Grade 11 Answers


Grade Eleven Answers


1)

Answer:

     5 tires   5000kms

     4 at each time

     4 * 5000km = 20,000km travelled by 4 tires.

     20,000/5 = 4000km each

     
     START OUT:


Distance    |
Travelled   |   #1	#2	#3	#4	#5
------------+-------------------------------------------
    1000    |	 x	 x	 x	 x
	    |
    2000    |	 x	 x	 x		 x
            |
    3000    |	 x	 x		 x	 x
	    |
    4000    |	 x		 x	 x	 x
	    |
    5000    |	 	 x	 x	 x	 x
            |


2)

Answer:

     
                 Area of the region = (3Pi-24)/4


3)

Answer:

	A_i=5/8*B_i

A_e=1/2*B_e

0.4*(5/8*B_i)=5/8*B_i - 1/2**B_e

0.375*B_i=1/2*B_i

B_e=0.75B_i Therefore Basil saves 25% of his income.


4)

Answer:

     

     Angle D = 40 degrees

     Let angle DFE = X
     
     Angle FBC = X

     Angle BCF = 180 - 2X

     Angle DEF = 180 - 40 - X = 140 - X
     
     Angle EAC = 140 - X

     Angle ACE = 180 - 2 (140 - X)

     = 180 - 280 + 2X

     = -100 + 2X

     180 - (-100 +2X + 180 - 2X) = Angle ACB

     100 Degrees = angle ACB


5)

Answer:

          
                
Length of ladder =[72+x2]1/2
Length of ladder = x+1
Therefore
(x+1)2=72 + x2
x2 + 2x + 1 = 49 + x2
2x + 1 = 49
2x = 48
x = 24
Therefore the ladder is originally 24 m from the wall.  It is 25m long (x+1)              


6)

Answer:

	Volume of 1/2 the tank
        = 100cm * 40cm * 60cm
        = 240000cm3
          1/4 (240000) = 60000cm3
          d * 100cm * 60cm = 60000
          d = 10cm


7)

Answer:

     4.5 min   45r/min = 202.5 revolutions

     202.5rev/33.3 r/m = 6.075 minutes.


8)

Answer:

     Area = 800m2
     Todd must mow 400m2
     length and width reduce by 2m

     Time around the lawn		Area remaining
	start				20*40=800 m2
	1 time				18*38=684 m2
	2 times				16*36=576 m2
	3 times				14*34=476 m2
	4 times				12*32=384 m2     


     About 3 and 1/2 times he would have to go around the lawn to
     do his share!!



9)

Answer:

     AB = ED = x meters
     CD = BC = (15 -x)
     Area of deck   -> A(x) = x (15-x) + x(15-2x)
     = -3x2 + 30x
     = -3(x2 - 10x + 25) + 75
     = -3(x-5)2 + 75


     Maximum value of A(x) is 75 and occurs when  x =5

     The dimensions of the deck are 5m * 10m * 10m * 5m


10)

Answer:

     (x+4)2 + (x-3)2 = (2x-5)2
     x2 + 8X + 16 + X2 - 6X + 9 = 4X2 - 20X + 25
     2X2 - 22X = 0
     2X (X-11) = 0
     2X = 0  X-11 = 0
     X=0   X=11
     X cannot = 0, therefore X = 11

     y2 = (11-3)2 + (11-5)2		z2 = 112 + 82

     y = (64+36)1/2 = 10		z = (121+64)1/2 = (185)1/2


11)

Answer:

          
                   6/h=sin2*theta
                     h=2sin theta*cos theta
                     h=3/(sin theta* cos theta)
                   L/h=1/cos theta=sec theta
                     L=3*sec2 theta* csc theta


12)

Answer:

            Let x = the number of jumps taken
     
	    3x = 45 + 2x
             x=45
            45 jumps he will have caught up with the rabbit


13)

Answer:

     (ac + bd)2 + (ad-bc)2 =
     (ac)2 + 2acbd + (bd)2 + (ad)2 - 2adbc (+bc)2 =
     (ac)2 + (bd)2 + (ad)2 + (bc)2 =
     (a2 + b2) (c2 +d2)

     Similarly (ac - bd)2 + (ad +bc)2 = (a2 + b2)(c2 + d2)
     
     a=2    b=3   c=1   d=6

     481 = (13)(37)
     =(4+9) (1+36)

     481 = (22 + 32)(12 + 62)
     = (2(1) + 3(6)2 + (2(6) - (3)(1))2
     = 202 + 92
     
     or   481 = (22 + 32)(12 +62)
     
