Maths Flashcards
milligrams unit?
mg
how to convert between grams and mg?
1000mg = 1 gram
how many grams in a tonne (t) ?
1mn grams in a tonne
how many ml in a litre
1000 ml = 1l
volume units?
- Cubic millimetres (mm3)
- Cubic centimetres (cm3)
- Cubic metres (m3)
- Millilitres (ml)
- Litres (l)
how many ml in a cm3?
1 ml = 1 cm3
l -> dm3 -> cm3
1 l = 1 dm3 = 1000 cm3
l -> m3?
1000 l = 1 m3
Small quantities of liquid (e.g. drinks, medicines) are measured in
ml and l.
Large quantities (e.g. swimming pools, reservoirs) are measured in
m3.
A century is
100 years
A millennium is
1000 years.
Compound units are formed when
two quantitative forms of measurement need to be combined (such as metres and seconds into metres per second)
≠ is the symbol for
‘is not equal to
< is the symbol for
‘is less than’
> is the symbol for
‘is greater than’
how many ml in a l?
1000
To add or subtract fractions,
each fraction must first be put over a common denominator.
The number you are dividing
is called the dividend.
The number you are dividing by
is called the divisor
The result is called the
quotient.
To multiply two fractions
,first turn any mixed numbers into improper (top-heavy) fractions, then multiply the numerators (the top numbers) and multiply the denominators (the bottom numbers).
if you want to / by a fraction,
flip the second fraction and change the / sign to x
- if you make the numbers bigger in a multiplication,
you have to make the answer smaller by the same factor (e.g. if you make each number bigger by 10, the answer has to be / (10x10 =100)
if both numbers in the division are being inc by the same amount?
leave the answer unchanged
Bar charts for categorical data?
A simple bar chart is a diagram in which the length of the bar is proportional to the frequency. A bar chart can be drawn with horizontal or vertical bars.
- can be grouped or stacked, can be used to show subcategories
when drawing a pictogram?
a key is needed to indicate what a symbol represents
vertical line charts?
- similar to bar charts
- but bars have no width as data is ungrouped
- bars separate as data is discrete
Frequency tables and vertical line graphs
are the easiest way of displaying categorical data if there are a large number of categories.
Vertical lines enable
easy comparison of frequencies but it is often easier to read the frequency accurately from a table.
For smaller numbers of categories,
bar charts, pictograms and pie charts are a good way of showing frequencies visually. If the categories are further broken into subcategories then bar charts are usually appropriate.
Time series tables and line graphs are used when .
comparing data over time and for showing a trend
discrete data?
can only take certain fixed values e.g. number of students is always a whole number
continuous data?
s data which can take on any values in a range and not just particular values.
class intervals ?
- Inequalities are used to express class intervals.
- Class intervals must be continuous so that the upper boundary of one class is the lower boundary of the next class.
- When using class intervals, make sure that every number belongs to only one class interval.
- Class intervals do not have to be of equal width.
class intervals and bounds?
The lower class boundary of the class interval is the smallest number that rounds up to the lower limit of the group, and the upper class boundary is the largest number which rounds down to the upper limit of the group.
Histograms are used when
you want to see the underlying shape of the distribution of the data
Histogram rules?
- The area (not the length) of the bar is proportional to the frequency.
- The bars are the same width as the class intervals (class width) and are bounded by the class intervals.
- Class intervals do not have to be equal so the bars can be of different widths.
- Bars are drawn on a continuous, linear, horizontal scale.
- There are no spaces between the bars unless a class interval contains no data.
- The vertical axis shows frequency density.
frequency density =?
freq/ class width
cumulative freq =?
Running totals
when is CF used?
when u wanna be able to make simple estimates of certain stats about the data e.g. medican, range, quintiles
how to draw a CF graph?
- can be used for discrete or continous
- running total vs UPPER CLASS limit
- curve is normally an elongated S shape
The interquartile range
is the difference between the two quartile values (3/4 and 1/4)
how to read quintile values?
read off CF, half, quarter otr 3/4 and then read down the graph (other axis).
CF on y axis.
upper and lower bounds?
add or minus 0.5. Its the lowest or highest value that can round up/ down to the number. The upper boundary of one class is the lower boundary of the next class, and the inequality signs will be the same throughout for consistency. 49.5 ≤h< 59.5
to find class width?
minus upper from lower limit
in a CF graph, the interval always starts at ?
- as you are saying this is how many there are up to the upper limit.
always plot the CF against?
the upper limit of the class interval
median?
If a list of n numbers is arranged in order of size, the median is the middle value of the list, which is the number in position n+1 /2 in the list.
freq table range?
If the data is displayed in a frequency table then the range can be found easily by identifying the largest value and smallest value and then subtracting. Care should be taken to calculate the range from the possible values, and not from the frequency column in the table.
