Download 8 32 ! 3 50 + 18 a) 16x2 ! 3 = 8 = 81 = 32

Math 154
Fall 2013
Instructor: G. Rodriguez
Exam 5 Study Guide
You are allowed to use one 3" by 5" index card on the exam as well as a scientific calculator.
For the exam you need to know how to do the following:
1. Simplify square root expressions. 9.2
a) Problem starts off as one square root.
72x 6 y 9
b) Problem starts off as the product of square roots.
6x 4 y 5 ! 18x 7 y 3
2. Add or subtract square root expressions. You might need to simplify square roots before they
can be combined. 9.3
8 32 ! 3 50 + 18
3. Multiply two square root expressions by using the FOIL method. If possible, simplify any
square roots that appear in the product. 9.3
4. Simplify
•
•
•
a)
c)
( 3 ! 2 5 )( 4 ! 6 5 )
a quotient involving square roots. 9.4
the quotient of two square roots
a fraction inside a square root
one where you have to ‘rationalize the denominator’
18m10
b)
49m9 n 4
4
d)
12
25x 5 y 3
36x 5 y13
5
18
5. Solve a radical equation containing square roots. Remember to check for extraneous
solutions.
a)
x+3+8=2
c)
5 x = x+4
b)
x+3!8=2
d)
8+ x!6 = x
6. Solve an application involving radicals. 9.6
A pendulum is a weight suspended from a pivot so that it can swing freely. The period of a
pendulum is the time it takes the pendulum to make one back and forth swing. The period, T,
in seconds is given by the formula T = 2! L , where L is the length, in feet, of the pendulum.
32
If a pendulum is made with a string that is 4 feet long, what is the period of the pendulum?
Round your answer to the nearest tenth.
7. Solve an equation using the square root property. 10.1
a) 16x 2 ! 3 = 8
b)
c)
( x ! 5)
( x + 3)
2
= 81
2
= 32
8. Solve an equation by completing the square. 10.2
x 2 + 7 = 6x
9. Solve an equation using the quadratic formula. 10.3
a) x 2 + 3x = 6
b) 3x 2 + 5 = 4x
c) 2x 2 + 10 = 9x
10.Solve application problems involving quadratic equations. 10.1, 10.3
Equation given: know how to use it
Area of a rectangle: use a=lw
Right triangle: use a2 + b2=c2
You can solve the equations by using the Zero-Product Rule (factoring), using the Square
Root Property, or using the Quadratic Formula.
Where necessary, round answers to the nearest tenth.
a) A piece of glass is to be made to protect the writing surface of a desk. The length of the
desktop is 16 inches greater than its width. Find the dimensions of the glass piece that is
to be made if the area of the desktop is 960 square inches.
b) The area of a rectangle is 200 square meters. Find the length and the width of the rectangle if
its length is 5 meters less than the twice the width.
c) Jake launches a model rocket from the ground. The height, h, of the rocket above the
ground at time t seconds after it is launched can be found by the formula h=–16t2+90t.
Find how long it will take for the rocket to reach a height of 100 feet.
d) 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 for the cannonball to
reach 192 feet?
e) A regulation soccer field is 100 yards by 60 yards. What is the length of the diagonal from
one corner of the field to the opposite corner of the field?
f) A guy wire 20 feet long is supporting a telephone pole as shown. Determine the height of
the pole.