Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Int 1 Unit 3 Nab Formula Multiply Bracket Multiply Bracket plus letter Factorise s+7=13 a+4 > 11 3z=14 5t>20 y=2x+3 Draw Line Trig Side Trig Angle Big to Standard Form Small to Standard Form Standard Form to Big Standard Form to Small Light Years What is a Formula The RHS of the formula is interpreted then the letters are replaced by numbers m = F= ma m xa F= F= F= a 7 7 x 21 3 = 3 Formula u= 7 a= v= 7u v= 7 3 4a at xt 3 + x + v= v= t= 4 + 19 12 BoDMas Multiply before Add Multiply out Brackets Simply multiply everything inside the bracket by what is outside the bracket 6 ( a + = 6 x = 6a 7 ) 6x + 42 Two “answers one for each term inside the brackets The + between the a and 7 tells you to subtract the answers Multiply out Brackets Simply multiply everything inside the bracket by what is outside the bracket 5( x = 5 x = 5x 3 ) 5x - 15 Two “answers one for each term inside the brackets The - between the x and 3 tells you to subtract the answers Simply multiply everything inside the bracket by what is outside the bracket 3 ( 2c + 9 ) x 3 x 3 + 5c 3 x 2xc 6cx c = 6 3x = All Maths “sums” involve BODMAS. ( B ) first Two answers, one for each term The + between the 2c and 9 tells you there is a + between the answers 27 Simply multiply everything inside the bracket by what is outside the bracket 3 ( 2c + = = 6c 11c 9 ) + 27 + + 5c + 5c 6c +5c = 27 The brackets equal 6c + 27 Three terms now The expression has been simplified to 11c + 27 The 1st and last terms are letter terms the middle a number A letter term plus a number Hide the middle term and addterm the two letter terms 11c Simply multiply everything inside the bracket by what is outside the bracket 5 ( 3b - 7 ) x 5 x 5 + 4b 5 x 3xb 15bx b = 15 5x = All Maths “sums” involve BODMAS. ( B ) first Two answers, one for each term The - between the 3b and 7 tells you there is a - between the answers 35 Simply multiply everything inside the bracket by what is outside the bracket 5 ( 3b - = = 7 ) 15b - 35 19b - + 4b + 4b 15b +4b = 19b 35 The brackets equal 15b -35 Three terms now The expression has been simplified to 19b - 35 The 1st and last terms are letter terms the middle a number A letter term plus a number Hide the middle term and addterm the two letter terms Factorisation 2d + x x = ( 8 + ) Factorising is the opposite of multiplying the contents of a bracket Need to find a number that you can multiply something to get 2d and 8. Find a common factor by a number ( or a term ) Factorising 2d + 2d is one term 8 8 is the 2nd term = 2 ( 2 d x + ) 4 2 x Concentrate on the number part of each … 2 and 8 2x4=8 2d 8 2 x d 2 x 4 2 is a COMMON FACTOR of 2d and 8 s + 7 = 13 s + 7 s Letters to the left = 13 = 13 - 7 = 6 Change from + 7 to - 7 = 6 Numbers to the right d - 9 = 28 d - 9 d Letters to the left = 28 = 28 + 9 = 37 Change from - 9 to + 9 = 37 Numbers to the right 3z = 14 3z 14 = 3 xz = 14 z = 14 x3 ÷3 z = 14 3 Opposite of Multiply is Letter on the left Divide Numbers on the right 4g = 21 4g 21 = 4 xg = 21 g = 21 x4 ÷4 g = 21 4 Opposite of Multiply is Letter on the left = 5.25 Divide Numbers on the right a + 4 > 11 a + 4 a > 11 > 11 - 4 > 7 Solve in the same way as equation but replace = with > Letters to the left Change from + 4 to - 4 Numbers to the right f-9<5 f - 9 f < 5 < 5 + 9 < 14 Solve in the same way as equation but replace = with > Letters to the left Change from - 9 to + 9 Numbers to the right 5t > 20 5t 20 > 5 xt > 20 t > 20 x5 ÷5 t > 4 Opposite of Multiply is Letter on the left Divide Numbers on the right 6d < 42 6d 42 < 6 xd < 42 d < 42 x6 ÷6 d < 7 Opposite of Multiply is Letter on the left Divide Numbers on the right y=2x-3 2 Y= -3 x x 0 1 Y -3 -1 2 1 3 4 3 5 x Y x= 0 Y= 2x0-3 -3 ( 0 , -3) x= 1 Y= 2x1-3 -1 ( 1 , -1) 1 ( 2 , 1) x= 2 Y= 2x2-3 x= 3 Y= 2x3-3 3 ( 3 , 3) x= 4 Y= 2x4-3 5 ( 4 , 5) = 0 2–3=3 -1 x=0 x=1 y= 2 x 0 x1 - 3 X X X X X