     =(2(1) - (3(6))2 + ((2)(6) + (3)(4))2
     = (-16)2 + 152


14)

Answer:

     300 Sheets * 12cm = 3600cm of sheets length
     
     

     Thickness of one sheet 40.72cm2/3600cm = .011cm
     
     6 - 4.8 = 1.2 cm
     In 1.2cm of radii and .011cm thickness
	.011(1.21/2)cm = 106 times


15)

Answer:

     k= 11.25
     k-5.00 entering casino
     2(k-5.00) -> leaving casino
     2(k-5.00)-5.00 (after paying for parking) 
     (2k - 10) -10.00 = 2k - 20(after paying asmission to the second casino)
     2(2k - 20) = 4k -40
     4k - 40 -5 = 0
     4k - 45 = 0
     k = 11.25


16)

Answer: BC=12.06 km

     


17)

Answer:

     (a) y = 16 + 15sin(Pi/60*750) = 31
     (b) T = 2*Pi/(Pi/60) = 120
Maximum height:
sin(Pi/60)*x = 1  ==> x=30  ==> max height = y = 31 meters.


18)

Answer: d = 2 *(7)1/2


     


19)

Answer:

          NOTE:  All logs in this answer are in base 3.

     40 = 20 + 5 log3(x+3)         120= 20 - 5 log3(x+3)
     20 = 5 log3(x+3)            100= 5 log3(x+3)
     4 = log(x+3)               20 + log3(x+3)
                                   320 = x+3
     X + 3 = 34 = 81              

     a)  x = 78                    b)  320 - 3 = x


20)

Answer:

     
	distance from (0,0) to y=2x-3
	d=|-3|/[(222+(-1)2)]1/2=3*[(5)/5]1/2

	r >= 3*[(5)/5]1/2 so the line and the 
	circle intersect.
        
       Mike was wrong!


21)

Answer:

     n + m = $42.50/$.50        n = # of odd numbered digits

     n + m = 85                 M = # of even numbered digits

     n - m = $5.50/$.50
     n - m = 11

     n + m = 85/ 2n = 96

     n = 48                   48 - m = 11
                              37 = m

     n = 48 -> odd digits
     3, 5, 7, 9 -> 4 single digit houses                         
     1. 13, 15.....44/2 = 22 double digit houses.    

     22+4=26 houses in all.

     The last number on the odd numbered side is 53.

     Even numbered side needs an additional 11 digits to be equivalent to 
     the other side.

     Trial and error should show that these are the missing numbers:

     8, 10, 12, 14, 16, 18 <- 11 digits.


22)

Answer:

     abc       100a + 10b + c

     a + b + c = 12

     a - b = b - c

     a > b + c

     a + b + c = 12

     -a + 2b -/+ c = 0/3b = 12

     b = 4

     a + c = 8

     8 - c > 4 + c

     4 > 2c
     
     c < 2

     abc is odd numbered so the digit "c" must be odd.

     Hence c = 1, a = 7   and b = 4

     DIGIT IS NUMBER 741


23)

Answer:

Let y = Freshman class
     Let x = Freshmen not from Dr. J.H.G. or Guysborough	
     300 + 1/2(400) + x = Freshman Class

     500 + x = y

     1/2 y = 300

     y = 600

     500 + x = 600

     x = 100

     100 must be coming from neither.


24)

Answer:

     m + n = 11 + 5 = 16

     

     


25)

Answer:

     1/2

TRICKY  ->  For those people who went through the problem to
answer the question, what is the probability of getting eleven
heads in a row with a fair coin?

     1/2 * 1/2... = (1/2)11 = 1/2048

     11 times


26)

Answer:

     
             21.5% of the field is not watered.


27)

Answer:

     Alf and Bert are guilty.  If Bert is innocent, then Bash is
     innocent and Alf if guilty; but Alf never works alone. 
     Therefore, no one is guilty.  Therefore, Bert cannot be
     innocent; he must be guilty.  If Bert is guilty, then Cash
     is innocent and Alf if guilty.


28)

Answer:

          
                    Area of the circles= 3*Pi/2
                         DC=AB=3
                         DA=CB=31/2+1
                    Area of rectangle =3(31/2+1)
                    Area not covered = 3*31/2+3-3*Pi/2


29)

Answer:

               

          

               3 + 4 = 7
               32 = 27     34 = 81

               54 + 43 = 625 + 64 = 689


b)

     2 @ 8 = -2

     A possible rule:  3 times the first number minus the second
                       number.


