Wednesday, May 26, 2010

P6 Angles A001





/_ ABE = 60 o                  (ABE is an equilateral triangle)

/_ EBC = 80 o – 60 o
                   = 20 o

/_ FCB = /_ FBC     (Since the 3 sides of Triangles BCD and
                                  BCF are the same)
            = 20 o ÷ 2      (Since EC divides /_ ACB equally
                                   as ABE is an equilateral triangle)
            = 10 o

/_ BDC = 180 o – 20 o – 10 o
             = 150 o

Tuesday, May 25, 2010

Speed P6 A003

A car took 8 h to travel from Singapore to Penang. A bus took 12 h to travel from Penang to Singapore. At what time did the 2 vehicles meet if both started at 9 a.m.?

Car: 8 h -- > 1 trip
       1 h -- > 1/8 trip

Bus: 12 h --> 1 trip
        1 h --> 1/12 trip

Combined: 1 h --> 1/8 + 1/12 = 5/24 trip

5/24 trip --> 1 h
24/24 trip --> 24 ÷ 5 x 1 = 4.8 h
                                      = 4 h 48 min

            3 h                     1 h           48 min
   !------------------!----------!------------!
9 am                 12 pm     1 pm        1.48 pm      (As start time is given as 9 a.m., do not give answer in 24 hour clock, unless the question told ask for it.) 

The two vehicles met at 1.48 p.m.

Speed P6 A002

Point P and Point Q are 40 km apart. A leopard runs from Point A to Point B at an average speed of 105 km/h. At the same time, a lion runs from Point B to Point A at an average speed of 95 km/h. How far would each animal have run when they meet on the way?



105 + 95 = 200 km/h      (Combined Speed)

40 ÷ 200 = 1/5 h     (Time for the 2 animals to meet)

105 x 1/5 = 21 km    (Distance ran by leopard)

40 – 21 = 19 km     (Distance ran by lion)

The leopard and lion would have run 21 km and 19 km respectively when they meet.


Alternative Method

DLeopard : DLion = SLeopard : DLion   (Time is a Constant; D = S x T)
                             = 105 : 95
                             = 21 : 19
 
40 u --> 40 km             (Remember to show your workings, else marks will be deducted.)
1 u --> 40 ÷ 40 = 1 km
 
21 u --> 21 km
 
19 u --> 19 km
 
The leopard and lion would have run 21 km and 19 km respectively when they meet.

Monday, May 24, 2010

Percentage P6

Mr.Wong had 207 apples and oranges. After he had sold 50% of the apples and 40% of the oranges,he had 45 more oranges than apples left.how many fruits did he have left?


                    
   [][][][][][][][][][][][]
A [      ][      ] <45><45>    )
            <45>                    ) 207
O [][][][][][] [][][][]        )

22 u --> 207 + 45 +45 = 297
1 u --> 297 ÷ 22 = 13.5

12 u --> 12 x 13.5 = 162

162 - 45 = 117 fruits

He had 117 fruits left.

Ratio P5

1. There were some flowers at a flower shop. The ratio of the number of roses to the number of tulips was 2:3. When 50 more roses and 30 more tulips were added, the ratio of the number of roses to the number of tulips became 5:6. How many flowers were there at first?


  R          T              6R           5T
-----------------------------------------
  2    :     3             12      :     15
+50       +30          +300         +150
-----------------------------------------
  5    :     6             30      :     30
-----------------------------------------
12 u + 300 --> 15 u + 150
3 u --> 300 – 150 = 150
1 u --> 150 ÷ 3 = 50

5 u --> 5 x 50 = 250 flowers

There were 250 flowers at first.


Alternative method

R        [  4 u ]<   50   >          2 : 3 = 4 : 6. Instead of                
T        [   6 u     ]<  30   >      using 2 and 4 units, use
                                                        4 and 6 units (because of 6 p)
----------------------------------
          [1 u][5]    x    5
R         [        5 p       ] 
T         [          6 p          ]
          [1 u][5]      x       6     Make use of T (before) to
                                          construct T (after)
5 u + 25 --> 4 u + 50          Compare R
1 u --> 50 – 25 = 25

10 u --> 10 x 25 = 250 flowers

There were 250 flowers at first.

Fraction P5

2. Joshua had 2/3 as many game cards as Nat. After Joshua bought another 20 game cards and Nat lost 29 game cards, Joshua now has 4/5 as many game cards as Nat. How many game cards did Nat have at first?

  J         N      5J        4N
-------------------------------
   2   :   3      10   :    12
+20     -29   +100     -116
--------------------------------
   4   :   5      20   :    20
--------------------------------

10 u + 100 --> 12 u – 116
2 u --> 100 + 116 = 216
1 u --> 216 ÷ 2 = 108

3 u --> 3 x 108 = 324 game cards

Nat had 324 game cards at first.


Alternative method


J          [    4 u    ][20]                 2 : 3 = 4 : 6. Instead of
N         [            6 u           ]        using 2 and 4 units, use
                                  [29]         4 and 6 units (because of 4 p)
------------------------------
           [1 u][5]    x   4
J          [       4 p       ]               Make use of J (before) to 
N         [         5 p          ]          construct J (after)
           [1 u][5]      x      5

6 u – 29 --> 5 u + 25               Compare N.
1 u --> 25 + 29 = 54

6 u --> 6 x 54 = 324 game cards

Nat had 324 game cards at first.