Symmetry
Should you ever have a broken leg, you might find the video 'Order of Rotational Symmetry' propitious.
Speed, Distance and Time
Many revision guides suggest 'SoDiT' as an impolite way of remembering the Speed/Distant/Time triangle. I prefer to think of the character Marjorie Dawes from Little Britain's Fat Fighters, whose catchphrase was 'DuST'.
Trigonometry
When I want to do a question on similar triangles I always make sure that they are in the same orientation.
Opposite means opposite and adjacent means next to.
When I see a sheep 100 m away it looks similar to a sheep standing next to me, but not exactly the same because perspective makes it smaller. In the same way, similar shapes look the same but are different sizes.
When I want to work out the angle of elevation of the Sun in the sky I use the word SunTan to remind me to use the Tan ratio.
Triangles have three sides.
The hypotenuse is the longest side of any right-angled triangle.
The mkyou2tube video 'SOHCAHTOA' explains the process, but not so you'd enjoy it.
When I was a lad, Papa Smurf taught me that Smurfs Own Hot Chocolate And Hot Tea Or Apple Juice, and from that day to this I have remembered the acronym SOHCAHTOAJ, which is practically useless with a J on the end.
When my automobile broke down on the way to a football match recently I passed the time solving trigonometry questions until Smurfette attached a cable between our vehicles and pulled my car to the game. I now jokingly refer to Smurfette as the ‘Soccer Tower’.
SOHCAHTOA only applies to triangles with right-angles.
When my car broke down on a hill with an unknown angle it was adjacent to a potenuse which had been placed high up on a wall. As a result the car was very difficult to shift. Ever since, I have always associated an unknown angle, adjacent and high potenuse with a CAH that needs a SHIFT.
The smallest angle in any triangle is opposite the shortest side.
Trigonometry can be used for analysing light and sound waves, measuring the height of a tree or contacting alien life forms.
If I choose to calculate my distance from a seagull far away at the summit of a cliff of known height (and assuming my clinometer has been used to measure the angle of elevation) then I know that I should use SOH because it's the note that follows FAR.
Moving on from SOHCAHTOA, mkyou2tube's 'Sine Rule Song' is an accurate description of what it is. And if you ever find yourself needing to solve a trigonometric equation, you could do a lot worse than hanging out with the cast of 'Sex And The City'.
Opposite means opposite and adjacent means next to.
When I see a sheep 100 m away it looks similar to a sheep standing next to me, but not exactly the same because perspective makes it smaller. In the same way, similar shapes look the same but are different sizes.
When I want to work out the angle of elevation of the Sun in the sky I use the word SunTan to remind me to use the Tan ratio.
Triangles have three sides.
The hypotenuse is the longest side of any right-angled triangle.
The mkyou2tube video 'SOHCAHTOA' explains the process, but not so you'd enjoy it.
When I was a lad, Papa Smurf taught me that Smurfs Own Hot Chocolate And Hot Tea Or Apple Juice, and from that day to this I have remembered the acronym SOHCAHTOAJ, which is practically useless with a J on the end.
When my automobile broke down on the way to a football match recently I passed the time solving trigonometry questions until Smurfette attached a cable between our vehicles and pulled my car to the game. I now jokingly refer to Smurfette as the ‘Soccer Tower’.
SOHCAHTOA only applies to triangles with right-angles.
When my car broke down on a hill with an unknown angle it was adjacent to a potenuse which had been placed high up on a wall. As a result the car was very difficult to shift. Ever since, I have always associated an unknown angle, adjacent and high potenuse with a CAH that needs a SHIFT.
The smallest angle in any triangle is opposite the shortest side.
Trigonometry can be used for analysing light and sound waves, measuring the height of a tree or contacting alien life forms.
If I choose to calculate my distance from a seagull far away at the summit of a cliff of known height (and assuming my clinometer has been used to measure the angle of elevation) then I know that I should use SOH because it's the note that follows FAR.
Moving on from SOHCAHTOA, mkyou2tube's 'Sine Rule Song' is an accurate description of what it is. And if you ever find yourself needing to solve a trigonometric equation, you could do a lot worse than hanging out with the cast of 'Sex And The City'.
Perimeter, Area and Volume
Mathematical nets don’t have holes but real nets do, that’s how I tell the difference.
Convince your pals that you can find the surface area of a shape by working out the area of each face and adding them up.
If you chop a triangle off the end of a rectangle, you can put in on the other end to make a parallelogram. Hey, presto, they’ve got the same area.
Fans of mkyou2tube (as few and far between as they may be) are well cated for when it comes to shapes. 'Area of a Trapezium' is a jolly singalong to the melody of 'Pop Goes the Weasel' and for circles there's 'Circumference is pi times diameter' and the 'Circle of Life'. And as if that wasn;t enough there's the classic homage to Robbie Williams, 'Angles', which is not just an ode to angles but Pythagoras' theorem and the areas of triangle, parallelogram and trapezium.
In relation to the previous post concerning angles, one might also wish to frequent the Wretch 32 tribute '(Pro)Traktor', extolling the joys of measuring equipment.
When purchasing pies from a supermarket, I always pick the circular pies to remind me that pi is related to circles and not squares.
In the comedy show Blackadder, whenever Baldrick says he has a cunning plan, Blackadder looks down on it. And hence a plan view is when you look down from above.
Contrary to popular opinion, there are 100 mm2 in 1 cm2 (where my website creator of choice refuses to permit the superscript required to write correctly mm2 or cm2 (there it goes again)).