30)

Answer:

               10        (3,6,6)   (6,6,3)
                         (4,5,6)   (6,5,4)
                         (4,6,5)   (6,4,5)
                         (5,4,6)   (6,3,6)
                         (5,6,4)   
                         (5,5,5)


31)

Answer:

     The family keeps the small cupboard (s) for daily access to
     wine.  When s becomes empty, they transfer the bottles from
     the main stock in the large cupboard (l).

     More than 1 times - s or l cannot be opened.

     n bottles of wine were bought
     they drink one immediately
     put 11 into s for consumption during the next 11 days
     n-12 -> in l.

     When l is exposed the second time only 10 bottles can be 
     transferred into s.

     Family takes 11 from l, drink 1, that day and put 10 into s
     for use for next 10 days, leaving n-12-11 bottles in l.  The
     next time l is opened only 9 can be put into s and 1 drunk
     immediately leaving n-12-11-10 bottles in l, exposed 3
     times.

     n - 12 - 11 - .....-3 - 2 bottles exposed 11 times.

     Now when l is opened, only one bottle must remain to be     
     drunk right away as it has been exposed 12 times.

     n - 12 - 11 - ..... - 3 - 2 = 1    Chateau family buy every
     78 days.


32)

Answer:

     How much is left unpainted?

     Original area = A

     1color    1st square - leaving  8/9 A
     2         8 squares - leaving 8/9 x 8/9 A unpainted
     3         8 x 8 squares - 8/9 x 8/9 x 8/9 A unpainted
     4         83  - (8/9)4 A unpainted
     5         84    (8/9)5 = .555 A
     6         85    (8/9)6 = .493 A remains

     So after 6 colors are used, over half the canvas is covered.

     TOTAL number of squares painted:

                    1 + 8 + 82 + 83 + 84 + 85 = 37449


33)

Answer:

               

          Volume = 2x x y/2 x 1 = xy cm3


34)

Answer:


          Line perpendicular to a, has slope - m
          and equation  p = -mx + b
                        o = -mx + b
                        +b = mx
                        +b/m = x         (b/m,0)

          a2 = mx + f <- line a2
          0 = m(b/m) + f
          -b = f

          The y intercept of y2 is -b


35)

Answer:

a)
          x = log103 / log2 3

          x = log102

b)

          0 - because the cot 90 degrees = 0 !!!


36)

Answer:


	  Player  |    Weight    |    Cumulative
	  Number  |              |     Average
	----------+--------------+--------------
	          |              |
	    1     |      x       |       x
	    2     |     x+2      |      x+1
	    3     |   (x+1)+3    |      x+2
	    4     |   (x+2)+4    |      x+3
	    5     |   (x+3)+5    |      x+4


Fifth player weighs 8 more kilograms than the first!

When difference is 2 lbs ->5th player weighs 16 more kilograms.


37)

Answer:

          n = # of coins in her purse.
          15n + 10 = 14(n+1)
          n=4

          4 coins totalling 60 cents are two nickels and two
          quarters.


38)

Answer:

"A" denotes the value of a unit of money at a given time, then 9A denotes 
its value a year later and (.9)n A is its value n years later.

          (.9)n A =< A/10

          (9/10)n =< 1/10

          log10(9/10)n =< log10 (1/10)

          n(2 log10  3 - 1) =< -1

          n >= 1/1-2 log10  3 = 21.7


39)

Answer:

     Let n be the last number on the board.  The largest possible
     average is obtained if the digit 1 is erased; the average is
     then

     (2+3+...+n)/(n-1)=((n+1)n/2-1)(n-1)=(n+2)/2

     The smallest average possible is obtained when n is erased the 
     average then:

     n(n-1)/2(n-1) = n/2          1+2+.......n-1/n-1

Thus

     n/2 <= 35 7/17 <= n+2/2


     n <= 70 14/17 <= n+2

     68 14/17 <= n <= 70 14/17

Therefore

     n = 69 pr 70.  Since 35 7/17 is the average of (n-1)   
     integers (35 7/17)(n-1) must be an integer and n is 69.
     If x is the number erased.

     1/2(69)(70)-x/68 = 35 7/17

     69 ??? 35 - x = 35 (7/17) 68

     x = 7


40)

Answer:

     All multiples of 8 fall into the second column.
     So 1000 must fall here!


