Unit4AssignmentSpring2018

Name:………………………………1.Evaluate(withoutusingacalculator)

2! = 81= 3! = 343! =

16! = 7! = 1024!" = 10! =

2.Theseirrationalnumbersliebetweenwhichtwointegers?

< 𝜋 < < 30 < < 50 < < 129 <

3.Useyourcalculatortoevaluatetheseirrationalnumbers,roundedtotwodecimalplaces:

27 = (2 d.p. ) 10! = (2 d. p. ) 𝜋! + 5 = (2 d.p. )

4.Simplifyfully(leaveasasquarerootofasmallervalue,multipliedbyaninteger):

27 = 48 =

75 = 1000 =

5.Expandandsimplifyfully:

(2𝑥 + 3)(𝑥 − 1)

3𝑥(𝑥 − 7) 4𝑝 𝑝 − 1 + 3(𝑝! + 2)

6.Factorfully

24𝑥𝑧! + 16𝑥𝑧

𝑥! − 16𝑥 + 55 2𝑥! − 17𝑥 + 21

7.Withoutusingacalculator,determinewhichofthefollowingisbigger.Explainyourreason.

𝜋 𝑜𝑟 𝜋!

3 Reason:

100! or 100! Reason:

4!! or 5!! Reason:8.Writeasasingleexponent:

2!×2! = 2! 3! ! = 4!

4! =

5!

5! =5!!×5! = 8!

8! =

9.Evaluate:

81!! =

27!! =

8!! =

1000!! =

32!! =

1024!! =

10.Evaluate:

2564

!!=

2564

!!!=

3!! =

27512

!!!=

49

!!

=17

!!

=

11.Simplify:

(9𝑥!)!! =

3𝑥!𝑦! ! =

3𝑥!𝑦! !

𝑥!𝑦 =

12𝑥!𝑦!

6𝑥𝑦!

!!

=

12.Simplifyasurdusingexponentnotation,using‘exponentdistributesoverproduct’:

48 = 48!! = 16×3

!! = 16

!!×3

!! = 4×3

!! = 4 3

200 =

13.

Completethetable:Shapenumber 1 2 3 4 5 … 10 … n

Area 36 … …

Fractionoflargesquare

14

… …

Whatarethecoordinatesofthepointthatmarksthetoprightcornerofthe5thsquare?Commentonanyobservations: