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Fundamentals Of Mathematics > Number And Algebra > Flashcards

Number And Algebra Flashcards

1
Q

Whole number definition?

A

Does not require a decimal or fraction. Cannot be a negative number.

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2
Q

Integer definition?

A

Whole numbers and their opposites (negatives)

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3
Q

Natural number definition?

A

Whole numbers excluding 0

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4
Q

What is a real number?

A

Most numbers. Those that can be found on a number line.

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5
Q

Rational number definition?

A

It can be expressed at a quotient of two integers (e.g. a fraction) with a denominator that is not zero

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6
Q

Irrational number definition?

A

It can NOT be expressed at a quotient of two integers (e.g. a fraction) with a denominator that is not zero

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7
Q

Symbol and magnitude of tera?

A

T 1 x 10^12

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8
Q

Symbol and magnitude of giga?

A

G 1 x 10^9

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9
Q

Symbol and magnitude of mega?

A

M 1 x 10^6

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10
Q

Symbol and magnitude of kilo?

A

K 1 x 10^3

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11
Q

Symbol and magnitude of deci?

A

d 1 x 10^-1

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12
Q

Symbol and magnitude of centi?

A

c 1 x 10^-2

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13
Q

Symbol and magnitude of milli?

A

m 1 x 10^-3

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14
Q

Symbol and magnitude of micro?

A

µ 1 x 10^-6

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15
Q

Symbol and magnitude of nano?

A

n 1 x 10^-9

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16
Q

Symbol and magnitude of pico?

A

p 1 x 10^-12

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17
Q

Divisibility test for 3?

A

If the sum of the digits are divisible by 3

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18
Q

Divisibility test for 4?

A

The number made by the last two digits is divisible by 4

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19
Q

Divisibility test for 6?

A

It is even and is it divisible by 3

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20
Q

Divisibility test for 7?

A

Double the last digit and subtract it from the number made by the remaining digits. The result must be divisible by 7.

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21
Q

Divisibility test for 8?

A

The number made by the last 3 digits are divisible by 8. Or half the number 3 times to see if the result is still a whole number.

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22
Q

Divisibility test for 9?

A

The sum of the digits are divisible by 9.

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23
Q

When we square an integer it is called?

A

A square number

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24
Q

Index law for multiplication?

A

Add the powers

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25
Q

Index law for division?

A

Subtract the powers

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26
Q

Index law for multiplication from a bracket?

A

Multiply the powers

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27
Q

All natural numbers to the power of 0 equal?

A

1

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28
Q

BIDMAS order

A 
Brackets
Indices
Division
Multiplication 
Addition
Subtraction
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29
Q

What is a prime number?

A

Positive integers which only have two factors, being 1 and itself

30
Q

What are the first 10 prime numbers?

A 
2
3
5
7
11
13
17
19
23
29
31
Q

Prime factorisation meaning?

A

Writing a number as a product of its primes.
Eg 100 2x2x5x5
Start using the lowest prime number to divide and continue until you get to a prime number

32
Q

How to calculate how many factors an integer has?

A

Prime factorise
Add 1 to each ‘power’ and multiple these together
E.g. 2x2x2x5
4x2=8 factors

33
Q

How to calculate the highest common factor?

A 
Prime factorise
Multiple any common factors to get the HCF
E.g.    210=2x3x5x7
          640=2x2x3x3x3x5
So you would multiply 2x3x5=30
34
Q

How to calculate to lowest common multiple?

A

Prime factorise

Multiply the highest amount of each factor

35
Q

What is a terminating number?

A

Numbers that come to a definite end

36
Q

What is a recurring number?

A

A number that does not have a definite end. If the last number recurs it will have a dot on the top. If a sequence recurs it will have a dot on the first and last number in the sequence

37
Q

How to add fractions?

A

Make a common denominator and the add the numerators

38
Q

How to subtract fractions?

A

Make a common denominator and subtract the numerator

39
Q

How to multiply fractions?

A

Multiply the numerators together and the denominators together

40
Q

How to divide fractions?

A

Turn the second fraction into a reciprocal (turn upside down) then multiple the denominators together and the numerators together

41
Q

How to convert measurements?

A

Make both measurements into metric. Find the difference of magnitude and multiply/divide as appropriate

42
Q

How to convert squared/cubes measurements?

A

Make both measurements into metric. Find the difference of magnitude and square it and multiply/divide as appropriate

43
Q

How many Kg in a tonne?

A

1000

44
Q

How many Kg in a ton (UK)

A

1016

45
Q

How many Kg in a ton (US)

A

907kg

46
Q

How many cm in an inch?

A

2.54

47
Q

How many Km in a mile?

A

1.6

48
Q

How many litres in a gallon?

A

4.5

49
Q

How many litres in a pint?

A

0.568

50
Q

How many lbs in a Kg?

A

2.2

51
Q

How many ml in 1cm(3)

A

1

52
Q

How many inches in a foot?

A

12

53
Q

How many feet in a yard?

A

3

54
Q

How to express fractional ratios as ratios with integer components?

A

Find LCM of denominators
Multiply the numerators by the LCM
Evaluate the fractions

55
Q

How to turn ratios into linear equations?

A

Turn the ratio into a division

Move the variable to the opposite side

56
Q

How to split a value into a ratio?

A

Divide the value by both parts of the ratio added together

Multiply by each side of the ratio

57
Q

How to calculate an amount of a percentage of another?

A

Divide the first amount by the ‘percentage of’ amount

Multiply by 100

58
Q

How to calculate percentages of amounts?

A

Divide by 100 to find 1%

Multiply by the percentage needed

59
Q

How to work out percentage increase?

A

Find the difference between amounts
Divide by initial value
Multiply by 100

60
Q

How to work out percentage decrease?

A

Find the difference between amounts (a minus amount)
Divide by initial value
Multiply by 100

61
Q

How to express negative indices as fractions?

A

Change it to a fraction
Turn fractions into reciprocal
Work out the now positive indices

62
Q

How are fractional indices related to roots?

A

Denominator of the indice is equivalent of the root of that same number
Numerator as a power of that root

63
Q

How to work out fractional indices?

A

Convert to root form

64
Q

What is factorising?

A

Putting an equation back into brackets

65
Q

How to factorise?

A

Find the HCF if both numbers and letters if possible
Put these outside the brackets
Figure out what is needed in the bracket
Check by expansion

66
Q

What does log a X mean?

A

What power of a gives X

67
Q

Law for adding logarithms?

A

Multiply

68
Q

Law for subtracting logarithms?

A

Divide

69
Q

Law for powers with logarithms?

A

Move the indices to the front of the log

70
Q

A logarithm of 1 to any base equals?

A

0

71
Q

Logarithms with the same number and base equal?

A

1

Fundamentals Of Mathematics (2 decks)

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