math exam review

7/24/2019 Math Exam Review

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Math Exam Review 2013

LINEAR SYSTEMS:

1. Verify that 1!"# i$ a $%&'ti%( t% the f%&&%w &i(ear $y$tem! )x * 3# + 2y + ,# - 10

3x+,# ,y + 3# - *21

2. The $'m %f tw% ('mer$ i$ ,2 a(/ their /iffere(e i$ 12. hat are the tw% ('mer$

3. rite %'t the fir$t f%'r term$ %f the $e'e(e /efi(e/ y the re'r$i%( f%rm'&a4

T(- 2 t(*1 * ( ! t1 - 3 ! ( 5 2

,. The f%&&%w ta&e $h%w$ f%'r $erie$ %f ('mer$. 6(e %f the$e 7e%metri! %(e %f the$e i$

arithmeti a(/ the %ther tw% are (either 7e%metri (%r arithmeti.


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a# 8%m9&ete the ta&e y $tati(7 the ty9e %f $erie$ that i$ $h%w(.

Serie$ Ty9e %f $erie$

1 + 11 + 111 + 1111 + 11111 + 1+ 3;, + =) + 0.>) + 0.>2) + 0.> +

1;2 + 2;3 + 3;, + ,;) + );" +

# ?%r the arithmeti $erie$! ?%r the 7e%metri $erie$!State the %mm%( /iffere(e. State the %mm%( rati%(.

). S%&ve a&7eraia&&y f%rxa(/y.

x 1 y 3 x + 1 y + "

,

) - 20 3 + 2 - ,


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@6 N6T S6LVE R6BLEMS. @E?INE VARIABLES AN@ RITE @6NTCE SYSTEM 6? EDATI6NS.

". Mr. 8a(e Fe&&y ea($ at G,.,0;H7 with $a&t water taffy at G>.00;H7 re$'&ti(7 i( at >0H7a(/y mixt're w%rth G,.>0;H7. C%w ma(y Hi&%7ram$ %f eah a(/y are i( the mixt're.

=. Tim r%w$ hi$ %at 3" Hm '9$tream i( 3 h%'r$. It taHe$ him 2 hr$ t% ret'r( /%w($tream.@etermi(e hi$ $9ee/ i( $ti&& water a(/ the $9ee/ %f the 'rre(t.

>. rite /%w( the f%rm'&a f%r t(a(/ '$e it t% fi(/ the i(/iate/ term:

a#


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10. ?%r the $erie$ 3 + " + 12 ++=">! /etermi(e:

a# the ('mer %f term$ i( the $erie$ # the $'m %f the $erie$.

11. The thir/ %f a 7e%metri $e'e(e i$ 1> a(/ the $eve(th term i$ 1,)>. @etermi(e the fir$t3 term %f the $e'e(e.


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12. The fifth term %f a( arithmeti $erie$ i$ 1" a(/ the $'m %f the fir$ term$ i$ 1,). @etermi(e

the va&'e %f the fir$t term a(/ the %mm%( /iffere(e.

13. 8&a$$ify eah $e'e(e %r 7e%metri! the( /etermi(e the va&'e %f the varia&e

re9re$e(ti(7 the '(H(%w( term i( eah a$e.

a# 3 != !11 !1)! x # *)! 1)! *,)! 13)! y

1,. A $e'e(e i$ /efi(e/ y the re'r$i%( f%rm'&a4t1- 1 ! t2- 2 ! t( - 3 x t(*1 2 x t(*2 ! (5- 3

a# @etermi(e the fir$t ) term$. # ex9re$$ t(i( term$ %f n.

1). S%&ve the f%&&%w $y$tem$ %f e'ati%($ a&7eraia&&y.

1 x * ,y - ) )x + y - 22 3 2


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1". rite a w%r/ 9r%&em that a( e m%/e&&e/ y x + y - >000the &i(ear $y$tem $h%w( %( the ri7ht. 0.0)x + 0.00

1=. A ar a(/ a tr'H &eave E/m%(t%( at the $ame time. The ar hea/ t% ea$t white the t'H

hea/$ we$t. the tr'H /r%ve 10Hm;h $&%wer tha( the ar . i( > h%'r$ the tr'H wa$ 1>,0Hm a9art. ?i(e the $9ee/ %f the ar a(/ the $9ee/ %f the tr'H.


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1>. The thir/ term %f a 7e%metri $e'e(e i$ 12 a(/ the $ixth term i$


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DA@RATI8S:

22. ?at%ri$e f'&&y.

a# 2x x + )# + =x + )# # x2

100

# x2


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2). ?at%ri$e f'&&y.

a# 1>x3+ "0x2+ )0x # "ax + 3x + ,a + 2

# 2 x * 2#2 x + 2 /#


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# 3x x * ,# - 2x * 1# + 3 /#

1

3 x2

4

3 x + 2 - 0

2=. hat va&'e$# %f k wi&& 7ive thi$ 'a/rati e'ati%($ %(e rea& r%%t1

2 x2+ Hx + > -

0


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2>. A 9it're that mea$'re$ 10m y >m i$ t% e $'rr%'(/e/y a mat ef%re ei(7 frame/. The wi/th %f the mat i$ t% ethe $ame %( a&& $i/e$ %f the 9it're. The area %f the mat i$ t%e'a& the area %f the 9it're! what '$ the wi/th %f the math!t% the nearest tenth of a centimetre

