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Fundamentals Of Mathematics > Number And Algebra > Flashcards

Number And Algebra Flashcards

(71 cards)

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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
Index law for division?
Subtract the powers
26
Index law for multiplication from a bracket?
Multiply the powers
27
All natural numbers to the power of 0 equal?
1
28
BIDMAS order
``` Brackets Indices Division Multiplication Addition Subtraction ```
29
What is a prime number?
Positive integers which only have two factors, being 1 and itself
30
What are the first 10 prime numbers?
``` 2 3 5 7 11 13 17 19 23 29 ```
31
Prime factorisation meaning?
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
How to calculate how many factors an integer has?
Prime factorise Add 1 to each ‘power’ and multiple these together E.g. 2x2x2x5 4x2=8 factors
33
How to calculate the highest common factor?
``` Prime factorise Multiple any common factors to get the HCF E.g. 210=2x3x5x7 640=2x2x3x3x3x5 So you would multiply 2x3x5=30 ```
34
How to calculate to lowest common multiple?
Prime factorise | Multiply the highest amount of each factor
35
What is a terminating number?
Numbers that come to a definite end
36
What is a recurring number?
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
How to add fractions?
Make a common denominator and the add the numerators
38
How to subtract fractions?
Make a common denominator and subtract the numerator
39
How to multiply fractions?
Multiply the numerators together and the denominators together
40
How to divide fractions?
Turn the second fraction into a reciprocal (turn upside down) then multiple the denominators together and the numerators together
41
How to convert measurements?
Make both measurements into metric. Find the difference of magnitude and multiply/divide as appropriate
42
How to convert squared/cubes measurements?
Make both measurements into metric. Find the difference of magnitude and square it and multiply/divide as appropriate
43
How many Kg in a tonne?
1000
44
How many Kg in a ton (UK)
1016
45
How many Kg in a ton (US)
907kg
46
How many cm in an inch?
2.54
47
How many Km in a mile?
1.6
48
How many litres in a gallon?
4.5
49
How many litres in a pint?
0.568
50
How many lbs in a Kg?
2.2
51
How many ml in 1cm(3)
1
52
How many inches in a foot?
12
53
How many feet in a yard?
3
54
How to express fractional ratios as ratios with integer components?
Find LCM of denominators Multiply the numerators by the LCM Evaluate the fractions
55
How to turn ratios into linear equations?
Turn the ratio into a division | Move the variable to the opposite side
56
How to split a value into a ratio?
Divide the value by both parts of the ratio added together | Multiply by each side of the ratio
57
How to calculate an amount of a percentage of another?
Divide the first amount by the ‘percentage of’ amount | Multiply by 100
58
How to calculate percentages of amounts?
Divide by 100 to find 1% | Multiply by the percentage needed
59
How to work out percentage increase?
Find the difference between amounts Divide by initial value Multiply by 100
60
How to work out percentage decrease?
Find the difference between amounts (a minus amount) Divide by initial value Multiply by 100
61
How to express negative indices as fractions?
Change it to a fraction Turn fractions into reciprocal Work out the now positive indices
62
How are fractional indices related to roots?
Denominator of the indice is equivalent of the root of that same number Numerator as a power of that root
63
How to work out fractional indices?
Convert to root form
64
What is factorising?
Putting an equation back into brackets
65
How to factorise?
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
What does log a X mean?
What power of a gives X
67
Law for adding logarithms?
Multiply
68
Law for subtracting logarithms?
Divide
69
Law for powers with logarithms?
Move the indices to the front of the log
70
A logarithm of 1 to any base equals?
0
71
Logarithms with the same number and base equal?
1

Fundamentals Of Mathematics (2 decks)

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