UNIT 3 Indices and Standard Form Activities

Transcription

1 UNIT 3 Indices nd Stndrd Form Activities Activities 3.1 Towers 3.2 Bode's Lw 3.3 Mesuring nd Stndrd Form 3.4 Stndrd Inde Form Notes nd Solutions (1 pge)

2 ACTIVITY 3.1 Towers How mny cubes re needed to build tower which hs 100 steps? At first sight, this might seem dunting but we will see wys of tckling this kind of problem by trying to find the formul which fits the dt. 1. Complete the following tble: No. of Steps No. of Cubes 1 6 From your tble you cn see tht the number of cubes needed increses much fster thn the number of steps - but how much fster? Compute the vlue of n 2 for n = 12,,..., nd lso for 2n nd 3n the tble below: n by completing n n n Which of the sequences given ppers closest to the sequence found in question 1? 3. From questions 1 nd 2, complete the tble: No. of Steps, n No. of Cubes n No. of Cubes 2 n Deduce the formul for the number of cubes in the form for some constnt k. number of cubes = 2n 2 kn 4. Now solve the problem of finding the number of cubes needed for the 100-step tower.

3 ACTIVITY 3.2 Bode's Lw In 1772, the Germn stronomer, Johnn Bode, published his lw which reltes the distnce rtio: n = distnce of the plnet from the Sun distnce of the Erth from the Sun to n, the number which Bode used to specify ech plnet, s shown in the following tble. n = 1 Venus n = 2 Erth n = 3 Mrs n = 4 n = 5 Jupiter n = 6 Sturn n = 7 Urnus n = 8 Neptune n = 9 Pluto PLUTO JUPITER MARS VENUS SUN MERCURY EARTH SATURN NEPTUNE URANUS Not to scle He stted his lw s: n = n 1 1. Use this formul to determine 1, 2,..., Find the first nd second differences of this sequence. Wht do you notice? Plnet Distnce from Sun (in millions of km) 3. The ctul distnces re given in the tble opposite. Find the ctul vlues of Mercury Venus =. 2 =. Erth 149.6,, 3 =, 4,... up to 10, Mrs Jupiter nd compre with predicted vlues from Bode's Lw, Sturn ignoring the 4 vlue. Urnus A lrge number of steroids re found t bout km from the Sun. Does Bode's Lw provide confirmtion tht there ws Neptune Pluto once single plnet t this distnce from the sun? [Hint: consider 4.] 5. Does the dt support the view tht Neptune nd Pluto were once single plnet?

4 ACTIVITY 3.3 Mesuring nd Stndrd Form We normlly mesure in units such s cm, m or km, s pproprite to prticulr problem. Using different units cn be good opportunity to use stndrd form. 1. The distnce between two towns is 108 km. Convert this distnce to m, cm nd mm, using stndrd form for your nswers The re of plot of lnd is 42 km 2. Convert this re to m, cm nd mm, using stndrd form for your nswers. 3. The rdius of plnet is 5000 km. Clculte the circumference of the plnet in m, cm nd mm. 4. Clculte the number of seconds in 1 yer, giving your nswer in stndrd form. 5. The volume of n dult humn is estimted t cm 3. Convert this volume to: () mm 3, (b) km 3, using stndrd form for your nswers. 6. A spceship trvels t speed of 2000 km/h. Convert this speed to mm/second.

5 ACTIVITY 3.4 Stndrd Inde Form The object of this gme is to clculte numbers in stndrd inde form to see which is the lrgest or smllest. It is suitble s whole-clss ctivity. For ech of the two numbers, nd b, given in stndrd form, determine which of b b b + b is the lrgest number nd which the smllest number. For emple: A: B: C: 3 4 = 4 10, b = = 5 10, b = = 3 10, b = Working in pirs, one pupil chooses the vlues for nd b nd sets the problem for their prtner; the problem is then repeted the other wy round. 2. Cn you find ny rules tht determine which of the numbers is the lrgest?