A cylinder is a prism but a cone is not.
Tin manufacturers: use hexagonal prisms rather than cylinders because they can tessellate.
The radius (r), vertical height (h) and slant height (l) of a cone satisfy Pythagoras’ theorem (r2 + h2 = l2) (but with the standard superscript 2s rather than this inaccurate kerfuffle).
You can't simplify a pi–term and a non–pi–term added together.
The people who write the formula page don’t want to tell you the area of a circle, but they do! It’s the middle bit if the volume of a cone formula.
The surface of a cylinder is like the base and lid of a baked bean can with a rectangular label wrapped around the can as well.
In Star Wars the characters often whizz around spherical planets shouting ‘May the Fours be with you’ and that’s how I remember that the formulae for spheres both contain a 4.
Similarly the name R2D2 reminds me that the formulae both contain an R too (but not a D too, no diameter required).
A sector is a fraction of a circle like a slice of pizza or cake.
A frustum is a cone with a smaller cone chopped off,
When sticking curved shapes’ formulae together in pursuit of an equation, it is very likely that each term in the equation will contain a p which can be cancelled out.
Due to the nature of areas of surfaces, it is not uncommon to be in receipt of a quadratic equation after putting all the information together (and there’s a good chance it’ll factorise too at your age).
When combining bits of shapes’ formulae, think carefully about which bits you need and which you don’t.
Never add surface areas and volumes.
I have never had a dream come true, so I often have to reach for my own way of recalling the relationship Density = Mass / Volume. I bring it all back to the vocal group S Club. Back in the day they had several television series such as Miami 7, LA7 and Hollywood 7 in which they were based in various locations, or alternatively they made their dens in different cities (den-sity). Rachel Stevens is Jewish, but if she were Catholic she presumably would have attended the odd Mass. And the word Volume contains the sound You, their 2002 hit single. All of which makes me think of their greatest hit Don't Stop Movin', which reminds me of the letters DMV, which brings it all back to the aforementioned formula. Time to Say Goodbye.
Convince your pals that you can find the surface area of a shape by working out the area of each face and adding them up.
If you chop a triangle off the end of a rectangle, you can put in on the other end to make a parallelogram. Hey, presto, they’ve got the same area.
Fans of mkyou2tube (as few and far between as they may be) are well cated for when it comes to shapes. 'Area of a Trapezium' is a jolly singalong to the melody of 'Pop Goes the Weasel' and for circles there's 'Circumference is pi times diameter' and the 'Circle of Life'. And as if that wasn;t enough there's the classic homage to Robbie Williams, 'Angles', which is not just an ode to angles but Pythagoras' theorem and the areas of triangle, parallelogram and trapezium.
In relation to the previous post concerning angles, one might also wish to frequent the Wretch 32 tribute '(Pro)Traktor', extolling the joys of measuring equipment.
When purchasing pies from a supermarket, I always pick the circular pies to remind me that pi is related to circles and not squares.
In the comedy show Blackadder, whenever Baldrick says he has a cunning plan, Blackadder looks down on it. And hence a plan view is when you look down from above.
Contrary to popular opinion, there are 100 mm2 in 1 cm2 (where my website creator of choice refuses to permit the superscript required to write correctly mm2 or cm2 (there it goes again)).
A cylinder is a prism but a cone is not.
Tin manufacturers: use hexagonal prisms rather than cylinders because they can tessellate.
The radius (r), vertical height (h) and slant height (l) of a cone satisfy Pythagoras’ theorem (r2 + h2 = l2) (but with the standard superscript 2s rather than this inaccurate kerfuffle).
You can't simplify a pi–term and a non–pi–term added together.
The people who write the formula page don’t want to tell you the area of a circle, but they do! It’s the middle bit if the volume of a cone formula.
The surface of a cylinder is like the base and lid of a baked bean can with a rectangular label wrapped around the can as well.
In Star Wars the characters often whizz around spherical planets shouting ‘May the Fours be with you’ and that’s how I remember that the formulae for spheres both contain a 4.
Similarly the name R2D2 reminds me that the formulae both contain an R too (but not a D too, no diameter required).
A sector is a fraction of a circle like a slice of pizza or cake.
A frustum is a cone with a smaller cone chopped off,
When sticking curved shapes’ formulae together in pursuit of an equation, it is very likely that each term in the equation will contain a p which can be cancelled out.
Due to the nature of areas of surfaces, it is not uncommon to be in receipt of a quadratic equation after putting all the information together (and there’s a good chance it’ll factorise too at your age).
When combining bits of shapes’ formulae, think carefully about which bits you need and which you don’t.
Never add surface areas and volumes.
I have never had a dream come true, so I often have to reach for my own way of recalling the relationship Density = Mass / Volume. I bring it all back to the vocal group S Club. Back in the day they had several television series such as Miami 7, LA7 and Hollywood 7 in which they were based in various locations, or alternatively they made their dens in different cities (den-sity). Rachel Stevens is Jewish, but if she were Catholic she presumably would have attended the odd Mass. And the word Volume contains the sound You, their 2002 hit single. All of which makes me think of their greatest hit Don't Stop Movin', which reminds me of the letters DMV, which brings it all back to the aforementioned formula. Time to Say Goodbye.
Vectors
Want to see some ladies being blown around by the wind in a chaotic ballad about 'Vectors' to the tune of 'What Makes You Beautiful' by the boys from One Direction? I very much doubt it.
Circle Theorems
Angles in circles? Whatever next? How about mkyou2tube's soothing video on 'Circle Theorems'?