2


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30. If a '$ trave&&e/ 10Hm;h fa$ter! it w%'&/ taHe 2 hr$ &e$ time t% maHe a 31)Hm tri9. hat

i$ it$ $9ee/

31. Three ('mer$ f%rm a( arithmeti $e'e(e! the %mm%( /iffere(e ei(7 11. If the fir$t

term i$ /erea$e/ y "! the $e%(/ ('mer i$ /erea$e/ y 1! a(/ the thir/ ('mer i$

/%'&e/ ! the re$'&ti(7 ('mer$ are i( a 7e%metri $e'e(e. @etermi(e the ('mer$ that

f%rm the arithmeti $e'e(e.


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32. Jra9h eah %f the f%&&%wi(7 'a/rati re&ati%($ %( their re$9etive 7ri/.

a# y - K x + )#x * 3# # y - *3x + )#2+ >

# y - 1;2 x * )#2 2 /# y - x + 3#2


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33. @etermi(e the e'ati%( %f the 9ara%&a i( eah a$e.

a# Ca$ x*i(tere9t$ %f 0 a(/ *" # ha$ a vertex at *3!2# a(/ ha$ a y*i(tere9t

a(/ 9a$$e$ thr%'7h the 9%i(t %f 20.2!,#.

3,. If *2!=# i$ the maxim'm 9%i(t %f the 9ara%&ay= -2x2 4px + q! /etermi(e the va&'e$ %f

the %($ta(tpa(/ q.

3). /e$rie the tra($f%rmati%($ that are (ee/e/ t% ma9 the 7ra9h y - x2%(t% the 7ra9h %f

y - *3x2+= .


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3". 8%($i/er a 'a/rati re&ati%(. The vertex i$ at 2!1# a(/ the y*i(tere9t i$ at 9 0!13#.

a# rite /%w( the e'ati%( %f the axi$ %f $ymmetry.# The e'ati%( %f the re&ati%( a( e writte( i( the f%rmy = a(x - h)2+ k .rite /%w( the

va&'e %f h a(/ k.

# rite /%w( the va&'e %f a.

/# rite the e'ati%( %f the re&ati%( i( the f%rmy = ax2 +b x +c .

3=. I( a te$t*y%'r*$tre(7th %%th! at a fair a 9a/ i$ $tr'H with a hammer. Thi$ 9r%Fet$ a

wei7ht '9 a vertia& $&i/e* t% ri(7 a e&& if y%' have hit the 9a/ har/ e(%'7h. he( the

9a/ i$ $tr'H with F'$t $'ffiie(t f%re t% ri(7 the e&&! the hei7ht %f the wei7ht! h ! i(

meter$ ! t ! $e%(/$ after the 9a/ i$ $tr'H i$ 7ive( y h = 8t- 5t .2

a# C%w hi7h i$ the wei7ht $e%(/ after the 9a$ i$ $tr'H

# C%w hi7h i$ the e&&

# C%w &%(7 after the 9a$ i$ $tr'H /%e$ the e&& ri(7


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3>. A 9ara%&a with the e'ati%( - x2i$ vertia&&y $trethe/ a%'t the x*axi$ y a fat%r %f

3;2 a(/ ref&ete/ i( the x*axi$! a(/ the( tra($&ate/ 3'(it$ t% the ri7ht a(/ 2 '(it$ '9. State

the e'ati%( %f the tra($f%rme/ 9ara%&a.

3


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,2. The 7ate t% the e(tra(e %f a fe(e/*%ff 7ar/e( i$ %r/ere/ y a 9ara%&i $ha9e/ arh.

The i($i/e /ime($i%($ %f the arh are 2m wi/e a(/ 3m hi7h.

a# @etermi(e the e'ati%( %f the 9ara%&a that m%/e&$ the i($i/e $ha9e %f the arh.

8&ear&y $tate where y%' are 9&ai(7 the %ri7i( %f the axe$.

# C%w wi/e i$ the arh etwee( the i($i/e e/7e$# at a hei7ht %f 2m a%ve the 7r%'(/.

r%'(/ y%'r a($wer t% 2 /eima& 9&ae$#

,3. The 9ara%&ay = 2x2+ bx + c9a$$e$ thr%'7h the 9%i(t$ 0! *2# a(/ 1! *3#. @etermi(e

the vertex %f the 9ara%&a. .

,,. The /ia7ram $h%w$ a 9&a( f%r a /eH whih i$ t% e 'i&t %( the %r(er %f a %tta7e. A

rai&i(7 i$ t% e %($tr'te/ ar%'(/ the f%'r %'ter e/7e$ %f the /eH. Jive( thatAB- @E - m! B8 - 8@ - (! a(/ the &e(7th %f the rai&i(7 i$ 30 meter$!


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a# Sh%w that the area %f the /eH i$ 7ive( y the ex9re$$i%(A = -m2+ !m.

# ?i(/ the /ime($i%($ %f the /eH whih wi&& have themaxim"marea.


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