Test 4 Autumn 05----Send your W-number and name to nalexander@igc.org for your grade !
From 5.7 to 9.3 (excluding Ch. 7)
answers: a b b b a (Note correction to  #5 answer.)     c c c b c      c d b c c        c c c c c    b d  b a a 
5.7
1.  A triangle is 10 cm wider than it is tall . The area is 5.5 cm2. 


Translate:
a5.5 = (1/2)(h + 10)h 
b5.5 = (1/2)(10)h 
c5.5 = (1/2)(b + 10)h 
dnota
2. Find the height h and the base b in the previous problem. Note: The scales of the above diagram may look  different than your calculated values. 
ah = -1 and b = 11
bh = 1 and b = 11
ch = 1   and b = -11
dnota
6.1
3. (x2    -  10x  + 21)/(x2   -  12x  + 35)
a(x  -  3)/(x  -  4)
b(x  - 3)/(x  -  5)
c(x  -  4)/(x  -  3)
dnota
6.2
4. Simplify. 
 

ax3(x -1)
bx(x -1)
cx2(x -1)
dnota
5. Simplify.


a1/(x -1)
bx/(x +1)
cx/(x -1)
dnota
6.3
6.  Find the LCM of  9a12b7   and 6a5b2
a18a5b2
b36a5b7
c18a12b7
dnota
6.4
7.  Add .  (x - y)/xy2   +   (x - y)/x2y
a[y(x - y)  -   x(x - y)]/x2y2
b[x(x - y)  -   y(x - y)]/x2y2
c [x(x - y)  +   y(x - y)]/x2y2
dnota
6.5.
8.  Simplify.

 



a0
b(1 -  x)/(2x + 3)
c(x  -  1)/(2x + 3)
dnota
9. Simplify.
a1
b(2y - x)/(x + 3y)
c(2y + 3x)/(2x + y)
dnota
10. Simplify. 


a 3
b(2y + 3x)/(x - 2y)
c(2y + x)/(x - 3y)
dnota
6.6
11. Solve.     x + 8/x = -9
ax = 8 or  1
bx = -8  or 1
cx = -8 or -1
dnota
Written problems.
8.1
12. Find the two square roots of 36.  
a6
b-6
c362
d6 or -6
e. nota
13. Simplify
a9 or -9
b9
c-9
dnota
14.Simplify. Assume that x is positive.
 

a7x2
b49x
c7x
dnota
15. Simplify.  Assume x is positive.

 

 
a. -10x
b. 100x 
c. 10x
d. nota
8.2
16. Simplify by factoring. 
a. 5

 

b.
c.
d. nota
17. Simplify .
a. x16
b. x72
c. x18
d. nota
9.1
18. Solve for x.    x2 = 100
a10
b-10
c-10  or 10 
dnota
19.  Solve for x.  50x2 = 70
a  
       


b
     


c
           or  



 
dnota
20. Solve for 9x2 = 81
a. 3
b. -3
c. -3 or 3
d. nota
21. Solve for x.   (x + 13)2 = 2 . The solution can be written:
a
b
c
dnota
9.3
22.

 This  problem deals with the solution to a quadratic equation of the form:

.    
The solution is given by the quadratic formula:

 

a

b

c

d

e. nota
23. Solve for x.  Solve by the quadratic formula. 
x2 - 4x = 21
a

b

cnota
d
24.   Solve using the quadratic formula. 
 x2 - 3x  =  8
The solution is:   
a
b
c
d
e. nota
25.Solve using the quadratic formula

 x2 -  8x + 1 =  0
a


b


cnota
d
 
Written Problems
26.  Sec. 6.6 Solve . 5/(x + 1) = 3/(x - 2)  Hint: Cross multiply.
27.  Sec. 8.6  Solve for x. Hint:  c2 = a 2 + b2, where c = 10. 
 
28. E. C. Sec. 6.7  Juanita can build   a small shed in 6 hours and Anton can build the same shed in 10 hours. How long would it take to build one if they worked together ?
a. Translate.
b. Solve.  Hint: See the first example in the section !!! t/6 + t/10  = 1. Solve for t. LCD = 30. Multiply both sides by 30 and solve. 30( t/6 + t/10) = 30·1 or 5t + 3t = 30 or t = 30/8 hours = 15/4 hours = 3.75 hours,
not bad !
29.  EC. Sec. 9.3 Solve using quadratic equation. x2 + 2x - 2 = 0. Plug into quadratic formula.
30. EC. Sec. 5.6 Solve by factoring.  x2 + 34x + 33  = 0 = (x + 1)(x + 33).  Now solve. x = -1,-33
31. EC. Sec. 5.6 Solve by factoring.  x2 + 4x + 3  = 0 = (x + 1)(x + 3).  Now solve. x = -1,-3
32. EC. Sec. 5.6 Solve by factoring.  x2 - 4x + 3  = 0 = (x - 1)(x - 3).  Now solve. x = 1,3
33. EC. Sec. 6.6 Solve.  x + 33/x = -34. Multiply both sides by x and add 34x to get:  x2 + 34x + 33  = 0 = (x + 1)(x + 33).  Now solve. Same as 30. x = -1,-33