y=3x+1 3 Y= X +1 x x 0 1 Y -3 -1 2 1 3 4 3 5 X x Y x= 0 Y= 3x0+1 1 ( 0 , 1) x= 1 Y= 3x1+1 4 ( 1 , 4) x= 2 Y= 3x2+1 7 ( 2 , 7) x= 3 Y= 3x3+1 10 ( 3 , 10) x= 4 Y= 3x4+1 13 ( 4 , 13) = 0 3 + 1 = 14 x=1 x=0 y= y= 33 xx 1x0 x + 1 X X X SohCahToa C H S = 13 Opp 61° Sin b T H A SOH = b O A O Hyp = 61° = 13 x Sin 61 b Opp 13 Hyp = = 11.37 = Identify sides then click letters in SohCahToa b on its own. Opposite of Div is mult SohCahToa = Opp 51° A T H TOA Tan 51° e Adj = 12 C H = e O A O S = = e Opp 12 Adj 12 x Tan 51 = = 14.819 Identify sides then click letters in SohCahToa No 51° Adj SohCahToa Hyp Cos 9 c° c° Adj = 5 = Adj 9 Hyp Cos-1 (0.55556...) cos-1 Ans 0.55555556 56.2510114 c° 5 5 ÷9 = 0.556 = 56.3 Move Cos to other side --- > Cos-1 Opp No = c° CAH = A T H C H S = O A O Adj sin cos SHIFT tan √ ² C x ÷ 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) Big to Standard Form 4 3 6 2 0 4 3 6 2 x 10 Move your finger, from point, until you get a whole number less than 10 Copy figure then add a point Copy other figure until all that is to be copied is zeros Add x 10 4 4 3 3 6 6 2 2 0 x 10 4 213 Count number of places from new position to old position This number goes above the 10 to indicate how often you multiply by 10 7 5 7 9 9 3 5 0 0 0 0 x 10 3 9 9 5 5 0 3 0 0 x 10 5 3 6 5 0 6 3 0 2 2 3 5 5 x 10 6 6 x 10 2 1 Small Numbers 0 0 0 0 5 5 3 3 6 6 2 2 x 10 -2 -3 -4 -1 Ignore the zeros at the front then cover until you get a number less than 10 Copy figure, add a point then other figure until all that is left are zeros Add x 10 The original position of the point is to THE LEFT Count …. 1 to left …. -1 …. 2 to left ….. -2 and so on -4 0.0005362 = 5.363 x 10 0 0 0 0 0 0 2 4 2 4 0 0 x 10 6 6 4 4 -3 6 6 x 10 -5 SF to normal = 4 3 6 2 4 3 6 2 x 10 0 0 7 0 0 Start as if there were no figures after point You have to multiply by 10 seven times. Instead of adding 7 zeros put 7 underlines The “lines” show where the point should go Copy other figure until all that is to be copied is zeros Fill remaining places with zeros 3 3 3 3 x 10 0 0 3 4 8 4 3 4 8 4 0 5 0 x 10 1 Add Point then other figures Small to normal 7 = 0 0 0 0 0 0 0 0 7 8 8 0 0 3 x 10 -8 3 Start as if there were no figures after point Positive means GO RIGHT ….. Negative means GO LEFT Need 8 underline going left starting under the 7 …. -8 …. 8 to LEFT The “lines” show where the point should go Put zeros above the lines Copy other figure until all that is to be copied is zeros Small to Normal 0 0 0 0 0 0 5 to the left of “line” 0 0 8 5 9 3 8 5 9 3 8 9 8 9 x 10 x 10 3 to the left of “line” -5 -3 Light Years Distances in the solar system are vast. Distance from the Sun to Pluto is 59 400 000 000 km or 5.95 x 1010 km To make sense of distance people often use time. For these extremely large distances scientists use the time that Light takes to go from one point to another As a comparison light takes about 1.27 seconds to go from the Moon to Earth. Light takes 4 Hours and 2 minutes to go from Pluto to the Earth About 22 000 times the time so about 22000 the distance Light Years Proxima Centauri is the closest star to the Solar System. It is 4.22 Light years away If it was possible to build a craft which could travel at the speed of light it would take over 4 years to get to this star. 4 hours into the journey it would pass Pluto having completed about 1 / 365 part of the journey 1 Light Year is 9.467 x 1012 km Distance to Proxima Centauri is 4.22 Light Year 4.22x9.47 x 1012 = 4.22 x 9.47 4.22 x 9.467 x 10x 12 4.22 E 12 12 Light Year 9.467 x 10 km 4.22 x =3.995 x 1013 km 7 Light Year 7x9.47 x 1012 = 7 x 9.467 7 7 x 9.47 x 10x E 12 12 32 x 9.467 7x =6.629 x 1013 km 32 Light Year 32x9.47 x 1012 = 32 32 x 9.47 x 10x E 12 12 Light Year 9.467 x 10 km 12 12 Light Year 9.467 x 10 km 32 x =3.0304 x 1014 km 0 (-) Ans On C √ ² 7 8 9 x √ ² C x ÷ 5 6 7 8 9 + - On 0 1 2 3 4 . = Ans (-) Test 0 4 5 6 ÷ 1 2 3 0 . - = +