Math 60 Test # 4 Fall 2015
________solutions_________________
Name
Instructor: Smith-Subbarao
Score: _______________
Percent: ______________
Directions:
 Show all work and circle/box your answers.

Partial credit may be given, even if the answer is incorrect, if your work is clear – attach additional scratch
pages you wish to be considered.

If you do not show your work, you may not get credit.

Unless otherwise instructed, leave all answers as fraction; improper fractions are OK.

Unless requested, you do not need to “rationalize” your denominator. However, please simplify all radicals.

Not all problems have the same weight.
NO: Telephones, Books, Notes; CALCULATORS ARE NOT ALLOWEED
Suggestions:
 Choose the problems you understand best to work first.
 If you get stuck, write down what you do understand for partial credit and move on
 Show your work clearly
 Check your solutions
 Evaluate your solutions for “reasonableness”
1.
Simplify each radical expression. Rationalize the denominator (10 pts)
a) √98 =7√2
b) √
44
9
9
=2√11/3
c)
√
d)
√14
=√7 /2
√8
e)
5
15
√6
=3√5 /5
= 5√6 /2
Solve each quadratic equation by extraction of roots/property of square root (i.e., take the square root of
both sides) (5 points each)
2. 3x2 = 25
x=±5/√3
3. (5x – 1) 2 = 9
5x = 1±3, x = 4/5, x = -2/5
4. 3(x – 3) 2 = 15
x=3±√5
Solve the quadratic equations by completing the square. (5 points each)
5. 2x2 – 8x – 64 = 0
x2 – 4x = 32
(x-2) = ±6
x = 8, x = -4
6. 2x2 – 6x = -4
(x-3/2)2 = -2 + 9/4 = 1/4
x = 3/2 ±1/2, x = 2, x = 1
Solve the quadratic equations by the quadratic formula. (5 points each)
7. 2x2 – 5x = 2
x=
5±√52 +4(2)(2)
4
= (5±√41)/4
8. 4x2 – 4x = 24
divide by 4 to save arithmetic
x2 – x – 6 = 0
1±√12 +24
2
= (15)/2, x = 3, x = -2
9. Find two consecutive integers whose product is 156. (10 points)
n(n+1)=156 = n2 + n
Numbers are 12, 13 or -12, -13
10. The sum of the squares of two consecutive even integers is 164. (10 points)
n2 + (n+2)2 = 164 = 2n2 + 4n + 4; divide by 2: n2 + 2n – 80 = 0
n = 8, 10 or -8, -10
Show all equations used to receive credit!!
11. Find the value of x in the following right triangle. (Hint: in a right triangle, the square of the longest
side, the hypotenuse, is equal to the sum of the squares of the other two sides.)
(10 points)
( x  2)
5
( x  1)
(x-1)2 + (x-2)2 = 25 = 2x2 + 6x -20 or x2 + 3x -10 = 0
x=2, x=5; can’t have x = 2. So x = 5
12. The length of a rectangle is three meters more than its width. If the area of the rectangle is 40
square meters find the length and the width.
(10 points)
L
W
L = W + 3, LW = area = 53. W(W+3) = W2 + 3W = 40; factoring, (W+8)(W-5) = 0, Can’t have W= -8, so
W = 5, L= 8
13.