Task 1:Imperial units of measurement were created in Britain during 1824 by the British weights and measures act and have also been improved since then.Common Imperial units:Measuring length:”inch”, “Foot”, “yard” and “mile”Measuring Mass:”Ounce (oz)”, “pound (lb)” and “stone”Measuring volume:”pint” and “gallon”Imperial to Metric:5/8 miles = 1 km39.37 inches = 1 m30.5 cm = 1 foot2.54 cm = 1 inch2.2 lb = 1 kg4.
5 litres = 1 gallon1 ¾ pints = 1 litreLength: MetricImperial1 millimetre =0.03937 in1 centimetre =0.3937 in1 meter =1.
0936 yd1 kilometre =0.6214 mileImperialMetric1 inch2.45 cm1 foot0.3048 m1 yard0.9144 m1 mile1.6093 km1 int nautical mile1.853 kmArea:MetricImperial1 sq cm0.
1550 in^21 sq m1.1960 yd^21 hectare2.4711 acres1 sq km0.
3861 mile^2ImperialMetric1 sq inch6.4516 cm^21 sq foot0.0929 m^21 sq yd0.8361 m^21 acre4046.9 m^21 sq mile2.59 mk^2Volume/capacity:MetricImperial1 cu cm0.0610 in^31 cu decimetre0.0353 ft^31 cu meter 1.
3080 yd ^31 litre2.113 fluid pt / 3.7854 litresImperialMetric1 cu inch 16.
387 cm^31 cu foot0.02832 m^31.0408 uk fl oz29.574 ml0.8327 uk pt0.4732 litres0.
8327 uk gal3.7854 litresMass:ImperialMetric1 ounce28.35 g1 pound0.4536 kg1 stone6.3503 kg1 hundredweight50.802 kg1 short ton0.
9072 t1 long ton1.0160 tMetricImperial1 milligram0.0154 grain1 gram0.0353 oz1 kilogram2.2046 lb1 tonne1.1023 short ton1 tonne0.9842 long tonBiology unit conversions:1 milligram0.0154 grainThe average weight of one ant is 3 milligrams, if 1 milligram is equal to 0.
0154 grains then how many grains does one ant weigh? 0.0154 x 3 would give the answer of one ants weight in grains which is 0.0462 imperial grainChemistry unit conversions:0.8327 uk gal3.7854 litres0.8327 uk gal is equal to 3.
7854 metric litres, if 2.4981 uk gallons of alcohol is stored in a chemistry lab then how many litres is this? 2.4981/0.8327 equals 3, so 3 x 3.7854 would equal how many litres is equivalent to 2.
4981 uk gallons which leaves the answer as 11.3562 metric litresPhysics unit conversions:1 mile1.6093 km1 mile is equal to 1.6093km, if a bird travels 8 miles while flying what is this in km?8 miles x 1.6093km = 12.8744 so the bird travelled 12.
8744km in Metric units.Task 3 (2):Example of rearranging an equation:V= 4/3 ? r3, To rearrange this equation first multiply both sides using 3 which equals 3V=4?r3, then divide by 4? on both sides which would equal 3v4?= r3, then remove the cubed which leaves the final answer as: 33V4?=rProblem 1: 5(-3x – 2) – (x – 3) = -4(4x + 5) + 13Solve the equationProblem 2:2(a -3) + 4b – 2(a -b -3) + 5Simplify the expressionProblem 3:|x – 2| – 4|-6|If x <2 simplifyProblem 4:Find the distance between the points (-4 , -5) and (-1 , -1).Problem 5:2x - 4y = 9Find the x intercept of the graph of the equation. Problem 6:Evaluate f(2) - f(1) f(x) = 6x + 1Problem 7:Find the slope of the line passing through the points (-1, -1) and (2 , 2).
