1.1 Arithmetic Flashcards
Numbers are represented by symbols. What are they called?
Digits (i.e 7=1 digit, 48=2 digits, 653= 3 digits,etc)
What is a whole number?
Any number that does not have a fractional part
What are the four basic math operators?
Add, subtract, multiply, divide
When numbers are combined by addition what is the resulting total called?
The sum
A number is subtracted from another number to find what is left. What’s this called?
The difference
When multiplying numbers together the result is called?
The product
When dividing numbers what is the result called?
The quotient
When the number being subtracted is the larger number is it positive or negative?
Negative
How is multiplication shown?
By an x or by a mid line dot -
When multiplying two positives what is the final product?
A positive
When multiplying two negatives. What is the final product?
A positive
When multiplying a positive and a negative. What is the final product?
A negative
When dividing two positive numbers what is the quotient?
A positive
When dividing two negative numbers what is the quotient?
A positive
When dividing a positive and a negative number what is the quotient?
A negative
What is BODMAS?
Brackets
Orders
Division
Multiplication
Addition
Substation
What does it mean when a number is squared? I.e 5^2
It multiples by itself twice
I.e 5x5=25
What is 10 to the power of 5?i.e 10^5
10x5=100,000
If a question only contains addition and subtraction what should you do?
Complete it from left to right
if a question only contains division and multiplication what should you do?
Complete it from left to right
What is the definition of a factor?
Is when a number will divide into a number without leaving a reminder
I.e 15/5=3 or 12/3=4
What is a prime number?
Is when a number can only be divided by itself and 1
What is the only even prime number?
2
What is the definition of he highest common factor?
The largest number that can be divided exactly into the numbers given
What is the definition of the lowest common multiple?
The lowest number on the lists of multiplication numbers
What is the definition of a comon factor?
A number that represents a portion or part of a quantity
What is the top number of a common factor called?
Numerator
What is the bottom number of a common fraction called?
Denominator
What does the numerator define in a common fraction?
The number of parts there are
What is the denominator defining in a common fraction?
The number of parts one unit is divided into
What must be the same when comparing two or more fractions?
The denominator should be the same (usually the lowest common multiple)
What is a mixed number?
A whole number and a proper fraction combined
When adding fractions what must be the same?
Denominator
Before multiplying mixed nu,bears what must you do first?
Converted into improper fractions
How do you divide two fractions by each other?
You must invert the second fraction (divisor) and then multiply. I.e 3/5 divide 7/8 turns into 3/5 multiply 8/7
True or false, the number of zeros right of the decimal point does not affect the value as long as no other number appears?
True
What must you do when multiplying decimals?
Count the amount of digits after the decimal point and then multiply like normal and then add the decimal point back the amount of digits you counted
When rounding numbers what should you always remember?
Round up when its 5 or more
Where does the word percentage come from?
Latin origins ‘per centum’ which means ‘out of one hundred’
How do you work out a percentage?
Divide by 100 and then multiply by the desired percentage
What must you do when told to express a number as a percentage?
Divide the number by the desired percentage and then times by 100
I.e express 12 by 50 is 12/50 x 100
How do you convert a fraction to a decimal?
Divide the numerator (top) by the Denominator (bottom)
How do you convert a fraction into a percentage?
Firstly convert it into a decimal and then multiply by 100
How do you convert a decimal to a fraction?
Write your decimal over 1 and then multiply top and bottom by 10 for every decimal place you have and then simplify
How do you convert a decimal to a percentage?
Multiply by 100
How do you convert a percentage to a decimal?
Divide by 100
How do you convert a percentage to a fraction?
Write you percentage over 100 and then simplify
What does the SI unit system stand for?
International system of units (french Système International d’Unités)
In the SI units system what is kilo,mega, giga watts equal to?
Kilo- 10^3 or 1,000
Mega- 10^6 or 1,000,000
Giga- 10^9 or 1,000,000,000
What is force measured in?
Newtons
What is the length of an inch?
2.54cm or 25.4mm
How long is a metre?
100cm or 3.3ft or 39.37in
How many units is a litre?
1,000cm^3 or 0.2642 US gal
What is the unit of a newton?
1N or 0.2248lb
What are the units of a pound in weight?
0.4536kg or 16oz
What is one bar of pressure equal to in lb/in?
14.6 lb/in^2
What is the unity of gravity?
9.8m/s
What is 1 hectopascals equal to?
100 pascals or 1mbar (millibar)
What is the definition of standard pressure?
An established or standard value for atmospheric pressure
In imperial units what is the standard atmospheric pressure?
14.696psi
What is the definition of a ratio?
Is a method of expressing the relative size of two or more quantities
How would you write a ratio of 1 to 75?
1:75
If you had a piston with 140in^3 at the bottom stroke and then 20in^3 at the top. What is the compression ratio?