The range for data presented in a grouped frequency table is the ?
difference between the lower limit of the lowest class interval and the higher limit of the highest class interval. It is an estimate because there is no information about whether or not these values are included in the data set.
how to calculate the mean of a grouped frequency data table?
- To calculate an estimate of the mean, an estimate of the sum of all the data values is made.
- An estimate of the sum of the data values is calculated by using the mid-interval value (half way point) for each class interval,
- multiplying the mid-interval values by the frequencies and then adding all of the frequencies
- It is an estimate because it assumes an even or symmetric distribution of data within the class intervals, which may not be the case.
+s of the mean?
The mean gives the arithmetic average and can be used for any numerical data; however, it is influenced by extreme values so may give a false view of the data.
mode +s and -s?
The mode can be used for any type of data, not just numerical data, such as favourite colours. When the mode is used for numerical data, it is possible for the mode to be the lowest or highest data value and not a central value.
median +s and -s?
The median is not influenced by extreme values so shows a good indication of the central values, but it can only be used for data which can be ordered by size.
-s of range?
The range of the data gives a complete view of the spread of the data, but it is heavily influenced by extreme values.
IQR +s and -s?
The interquartile range shows the spread of the middle 50% of the data. It shows the positive difference between the lower quartile (the value 1/4 of the way through the data when listed in order) and the upper quartile (the value 3/4 of the way through the data when listed in order), so gives a good picture of the central data. The interquartile range is not affected by extreme values, but it does not give a complete picture of the range.
calc median from CF graph?
To calculate an estimate of the median from a histogram, first calculate the frequency represented by each block of the histogram. As frequency density is defined as f/CW frequency is found by multiplying frequency density by class width. The frequencies are added to give the total number of data items (n). The estimated median is then item n+12 and its position and class are calculated in the same way as for grouped data. The quartiles are estimated in a similar way.
when you’re multiplying?
if u inc the numbers by a certain amount then u have to decrease the answer by that amount BUT in division if u change the numbers (multiply or divide BY THE SAME AMOUNT E.G. EACH BY 10) you don’t have to decrease the end number.
The lowest common multiple (LCM) for two or more numbers is
the smallest number that will divide by all the numbers in the question.
What is a multiple?
A multiple of a number lies in the times table of that number.
A factor of a number will
divide into that number exactly (with no remainder). They are also known as divisors.
HCF?
for two or more numbers is the largest number that will divide exactly into all the numbers in the question.
a number is divisible by 3 if
the sum of its digits is divisible by 3
to find if a number is divisible by 7,
subtract 2 times the last digit from the other digits and then check if this is divisible by 7
the 10 prime numbers under 30 are?
2, 3, 5, 7, 11, 13, 17, 19, 23 and 29
- 2 is the only even prime number
- Apart from 2 and 5, all primes end in 1, 3, 7 or 9.
multiples are?
BIGGER than the numbers but factors are SMALLER
1 is always a ?
common factor
hint: when checking if a number is prime,
check to see if it divides by prime numbers. Work through the prime numbers in increasing order.
HCF & LCM?
- first draw a prime factor tree then draw a ven diagram
- HCF: multiply numbers in overlap
- LCM: multiply all numbers in ven
how to check HCF and LCM?
If you find the LCM and HCF of two numbers, and multiply them together, it’s the same as multiplying the two numbers together.
180 × 420 = 75 600 and 60 × 1260 = 75 600
Using prime factorisation to work out square root?
- if PF can be split into 2 identical halves
- take one half and multiply it out - square root
The cube of a positive number is a positive number,
but the cube of a negative number is a negative number.
The cube root of a positive number is positive,
and the cube root of a negative number is negative.
index laws?
- multiply powers of the same base: add indices
- divide powers of the same base: substract indices
Any number raised to the power 0 is
equal to 1.
fractions indicies?
the power applies to both denominator and numerator
a number raised to a negative power?
A number raised to a negative power can be written as 1 over the number to the positive power.
to raise a power to a further power,
multiply the powers. (brackets)
fractional powers?
- The power 1/2 is the same as the square root.
- The power 1/3 is the same as the cube root.
- The power 1/4 is the same as the fourth root etc.
the bottom number is the square root and the top is times
standard form trick?
count the number of decimal places moved!! and negative if the number becomes smaller!
To add (or subtract) numbers in standard form,
take the numbers out of standard form first - this isn’t needed for multiplication and division
Surds cannot be simply
added and subtracted but they can be multiplied and /
If the denominator is of the form
x+√y then multiply numerator and denominator by x−√y so the denominator is a difference of two squares - change the sign on the surds and multiply top and bottom by this
Both sides of the ratio can be multiplied or divided by the
same positive number without changing the ratio. - simplifying ratios
