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CSET Subtest Two > Domain One – Number Sense > Flashcards

Domain One – Number Sense Flashcards

1
Q

=

A

Equal to

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2
Q

≠

A

Not equal to

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3
Q

>

A

Greater than

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4
Q
A

Less than

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5
Q

≥

A

Greater than or equal to

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6
Q

≤

A

Less than or equal to

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7
Q

||

A

Parallel to

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8
Q

Upside down T

A

Perpendicular to

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9
Q

≈

A

Approximately equal to

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10
Q

Natural numbers

A 
Counting numbers (1,2,3,4…); numbers you would naturally count by 
*not 0
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11
Q

Whole numbers

A

All natural numbers and 0

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12
Q

Integers

A

All whole numbers and their opposites (-3,-2,-1,0,1,2,3)

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13
Q

Rational numbers

A

All values that can be expressed in the form a/b, a & b are integers and b ≠ 0, or when they are expressed in decimal form, the expression either terminates or has a repeating pattern

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14
Q

Irrational numbers

A

All values that exist, but are not rational

Example: Pi (does not terminate or repeat), square root of 2 (does not terminate or repeat)

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15
Q

Real numbers

A

All rational and irrational numbers

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16
Q

Prime numbers

A

A natural number greater than 1, and that only has itself and 1 as its divisors (exactly two divisors)

Examples: 2,3,5,7,11,13,17

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17
Q

Composite numbers

A

A natural number greater than 1 that is not a prime number (at least three divisors)

Examples: 4,6,8,9,10,12,14

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18
Q

Square numbers

A

The results of taking integers and raising them to the 2nd power (numbers multiplied by themselves)

Examples: 1,4,9,16,25,36,49

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19
Q

Cube numbers

A

Results of taking integers and raising them to the third power (cubed)

Examples: 1,8,27,64,125,216,343

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20
Q

Length

A 
12 inches (in) = 1 foot
3 feet = 1 yard
36 inches = 1 yard
1760 yards = 1 mile
5280 feet = 1 mile
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21
Q

Area

A

144 square inches = 1 square foot

9 square feet = 1 square yard

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22
Q

Weight

A

16 ounces = 1 pound

2,000 pounds = 1 ton (T)

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23
Q

Capacity

A

2 cups = 1 pint (pt)
2 pints = 1 quart (qt)
4 quarts = 1 gallon (gal)
4 pecks = 1 bushel

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24
Q

Time

A

365 days = 1 year
52 weeks = 1 year
10 years = 1 decade
100 years = 1 century

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25
Q

Weight (gram)

A 
Kilogram (kg) 1,000 grams
Hectogram (hg) 100 grams
Decagram (dag) 10 grams
Gram (g) 1 gram
Decigram (dg) 0.1 gram
Centigram (cg) 0.01 gram
Milligram (mg) 0.001 gram
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26
Q

Volume (Liter)

A 
Kiloliter (kl/kL) 1000 liters
Hectoliter (hl/hL) 100 liters
Decaliter (dal or daL) 10 liters
Liter (l/L) 1 liter
Deciliter (dl/dL) 0.1 liter
Centiliter (cl/cL) 0.01 liter
Milliliter (ml/mL) 0.001 liter
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27
Q

Length (meter)

A 
Kilometer (km) 1000 meters
Hectometer (hm) 100 meters
Decameter (dam) 10 meters
Meter (m) 1 meter
Decimeter (dm) 0.1 meter
Centimeter (cm) 0.01 meter
Millimeter (mm) 0.001 meter
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28
Q

Metric system

A

Milli - 1/1000
Centi - 1/100
Deci - 1/10

Basic unit: deca = 10, hecto = 100, kilo = 1000

29
Q

Commutative property

A

The order in which addition or multiplication is done does not affect the answer

A+B=B+A
Ab=ba

30
Q

Associative property

A

The grouping, without changing the order, does not affect the answer

A+(b+c)=(a+b)+c
A(bc)=(ab)c

31
Q

Distributive property

A

Multiplication outside parentheses distributing over either addition or subtraction inside parentheses does not affect the answer

In general:
A(b+c)=ab+ac
A(b-c)=ab-ac

*cannot be used with only one operation (example: 3(4x5)≠3(4)x3(5) = 60≠80

32
Q

Special properties of 0 and 1

A

Identity number: value that when added or multiplied with another number does not change the value of that number

Addition: 0; any number added to 0 gives that same number; 0+3=3+0=3 (additive identity)
Multiplication: 1; any number multiplied by 1, gives that number; 1(3)=3(1)=3 (multiplicative identity)

33
Q

Inverses

A

The additive inverse of a number (the opposite) is a value that when added to any number equals 0
** any number added to its additive inverse equals zero

7 + (-7) = 0

The multiplicative inverse of a number (the reciprocal). is a value that when multiplied with any non-zero number equals 1; any non-zero number multiplied with its multiplicative inverse equals 1

4/5 x 5/4 = 1

34
Q

Fractions

A

Two numbers separated by a bar which indicates division

Numerator(above the bar) and denominator (below the bar)

35
Q

Proper fractions

A

The numerator is smaller than the denominator
Have a value of less than 1
Example: 3/5

36
Q

Improper fractions

A

Numerator is the same or more than the denominator
Have a value equal to or more than 1

6/6 = 1, 5/4 = 1 1/4

37
Q

Mixed numbers

A

Whole number combined with a proper fraction

Improper fraction -> divide the demonization into the numerator

To change from a mixed number back to an improper fraction: multiply the whole number by the denominator, add the numerator, and then place that value over the denominator (6 2/5 —> 32/5)

38
Q

Reducing/ simplifying fractions

A

Find the GCF (greatest common factor) for both the numerator and denominator and then divide them both by that value