Problem 8:Find the slope of the line 5x – 5y = 7Problem 9:Find the equation of the line that passes through the points (-1 , -1) and (-1 , 2).Problem 10:Solve the equation |-2x + 2| -3 = -3Answers:Problem 1:Given the equation 5(-3x – 2) – (x – 3) = -4(4x + 5) + 13 Multiply factors. -15x – 10 – x + 3 = -16x – 20 +13 Group like terms.-16x – 7 = -16x – 7 Add 16x + 7 to both sides and write the equation as follows 0 = 0 Problem 2:Given the algebraic expression 2(a -3) + 4b – 2(a -b -3) + 5 Multiply factors.
= 2a – 6 + 4b -2a + 2b + 6 + 5 Group like terms. = 6b + 5Problem 3:Given the expression |x – 2| – 4|-6| If x < ;2 then x - 2 < 2 and if x - 2 < 2 the |x - 2| = -(x - 2). Substitute |x - 2| by -(x - 2) and |-6| by 6 . |x - 2| - 4|-6| = -(x - 2) -4(6) = -x -22Problem 4:The distance d between points (-4 , -5) and (-1 , -1) is given byd = sqrt (-1 - -4) 2 + (-1 - -5) 2 Simplify.
d = sqrt(9 + 16) = 5Problem 5:Given the equation 2x – 4y = 9 To find the x intercept we set y = 0 and solve for x. 2x – 0 = 9 Solve for x. x = 9 / 2 The x intercept is at the point (9/2 , 0).
Problem 6:Given the function f(x) = 6x + 1 f(2) – f(1) is given by. f(2) – f(1) = (6*2 + 1) – (6*1 + 1) = 6Problem 7:Given the points (-1, -1) and (2 , 2), the slope m is given by m = (y2 – y1) / (x2 – x1) = (2 – -1) / (2 – -1) = 1Problem 8:Given the line5x – 5y = 7 Rewrite the equation in slope intercept form y = mx + b and identify the value of m the slope. -5y = -5x + 7 y = x – 7/5 The slope is given by the coefficient of x which is 1.
Problem 9:To find the equation of the line through the points (-1 , -1) and (-1 , 2), we first use the slope m. m = (y2 – y1) / (x2 – x1) = (2 – -1) / (-1 – -1) = 3 / 0 The slope is indefined which means the line is perpendicular to the x axis and its equation has the form x = constant. Since both points have equal x coordinates -1, the equation is given by: x = -1Problem 10:The equation to solve is given by.
|-2x + 2| -3 = -3 Add 3 to both sides of the equation and simplify. 1 |-2x + 2| = 0 |-2x + 2| is equal to 0 if -2x + 2 = 0. Solve for x to obtain x = 1Task 2 (3):Standard Form:Standard form is used to write very large or very small numbers in a more simpler easier method by the use of powers. The powers are negative during the use of small numbers while big numbers have a positive power. There are some rules that have to be followed with standard form, one of them is that the number must be written between 1 and 10 followed by the power.
If you wanted to write 81 900 000 000 000 in standard form it would appear like so: 8.19×10^13. The power is by 13 because of the decimal point being moved 13 times to make the number smaller so it appears as 8.19 to follow the rule.
If you wanted to write a smaller number like 0.000 0012 then it would have a minus power instead and look like 1.2×10^-6, the power is a minus this time because the number is much smaller instead of much larger and the decimal point moves to the right instead of the left like the larger number in order to follow the rule of being between 1 and 10. To turn a number written in standard form back into a normal number then the powers must be used like a calculation, for example 8.
19×10^13 would be carried out like 8.19 x 10000000000000 which equals 81900000000000. Standard form is often used in science.
Standard form and Microscopes:Standard form and Measurements of concentration in chemistry:Concentration in chemistry can be several things such as molar concentration, mass concentration, volume concentration and number concentration. The concentration of any solution is measured by using moles, more specifically moles per cubic decimetre which when shortened means mol/dm3. If the concentration of a solution is higher the more of a certain substance will be found in that solution. Calculating and standard form examples: if 0.
