Percentage P6 2010 SA2 NY P2 Q1

Challenging P6 2010 SA2 NY P2 Q2

Fraction P6 2010 SA2 NY P2 Q3

Volume P6 2010 SA2 NY P2 Q4

Area & Perimeter P6 2010 SA2 NY P2 Q5

Whole Number P6 2010 SA2 NY P2 Q6

Decimal P6 2010 SA2 NY P2 Q7

Angle P6 2010 SA2 NY P2 Q8

Percentage P6 2010 SA2 P2 NY P2 Q9

Volume P6 2010 SA2 Nanyang P2 Q 11

40 x 20 x 10 = 8000   Amount of water upto bottom of cube

12000 - 8000 = 4000 cm3   Amount of water from above bottom of cube

40 x 20 = 800

10 x 10 = 100

800 - 100 = 700 cm2   Area of water just above bottom of cube

4000 / 700 = 5.71  Height of water above bottom of cube

5.71 + 10 = 15.71 cm    Height of water

It was 15.71 cm.

Angle P6 2010 SA2 NY P2 Q12

Decimal P6 2010 SA2 Nanyang P2 Q13

Quiny and Mandy saved $5748.40 altogether. 0.4 of Quiny’s savings was $431.50 more than 0.2 of Mandy’s savings. How much more money than Quiny did Mandy save? [4 marks][Answer given: $477.80]


Quiny's money --> 10 Q
Mandy's money --> 10M
4 Q --> 2 M + $431.50

2 M --> 4 Q - $431.50

10 M --> 20 Q - 5 x 431.50 = 20 Q - $2157.50


10 Q + 10 M --> $5748.40

30 Q --> 5748.40 + 2157.50 = 7509.90

10 Q --> 7509.90/3 = $2635.30

10 M --> 2 x 2635.30 - 2157.50 = $3113.10

10 M - 10 Q --> 3113.10 - 2635.30 = $477.80

It was $477.80.


Model Drawing
------------------

431.50 / 2 = $215..75   0.4 = 4/10 = 2/5

Compare 2 units of Q (total 5 units) with 2 units of M (total 10 units)
Q  [][215.75][][          ][][           ][][            ][][             ]   ] $5748.40
M [][][][][][][][][][]                                                            ]

215.75 x 5 = 1078.75

15 u --> 5748.40 - 431.50 = 4669.65

5 u --> 5/15 x 4669.75 = 1556.55

1078.75 - 1556.55 = $477.80

It was $477.80.

Average P6 2010 SA2 NY P2 Q14

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.

Fraction P6 2010 SA2 Nanyang P2 Q16

Mrs Reuten bought some pizzas for a group of children. The girls received thrice as many pizzas as the boys. There were an equal number of girls and boys. Each boy ate 2/9 of a pizza and the boys finished all the pizzas given to them. Each girl ate 1/6 of a pizza and the girls had 4½ pizzas left. How many pizzas did Mrs Reuten buy? [5 marks][Answer given: 8 pizzas]


2/9 : 1/6 = 4 : 3       Multiply by 18

G [][][][][][][][][][][][]
B [][][][]

9 u --> 4 1/2

16 u --> 16/9 x 9/2 = 8 pizzas

It was 8 pizzas.

Ratio P6 2010 SA2 Nanyang P2 Q17

There were some blue marbles and white marbles in a bag. If 70 blue marbles were to be removed from the bag, the ratio of the number of blue marbles to the number of white marbles would be 3 : 4. If 112 white marbles were to be removed from the bag instead, the ratio of the number of blue marbles to the number of white marbles would be 8 : 7. When 48 more blue marbles were to be added into the bag, what percentage of all the marbles would be blue marbles? [5 marks][Answer given: 49.6%]


B           W
- 70
--------------
 3      :    4
--------------

4 B - 4 x 70 --> 3 W

4 B --> 3 W + 280

28 B -->: 21 W + 7 x 280 = 21 W + 1960 


B            W
           - 112
---------------
8     :       7
---------------

7 B --> 8 W - 8 x 112 = 8 W - 896

28 B --> 32 W - 4 x 896 = 32 W - 3584


32 W - 3584 --> 21 W + 1960

11 W --> 1960 + 3584 = 5544

W --> 5544/11 = 504

4 B --> 3 x 504 + 280 = 1792

B --> 1792/4 = 448

448 + 48 = 496 blue marbles

496 + 504 = 1000

496/1000 x 100% = 49.6%

It was 49.6%.


