MTH 234 Groupwork 1 (1.20.14) - Algebra Review
”Each layer of mathematics uses 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. Then 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 problems.” - Lena Folwaczny
You are expected to know how to do all the problems below
before entering this class, but don’t worry if you can’t finish them
during discussion section. Just make sure you can do them.
If you can’t remember how to do something, ask your neighbors or your
TA. We’ll go over questions about class structure tomorrow in lecture.
1. Find the slopes of lines parallel and perpendicular to to 6x - 3y = 12.
2. Find an equation in slope intercept form for the line through (2/3,
1/2) and (1/4, -2). Sketch a quick graph of this line.
3. Do the points (4,3), (2,0), and (-18, -12) all lie on the same line?
4. Find k so that the line through (4, -1) and (k, 2) is parallel to 2x +
3y = 6.
5. The mortality rate for children under 5 years of age around the world
has been declining in a roughly linear fashion in recent years. The rate
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.
6. Multiply and simplify (18u9 n7 )(−8u1 0n5 )
1
7. Divide and simplify
56a−11 b8
68a16 b−15
8. Simplify and give answers using positive exponents (−3c−10 d14 )−3
9. Simplify
p
4
625y 8
10. Simplify the expressio using positive exponents only
m3/4 n−3/4
(m2 n)1/2
11. Find all solutions to (x − 7)2 = 81
12. Solve (x + 6)(x − 4) = 11
13. Solve
24
x
=x−5
14. Solve 2x4 − 15x2 − 27 = 0
15. Factor out the greatest common factor and write your answer in factored form: (x − 5)(x + 3) + (x − 5)(x + 8)
16. Factor 8st + 28t − 10s − 35
17. Factor 49c2 − 112c + 64
18. Factor 81s2 − 100
19. Simplify
t2 − 49
t2 − 14t + 49
20. Simplify
5
1
−
3
9z y 15z 2 y
2
c2 − d2
cd
21. Simplify
c−d
d
22. 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.
23. A train leaves a station and travels north at 85 km/hr. Four hours
later, a second train leaves on a parallel track and travels north at
125 km/hr. How far from the station will they meet? To familiarize
yourself with the problem, complete the following chart.
SLOW TRAIN
FAST TRAIN
DISTANCE
d
RATE
TIME
EQUATION
d=
125
How far from the station do the 2 trains meet?
24. The amount of money in a savings account changed from $250 to $255.
What was the percent of increase?
25. 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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