4(16) = 2

log<span>10</span>(10000) = 4

log25(5) = 1/2

log5(x) = 3 x = 125

logb(36) = 2 b= 6

log10(100) = c c = 2

64
Q

Properties of logs

Explain the product of two in a logarithm

A

The logarithm of the product of two numbers equal the sum of the individual logarithms

logb(s x t) = logb(s) + logb(t)

65
Q

Properties of logs

Explain the quotient of two in a logarithm

A

The logarithm of the quotient of two numbers equal the numerator minus the logarithm of the denominator

logb (s / t) = logb(s) - logb(t)

66
Q

Properties of logs

Explain the logarithm of a power with a positive base

A

Exponent of the power muliplied by the logarithm of the base of that power

logb(sp) = p x logb(s)

67
Q

Explain the answer to the following log base 10

log10(0.01) = ?

log10(0.1) = ?

log10(1) = ?

log10(10) = ?

log10(100) = ?

log10(1000) = ?

A

An increase of one logarithmic unit (in base 10) corresponds to a muliplication of 10 of the actual total

log10(0.01) = -2, since 10-2 = 0.01

log10(0.1) = -1, since 10-1 = 0.1

log10(1) = 0, since 10<span>0</span> = 1

log10(10) = 1, since 10<span>1</span> = 10

log10(100) = 2, since 10<span>2</span> = 100

log10(1000) = 3, since 10<span>3</span> = 1000

68
Q

How many integers are between:

-2 3/4 to 1 1/4

A

4

include 0 as an integer

69
Q
A

DAT Study Cards (5 decks)

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