140 over 20 which is simplified to 7:1
When working out gear ratio what is the calculation?
Driven over drive
If you had a drive gear with 40 teeth and a driven gear with 20 teeth what would the gear ratio be?
20:40 or simplified into 1:2
What Is the definition of direct proportion?
If one amount increase or decreases then another amount must increase or decrease
What is the definition of inverse proportion?
When one value increase and the other value decreases
What is the definition of an average?
Is a number expressing the central or typical value in a set of data
What are the three common ways of calculating the average?
Mean, mode, median
What is the most common form of average?
Mean
If the type of average is not specified what type of average should you use?
The mean
How do you work out the mean average?
By dividing the sum of values by the total number of values
What is the mode average?
Is the most frequently occurring data value?
What is the median average?
The middle number when all the data values are listed in order according to size
When asked to find the range, what must you do?
It is the difference between the highest value and the lowest value
When calculating the median average, what must you do when there is two middle numbers?
Add together and then divide by 2
What is a 2D shape?
Figures that can be drawn on a flat surface
How do you calculate the perimeter of a 2D shape?
By adding the length of all the straight sides
The perimeter of a circle is curved, what is this called?
The circumference
How do you calculate the circumference of a circle?
2 x pie x radius
What is the SI unit for area?
A square metre or M^2
What is the imperial unit for area?
Square inch, square foot or square yard
How do you work out the area of a square?
By multiplying two sides?
How do you you work out the area of a triangle?
(Base x height) divide by 2
How do you work out the area of a rectangle?
Multiply the base and the height
How do you work out the area of a parallelogram?
Base x perpendicular height
How do you calculate the area of a trapezium?
(The short top + the base) divide by 2 and multiply by the height
How do you calculate the area of a circle?
Pie x radius^2
How do you calculate a small section of a circle?
(Pie x radius^2) x (angle over 360)
What are the two different measures used for measuring 3D shapes?
Surface area and volume
What is the definition of surface area?
The total area of the surface of an object
What are the 3 types of surface area?
Curved surface area (CSA)
Lateral surface area (LSA)
Total surface area (TSA)
What is the definition of a curved surface area?
Area of all curved regions
What is the definition of lateral surface area?
Area of all curved regions and all the flat surface excluding base areas
What is the definition of total surface area?
Area of all the surfaces including the base of a 3D object
what is the definition of volume when relating to a 3D shape?
The total space occupied by the 3D shape or solid
What is the SI unit for volume?
Cubic metre or m^3
How do you calculate the volume of a cylinder?
Pie x radius^2 x height
How do you calculate the surface area of a cylinder?
2 x pie x radius x (radius + height )
How do you calculate the volume of a cone?
1/3 x pie x radius^2 x height
How do you calculate the volume of a sphere?
4/3 x pie x radius^3
How do you calculate the surface area of a sphere?
4 x pie x radius^2
How do you calculate the volume of a cube?
Length^3
How do you calculate the surface area of a cube?
6 x length^2
How do you calculate the volume of a cuboid?
Length x width x height
How do you calculate the surface area of a cuboid?
2 (length x width + width x height + height x length)
What does it mean when a number is squared or to the power of two?
It is multiplied by itself twice
When a number is multiplied by itself, what is this said to be?
To be raised to a given power (i.e 8^4 is 8 to the power of 4)
When a number is given a power it sometimes has a different name for the power, what is this name?
Exponent
In engineering notation what must the exponent be divisible by?
3 (i.e x10^3, x10^6, x10^9)
When a number is expressed into scientific/normal notation, what happens to the number?
The number is expressed in terms of a power of ten (i.e 360,000 is 3.6 x10^5)
When a number is in its ordinary notation form what does this look like?
The number is expressed in its longest form (no simplifying)
When told to convert ordinary notation to scientific notation, what must you do?
Convert it into a given power (i.e 36,800,000 is 3.68 x10^7)
What happens when converting a negative ordinary notation into scientific notation? i.e 3.68x10^-4
The number gets smaller as you have to move the decimal place left instead of right (i.e 0.000368)
When adding, subtracting, multiplying, or dividing in scientific or engineering notation, what must you do?
Express the numbers in ordinary notation then calculate as normal then turn back into the notation
What is the definition of a root √ number?
When multiplied by itself a certain number of times it produces that number under the root √
If there is only the root sign √ over a number and no index, what is it asking you to do?
You to find the square root (√ is the same as 2^ √)
If an index number is shown before the root sign √ what is it asking you to do? (I.e 3^√64)
To root to that number (i.e 3^√64 = 4)
What’s the difference between gear ratio and teeth ratio?
Gear ratio counts the difference in rotation and teeth ratio counts the difference in teeth
What is the calculation used to convert between Celsius and Fahrenheit?
F=1.8xC+32
What should you do if you’re subtracting a negative number? I.e -25 - -8=
You should add it i.e -25 - -8= -17