41)

Answer:

              

     Extend BN past N and meets AC at E
     Triangle BNA = Triangle ENA
     congruent                          

                         Since angle BAN = angle EAN
                         AN = AN
                         Angle ANB = angle ANE


     Therefore N is the midpoint of BE
     and AB = AE = 14
     Therefore EC = 5
     MN is the line joining the midpoints of sides BC and BE of
     triangle CBE, its length is 1/2(EC) = 5/2


42)

Answer:

     Let W, X, Y, Z be amounts paid by Mark, Mike, Lawrence and 
     Joshua respectively.

     w+x+y+z = 60
     w=1/2(x+y+z) = 1/2(60-w)   w=20
     x=1/3(w+x+z) = 1/4(60-y)   y=12
     1/4(20+15+z) = 12
     20+15+z= 48
     z=48-35 = 13

     Joshua paid $13.00 for the motorbike!


43)

Answer:

               

     Assume it come to rest with one end against the rim at the  
     bottom of the pan and the other end touching the side at point A.

     y = (262 - 242)1/2 

       = 10cm
     
     The minimum depth = 10cm

     Radius of pan = 12cm

     V = ((12)2 * 10)Pi = 4523.9cm2


44)

Answer:

     Jerome rides x km at 12 km/hr
       "    walks 16-x km at 5 km/hr

     Total time Jerome = x/12 + (16-x)/5

     Meanwhile...

     4 km/hr walks x to the bike
     10 km/hr rides 16-x km to home

     Total time Fred = (16-x)/10 + x/4

                       (16-x)/10 + x/4 = x/12 + (16-x)/5
                       
                       x = 6 km

     They take 2 1/2 hours to get home.
     Jerome should ride for 1/2 hour.


45)

Answer:

     m = k and m = n-k stars are of identical shapes.

     Ex:  n = 7, M=1, and m=6 produce the same star.

     m=2, m=5, m=3, and m=4.  When m and n share a common factor > 1, the 
     other star can be split into two or more smaller ones.

     If m = n/2, the figure produced is not a star but two coincident 
     straight lines.


     
	       |           M	       |  Total number
	       | 	               |    of Stars
	-------+-----------------------+----------------
	   7   |  1     2     3        |       3
	       |		       |
	   8   |  1           3        |       2
	       |		       |
	   9   |  1     2          4   |       3
	       |		       |
	  10   |  1           3        |       2
	       |                       |
	  15   |  1     2         4    |       4



46)

Answer:

     Area = 2 + 8 + 32 = 42
     Area of triangle = 1/2 (4 + 2 + 8) -4 = 28

     Area of shaded region = 14 units2


47)

Answer:

               29

     The enemy will count the number of troops in the corner position twice.

     
							 30th
	
	5  5  5		6  4  5		6  4  5		8     7
	5     5	   ->	4     5   ->	4     4	 ->....
	5  5  5		5  3  5		5  4  6		7     8

                                             When the general 
                                             jumps into the
                                             corner.

     When the reinforcements arrive the enemy are about to charge
     so there are 29 active defenders left.


48)

Answer:

                    
                                     _            _
     Porche travels (x+15km/hr) * (1.3 hours) = 1.3x + 20km
                             _           _
     Chevette    x km/hr * 1.3 hours = 1.3x km

                    _          _
     (100km)2 = (1.3x)2 + (1.3x + 20)2
               _        _         _
     1002 = 1.3x2 + 1.3x2 + 53.3x + 400
               _         _
     1002 = 3.5x2 + 53.3x + 400
           _         _
     0 = 3.5x2 + 53.3x - 9600
              _          _          _                   _
     x = [-53.3 +/- [(53.3)2 - 4(3.5)(-9600)]1/2] / 2(3.5)
              _         _
       = [-53.3 +/- 373.3] / 7.111

     x = 45 km/hr

     Chevette was travelling at 45 km/hr
     Porche was travelling at 60 km/hr


49)

Answer:

     10x + 15Y = 360
     10(x-2) + 15 (y/2) = 220

     10x + 15y = 360
     -20(x-2) - 15y = - 440  / 10x - 20x + 40 = -80

     -10X = -120

     X = 12 CATS

     10(12) + 15Y = 360
     15Y = 240
     Y = 16
     
     12 Cats
     16 Canaries


50)

Answer:


          NOT POSSIBLE                    POSSIBLE
          Father   36                        49
          Mother   18                        36
          Daughter  9                         9


51)

Answer:

  The thief stole 36 diamonds originally!!