Algebra Review
Each layer of mathematics us es the layer below it to solve its problems.
First you learn numbers, the fundamental building blocks of mathematics.
Then you learn arithmetic, in which you use numbers to solve arithmetic
problems. Th en you learn algebra, in which you use arithmetic to solve algebra problems. And then you have calculus, in which you use algebra to
solve calculus pr-oblems.
You are expected to know how to do all the problems below
before entering this class. Don't worry if you can't finish them
during discussion section. Just make sure you can do them.
1. Find the slopes of lines parallel and perpendicular to to 6x - 3y = 12.
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d :: - If +1 -x
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2. Find an equation in ~e i~c~m for the line through (2/3,
1/ 2) and (1 / 4, -2). Sketch a quick graph of this line.
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The morf ality rate for children under 5 years of age around the world
has been declining in a roughly linear fashion in recent years. The rate _) j= 6~- -~
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3.
=
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:::
per 1000 live births was 90 in 1990 and 65 in 2008. (Source: World
Health Organization). Determine a linear equation that approximates
the mortality rate in terms of time t, where t represents the number
of years since 1990. If this trend continues, in what year will the mortality rate first drop to 50 or below per 1000 live births.
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4. Multiply and simplify (18u 9 n 7 )( -8u 1 0n 5 )
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2
~ -llt-X-t<+i =-
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10. Solve (x
+ 6)(x- 4) = 11
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(X+ l
--x'+-L-X- :1!":::-o
11 . Solve
24
X
){~-J-).::
-r~ -lV~
0
t
= x - 5
--x}_- t-x- 2it =- o
(:r- '? )(:[-t 3) ::::-0
12. Factor 8st + 28t - lOs - 35
L_ -.1.$
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--5
Lf
0
13. Factor 49c2
tr7-::-7
So
2
X
1
~\)
Q- s-t l)l4- t
-5
4--t
112c + 64
-
6cr ; _ ~~ (ij i(g) ~n~
,
f7c -f)-v
14. Factor 8ls 2
lA ).f
.:L-S
100
-
(i>- 6"'- ;: eo.-~ )
( th)
t1
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15. Simplify
2
2
t
(q) -lo) (1.5 tto)
49
-
t -14t+49
~ ::: (()t-~~--H..)
-(o..- b)~
L - b )"}.
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5
16. Simplify - 3
9z y
-
-
1
15z 2 y
-
(i -1 ) l t-+ l )
~
==- 0!~
t~
-
-s 1
c2 -
17. Simplify
(}- J2
d2
cd
c-d
d
-- -cT·
-
d
c-J
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18. The perimeter of a standard-sized rectangular rug is 24 ft. The length
is 2 ft longer than the width. Find the dimensions of the rug.
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tt -_) 21}(-t 2
:::.\ 2- -':)
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w ·,o{+~ =-k
{eY\~th := t -1:2. ~l
19. A car normally depreciates 30% of its original value in the first year.
The car is worth $12,180 after the first year. What was the original
value?
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