39
Q

Adding fractions

A

Denominators must be changed to their LCM (least common multiple) or their LCD (least common denominator)
Smallest value that can be divided into the denominators without a remainder, then multiple the numerator by the number needed to multiply by to get the LCD

40
Q

Adding mixed numbers

A

Same rule as adding fractions, just make sure to add the whole numbers to arrive at a final answer

41
Q

Subtracting fractions

A

Find the LCD, and then subtract the numerators

42
Q

Subtracting mixed numbers

A

May have to borrow from the whole number just like when you subtract ordinary numbers

43
Q

Multiplying fractions

A

Multiply the numerators and then the denominators, reduce if necessary

**can reduce early in the operations, only when multiplying NOT adding or subtracting

44
Q

Multiplying mixed numbers

A

First change the mixed number to an improper fraction, then multiply

Changing Mixed to Improper Fraction:

  1. Multiply the whole number by the denominator of the fraction
  2. Add this to the numerator of the fraction
  3. This is the new numerator
  4. The denominator remains the same
  5. Change answer back to a mixed number if necessary and then reduce
45
Q

Dividing fractions

A

Invert the second fraction, multiply, and then reduce if necessary

46
Q

Simplifying fractions

A

If the numerator or denominator contains several numbers, then these must be combined into one, and then reduced if necessary

47
Q

Place value

A

The position of a number written in decimal form
109,876,543,210.12345
Hundred billions, ten billions, billions, hundred millions, ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones, tenths, hundredths, thousandths, ten thousandths, hundred thousandths

48
Q

Rounding off

A
  1. Underline the place value being rounded off to
  2. Look to the immediate right (One place) to the right of the underlined value
  3. If the number is 5 or higher, you round up that place by one. If it is four or less, it will be the same, and everything to the right is now 0
49
Q

Decimals

A

Numbers to the left of the decimal: whole numbers

Numbers to the right: fractions with the denominators of 10,100,1000,10000, etc.

50
Q

Adding and subtracting decimals

A

Line up the decimal points, and add or subtract like normal

*adding 0’s can help make the problem more approachable; whole numbers can add a decimal point to their right and add any amount of zeros

51
Q

Multiplying decimals

A

Multiply as usual, count the total number of digits above the line which are to the right of all decimal points. Add the decimal point in your answer so there is the same number of digits to the right as there were above the line.

52
Q

Dividing decimals

A

If the divisor has a decimal, move it to the right as many places as necessary until it is a whole number. Then move the decimal point in the dividend (the number being divided into) the same number of places

*sometimes you have to add zeros to the dividend (the number inside the division sign)

53
Q

Decimals to percents

A
  1. Move the decimal point two places to the right

2. Insert a percent sign

54
Q

Percents to decimals

A
  1. Eliminate the percent sign

2. Move the decimal point two places to the left (sometimes adding zeros will be necessary)

55
Q

Fractions to percents

A
  1. Multiply by 100%
56
Q

Percents to fractions

A
  1. Divide the percent by 100
  2. Eliminate the percent sign
  3. Reduce if necessary
57
Q

Fractions to decimals

A

Do what the operation says

13/20 = 13 divided by 20

58
Q

Decimals to fractions

A
  1. Read it (0.8 = eight-tenths)
  2. Write it (8/10)
  3. Reduce it (4/5)
59
Q

Finding percentage

A

Change the percentage to a fraction or a decimal and then multiply
** of = multiply
Example: What is 20% of 80? (20/100) x 80 = 1600/10 = 16 OR .20 x 80 = 16.00 = 16

60
Q

Percentage increase/decrease

A

Change/starting point x 100% = percentage change

Example: Percent increase of salary from $150-$200: $50 change; 50/150 x 100% = 1/3 x 100% = 33 1/3% increase

61
Q

Square/square root

A

To square: multiply it by itself
*perfect squares: square of a whole number
Square roots of nonperfect squares can be approximated: square root of 2 ≈ 1.4, square root of 3 ≈ 1.7

Square Root Rules:

  • two numbers multiplied under a radical (square root) sign equal the product of the two square roots and same with division
  • adding and subtracting under a radical sign requires that the numbers must be combined under the radical before any computation can be done

Approximating:
- utilize the perfect squares closest to it

62
Q

Simplifying square roots

A
  1. Factor the number into two numbers, one (or more) of which is a perfect square
  2. Take the square root of the perfect square(s)
  3. Leave the others under the radical sign
63
Q

Scientific notation

A

Very small or large numbers
Begins with a positive number that is greater to or equal to one, but less than 10, multiplied by an integer power of 10.
If the original value is larger than one, the exponent by 10 will be positive, if less than one, the exponent will be negative, for values between 0 and 1 the exponent is negative

64
Q

Adding signed numbers

A

When two numbers have the same sign, add the absolute values (pure) and keep the same sign.
* if no sign, assumed to be positive

If they have different signs, subtract the absolute and then keep the sign of the larger pure number value

65
Q

Subtracting signed numbers

A

Add the opposite; change the sign of the number being subtracted and then proceed like an addition problem

66
Q

Multiplying or dividing signed numbers

A

Product of two numbers with the same sign will produce a positive answer
Product of two numbers with different signs will produce a negative answer

67
Q

Parentheses

A

Grouping symbols
Evaluate everything inside of the parentheses before doing any other operations

  • if multiple, start with the most inside parentheses first and work your way out
68
Q

Order of operations

A

PEMDAS: Please Excuse My Dear Aunt Sally

Parentheses (simplify all expressions)
Exponents (apply exponents to their appropriate bases)
Multiplication or Division (multiplication or division in the order from left to right)
Addition or Subtraction (order from left to right)

CSET Subtest Two (7 decks)

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