Alternative method
----------------------

3 u + 70 --> 8 p

4 u - 112 --> 7 p

12 u --> 32 p - 4 x 70 = 32 p - 280

12 u --> 21 p + 3 x 112 = 21 p + 336

32 p - 280 --> 21 p + 336

11 p --> 336 + 280 = 616

1 p --> 616 / 11 = 46

8 p --> 8 x 56 = 448

448 + 48 = 496 blue marbles

15 p --> 15 x 56 = 840

840 + 112 + 48 = 1000 marbles

496/1000 x 100% = 49.6%

It was 49.6%.

Circle P6 2010 SA2 Nanyang P2 Q18

18. The figure below is created using the curved lines (arcs) of quadrants with radius 1 cm, 2 cm and 3 cm. Find the area of the shaded parts.
(Take pi as 3.14)

Circle of radius 3 cm  -  4 x Right-angled triangles of sides 3 cm -
[Circle of radius 1 cm  -  4 x  Right-angled triangles of sides 1 cm]
4 x Right-angled triangles  =  1/2  x  Diagonal  x  Diagonal

3.14 x 1 x 1 = 3.14

1/2 x 2 x 2 = 2

3.14 - 2 = 1.14

3.14 x 3 x 3 = 28.26

1/2 x 6 x 6 = 18

28.26 - 18 - 1.14 = 9.12 cm2

It was 9.12 cm2.

Ratio P6 2010 SA2 Nanyang P1 Q21

The cost of 3 mangoes is the same as the cost of 5 grapefruits. The cost of 3 mangoes is also the same as the cost of 10 pears. Find the ratio of the cost of a mango to the cost of a grapefruit to the cost of a pear.
(Ans : 10 : 6 : 3)

3 M --> 5 G

M/G --> 5/3 = 10/6


3 M --> 10 P

M/P --> 10/3

M : G : P = 10 : 6 : 3


Alternative method
----------------------
Assume 3 mangoes = 5 grapefruits = 10 pears = $1
1 M --> 1/3

1 G --> 1/5

1 P --> 1/10

M : G : P = 1/3 : 1/5 : 1/10
               = 10 : 6 : 3    Multiply by 30

Area P6 2010 SA2 Nanyang P1 Q30

The figure below is formed by stacking 4 pieces of square paper one on top of another. The papers have different prints and sizes of sides 3cm, 4cm, 5cm and 6cm. The 6-cm piece is placed at the bottom of the stack, followed by the 5-cm piece, then the 4-cm piece and the 3-cm piece is placed right on top.

Find the sum of the area A and B. (ans : 8 cm2)

6 - 1 = 5

5 - 3 = 2

6 - 4 = 2

2 x 2 = 4

4 x 2 = 8 cm2

Ratio P6 2009 SA2 P2 Nanyang Q12

Given that p : (q + r) = 1 : 3, r : (q + s) = 1 : 2 and p : s = 2 : 5.
(a) Find p : q : r : s.
(b) Find (r + q) : (p + s).

                   x 3
p : s = 2 : 5 = 6 : 15

                           x 2       x 3 
p : (q + r) = 1 : 3 = 2 : 6 = 6 : 18

                                            x 3
s + (q + r) = 5 + 6 = 11 ............... 33

                          x 11 
r : (q + s) = 1 : 2 = 11 : 22

s = 15, (q + s) = 22, so q = 22 - 15 = 7

a) p : q : r : s = 6 : 7 : 11 : 15

b) (r + q) : (p + s) = (11 + 7) : (6 + 15)
                             = 18 : 21
                             = 6 : 7