Challenging P5 Chong Fu

Nicholas has two 6-sided dice. One dice has numbers 1 ,3, 5, 7, 11 and 13 while the other dice has numbers 4, 8, 18, 24, 30 and 36. The dice are tossed together and their values added.
a)What fraction of the outcomes adds up to a sum divisible by 7?
b)What fraction of the outcomes adds up to a sum divisible by 3?


There are 36 outcomes (6 x 6 = 36)

Multiples of 7 --> 6 outcomes
(3 + 4, 3 + 18, 5 + 30, 11 + 24, 13 + 8, 13 + 36)

6 ÷ 36 = 1/6

a) Fraction of outcomes of sum divisble by 7 is 1/6.


Multiples of 3 --> 9 outcomes
(1 + 8, 3+ 18, 3 + 24, 3 + 30, 3 + 36, 5 + 4, 7 + 8, 11 + 4, 13 + 8)

9 ÷ 36 = 1/4

b)Fraction of outcomes of sum divisible by 3 is 1/4.

Challenging P5 2009 SA1 P2 CHIJ Q16

16. Look at the pattern below.

a) At what position does the number 12 first appear? [3]

b) What is the sum of the first 32 numbers? [2]

1st group -- > 1 , 2 , 3

2nd group -- > 2 , 3 , 4

3rd group -- > 3 , 4 , 5

….

10th group -- > 10 , 11 , 12

10 x 3 = 30 -- > 30th position

a) The number 12 first appears at the 30th position.

1, 2, 3, … 10

(1 + 10) x 10 ÷ 2 = 55

2, 3, 4, … 11

(2 + 11) x 10 ÷ 2 = 65

3, 4, 5, .. 12

(3 + 12) x 10 ÷ 2 = 75

55 + 65 + 75 + 11 + 12 = 218

or

3, 4, 5, … 10

(3 + 10) x 8 ÷ 2 = 52

(1 + 2 + 2 + 3 x 52 + 11 + 11 + 12) + (11 + 12) = 218

b) The sum of the first 32 numbers is 218.

Challenging P5 2009 SA1 P2 MGS Q17

17. The following figures are made up of 2-cm squares.

a) What is the perimeter of Figure 3?

b) How many squares are there in Figure 6?

c) Which figure has an area of 220 cm²?

By moving all sides out, we get a big square.

3 x 4 = 12

12 x 2 = 24 cm

a) The perimeter of Figure 3 is 24 cm.

1

1 + 2

1 + 2 + 3

..

1 + 2 + 3 + 4 + 5 + 6 = 21 squares

b) There are 21 squares in Figure 6.

2 x 2 = 4

220 ÷ 4 = 55 squares

21 + 7 = 28

28 + 8 = 36

36 + 9 = 45

45 + 10 = 55 -- > Figure 10

c) Figure 10 has an area of 220 cm².

Challenging P5 2009 SA1 P1 MGS Q13

13. The picture below shows a dart board. Benny threw 3 darts and all the 3 darts hit the board. Which of the following is NOT likely to be his score?

(1)  75

(2)  80

(3)  125

(4)  135

Tabulate out the possible numbers to help you to see and calculate the total.

1st dart  2nd dart  3rd dart

--------------------------------

  5                5                5

 25              25              25

 50              50              50

100            100            100             

25 + 25 + 25 = 75 √

5 + 25 + 50 = 80 √

25 + 50 + 50 = 125 √

So 135 is NOT a likely score and the answer (4).