Challenging P6 2011 Nanyang SA2 P2 Q14

(a) 16, 17, 18, 19, 20, 21

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
= (1 + 10)/2  x 10 = 55
{Aveage x Number of numbers}
{Average = Sum of first and last numbers divided by 2}

(b) It is 55

1 + 2 + 3 + ..... + 99 + 100
= (1 + 100)/2 x 100 = 5050

5050 - 99  =  4951

c) It is 4951.

Challenging P6 2010 SA2 NY P2 Q2

Challenging P6 2010 SA2 Nanyang P2 Q15

The table below shows the day of the week that 1st January falls on from the year 1981 to 2000. Note that Day 1 of a week is a Monday and Day 7 is Sunday. There are 31 days in the month of January.

a) What number does the letter C represent ? (Ans : 3)

b) What number does the letter F represent ? (Ans : 7)

c) Which day of the week will 1st February 2012 fall on ? (Ans : Wednesday)

2003 - 1981 = 22 years

22/4 = 5 leap years (max)   Leap year --> 366 days

22 x 365 + 5 =8035 days    Account for leap years

8035 + 4 = 8039     Since 1 Jan 1981 is 4 (Thursday).

8039/7 = 1148 r 3

a) It was 3.

2006 - 1981 = 25 years

25/4 = 6 leap years (max)

25 x 365 + 6 + 4 = 9135

9135/7 = 1305 or 1304 r 7   Need to express with a remainder

b) It was 7.

2012 - 1981 = 31 years

31/4 = 7 leap years (max)

31 x 365 + 31 + 7 + 4 = 11357 days

11357/7 = 1622 r 3

3 --> Wednesday

c) It is Wednesday.

Challenging P6 SA1 P2 NY Q15

15. The series of figures below are made of cubes. Study the diagram below and answer the following questions.

a) How many cubes are there in Figure 6? [2]

b) Which figure will have 120 cubes? [2]

1

1 + 3 = 4                                            1 + 2 = 3

1 + 3 + 6 = 10                                    1 + 2 + 3 = 6

1 + 3 + 6 + 10 = 20                            1 + 2 + 3 + 4 = 10

1 + 3 + 6 + 10 + 15 = 35                    1 + 2 + 3 + 4 + 5 = 15

1 + 3 + 6 + 10 + 15 + 21 = 56            1 + 2 + 3 + 4 + 5 + 6 = 21

a) There are 56 cubes in Figure 6.

56 + 28 = 84                                    21 + 7 = 28

84 + 36 = 120 --> Figure 8                28 + 8 = 36

b) Figure 8 will have 120 cubes.