Math 154
Fall 2013
Instructor: G. Rodriguez
Exam 4 Study Guide
You are allowed to use one 3" by 5" index card on the exam as well as a scientific calculator.
1. Factor a polynomial using a combination of factoring methods. 7.1-7.5
NOTE: For the factoring problems the instructions will be: “Factor the polynomial completely,
or state that the polynomial is prime”. It will be up to you to figure out which factoring
method(s) to use.
•
•
•
•
•
Factor
Factor
Factor
Factor
Factor
a.
b.
c.
d.
e.
a
a
a
a
a
polynomial by factoring out the GCF of all the terms.
polynomial by grouping. 7.2
trinomial of the form x2 + bx + c. 7.3
trinomial of the form ax2 + bx + c. 7.4
difference of squares. 7.5
3x 2 ! 33x + 90
3x 2 + 22x ! 16
6x 3 + 26x 2 + 24x
x 3 ! 5x 2 ! 16x + 80
5x 4 ! 25x 3 + 30x 2
7.1
10x 3 + 250x
3
g. 10x ! 250x
2
h. 4x ! 40x + 84
2
i. 4x + 4x ! 35
2
j. 4x + 23x ! 35
f.
2. Solve a quadratic equation by factoring. 7.6
b. 3x + 2
a. 4x 2 + 84 = 40x
(
)( x + 1 ) = 4
3. Solve an application problem by using a quadratic equation. 7.7
a. equation is given: know how to use it to answer the question asked
When a cannon is fired, the height, h, in feet, of the cannonball after t seconds can be
found by using the formula h =–16t2 +128t. How long will it take the cannonball to reach
192ft?
b. area of a rectangle: use a=lw
The area of a rectangle is 80 square inches. Determine the length and the width of the
rectangle if its width is 2 inch shorter than the length.
c. right triangle: use the Pythagorean Theorem a2 + b2 =c2
Rachel bought a framed piece of artwork. The diagonal of the frame is 20 inches. If the
length of the frame is 4 inches greater than its width, find the dimensions of the frame.
4. Find all numbers for which a rational expression is defined. 8.1
7!x
x + 3x ! 10
2
5. Multiply two rational expressions. Simplify the result. 8.2
3x 2 ! 13x ! 10 x 2 + x ! 2
" 2
x2 ! x ! 6
3x ! x ! 2
6. Divide two rational expressions. Simplify the result. 8.2
q 2 ! 11q + 30
q 2 ! 2q ! 24
÷ 2
2
2q ! 7q ! 15
q ! q ! 20
7. Add or subtract two rational expressions with the SAME denominator. Simplify the result, if
possible. 8.3
x2 ! 2
!3x + 8
! 2
2
x + 2x ! 8 x + 2x ! 8
8. Simplify a rational expression. 8.1
a.
7!x
2
x ! 2x ! 35
b.
p 2 ! 10 p + 25
p 2 ! 25
9. Add or subtract two rational expressions with the DIFFERENT denominators. Simplify the
result, if possible. 8.4
a.
y
3
+ 2
y + 7y + 12
y ! y ! 20
b.
x2 ! 3
x!4
!
x+4
x + 2x ! 8
c.
5
5
!
5x ! 3 3 ! 5x
2
2
10.Solve a rational equation. Remember you have to check the proposed solution in the original
equation to eliminate any values that would make an expression undefined. 8.6
a.
b.
5
3
8
!
= 2
x!4
x+4
x ! 16
x +
12
= !7
x
c.
d.
1
1
2
+ = 2
y !1 2
y !1
x2
25
=
x!5
x!5
11. Solve an application involving rational equations. 8.7
motion: use t= d/r
a. Mary and Jay begin skiing the same cross-country ski trail at the same time. Mary, who
averages 8 miles per hour, finishes the trail 0.5 hours sooner than Jay, who averages 6
miles per hour. Determine the length of the trail.
b. As part of his triathlon training, Jay jogs a distance of 7.5 miles and then rides his bicycle
at three times his jogging speed for another 15 miles. If the total time spent jogging and
cycling was 2.5 hours, determine the speeds at which he jogs and cycles.
c. Alan is in the process of getting his pilot’s license. As part of his training he flew his
instructor from a small airport near Pasadena to another small airport near San Diego at
an average speed of 100 miles per hour. On the return trip he followed the same route
and his average speed was 125 miles per hour. If Alan’s total flying time was 2 hours,
how far apart were the two airports? Round your answer to the nearest tenth.
d. A truck can travel 220 miles in the same time that it takes a car to travel 260 miles. If the
truck's rate is 10 miles per hour slower than the car's rate, find the average rate for each.
work: showed you two methods; can use either one
e. At a salt mine, one conveyor belt requires 20 minutes to fill a large truck with ore. A
second conveyor belt requires 30 minutes to fill the same truck with ore. How long would
it take to fill the truck with ore if both conveyor belts are used?
f. A construction company with two backhoes is to build a trench. The larger backhoe can
dig the entire trench by itself in 14 days. The smaller backhoe can dig the entire trench by
itself in 18 days. The larger backhoe begins working on the trench by itself but after 8
days it gets transferred to different job and the smaller backhoe is brought in to finish
digging the trench. How long will it take the smaller backhoe to complete the job? Round
your answer to the nearest tenth.