5 mol of a solution is dissolved in 250cm cubed of solution then to discover the concentration 250cm cubed needs to be divided by 1000 which leaves you with 0.25dm cubed, With this the concentration can be worked out by dividing 0.5 by 0.25 which is 2.0 mol/dm cubed. The amount of different substances in a solution if the volume and concentration is available.Standard form and Distance in physics using the wavelengths of different forms of radiation:Wavelengths refers to the electromagnetic spectrum and its waves such as infrared light,microwaves,radio waves, gamma rays,ultraviolet light,visible light and X-rays. Standard form comes into use when measuring the frequencies of the different waves for example Gamma rays have frequencies of 3*1019 and have wavelengths of 10-11 .
Example of calculating the frequency of a radio wave: Using the equation Frequency = 1/time period, where F is the waves produced per second represented by Hz and T is the time it takes for one oscillation. What is the frequency of a radio wave if its time period is 0.0000003333333? This can be done with the equation since f would equal 1 divided by T, where T is 0.0000003333333 so 1 / 0.
0000003333333 which is equal to 3,000,000 Hz.Collecting data in scienceCollecting and presenting data with a high standard is very important in every aspect of science, Analysing data and looking/comparing results becomes more difficult and less accurate if the data collected isn’t of a high standard as well as not being properly recorded.Primary data:Primary data is data thats obtained for the purpose of an experiment or project and has no other reason to be collected. It’s collected/viewed from someone personally/directly involved with something and is an advantage because its directly related with the work you’re doing but can also take time and accuracy to obtain.Secondary data:Secondary data is like primary data except it was collected or observed by another person and could be information that can be found online about an experiment or project instead of being collected by a person themselves as it can be costly.
The data could be collected by a school or organisation who decided to make the data they collected public for others to use.Random and systematic errors:Random and systematic errors are errors that occur while collecting data but can also appear at a later date during calculations or other cases as well as a device producing an error during collection. Random errors are when the person recording results isn’t able to take the same measurement multiple times in order to get the same results. Systematic errors are consistent in terms of being an error and can be done multiple times as they’re caused by a mistake from the whole experiment which makes them appear commonly and be similar or the same each time.
Random errors are usually human error and their effects or the error themselves can be reduced by completing an average over a large amount of data. Systematic errors are due to faulty equipment being used or a variable being set up incorrectly which means they’re harder to detect as the error repeats itself making it look more common than an anomaly.Equation for calculating % error and example calculation:The % error equation is useful for finding out the accuracy of calculations/data used.
The equation is as follows: Percent error = Experimental valuee – accepted valueaccepted valuex 100% Where experimental value is the calculated value from the data and accepted value is the known value from the data. If the result is close to 0 or is 0 then the data you collected is either correct or close to the target value of the calculation, if the answer is far from 0 then your results are far from your target value which could indicate an error with a calculation or equipment involved. Here is an example: The calculated density of a cube of copper is 2.68g cm3 but should really be 2.7g cm3 which suggests an error has been made. To calculate the percent error subtract 2.
68 from 2.7 which leaves 0.02 which is the error, then divide the error by the accepted value which is 2.
7g so 0.02/2.7g which equals 0.0074074, then multiply this answer by 100% which reveals the percent error to be 0.74% Continuous data:Continuous data is data that’s able to be easily measured from observed results and can be reoccuring or able to be made smaller by dividings after being recorded. Or on a scale for example measurements such as length.Discrete data:Discrete data is data that can be categorized into different subjects or subcategories which are used to classify them.
Discrete data cannot be infinite and cannot be subdivided any further for example categories of genres of films out of a total amount.Mean, median and mode:The mean, median and mode are all types of averages just different types, the mean being where all of the numerical values are added together before being divided by the total value of all the numbers added together which leaves an overall average. The median is the middle numerical value from an ordered list of numbers in terms of their value and the mode is the value that is the most common and doesn’t need to be a numerical value.Data:7, 4, 8, 6, 7, 5, 4, 1, 2, 3, 4, 5, 6, 4, 3Mean = 7+4+8+6+7+5+4+1+2+3+4+5+6+4+3 = 69Median = 1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8 The middle number is 4Mode: 1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8 The number repeated the most is 4 so that makes it the mode