Tuesday, April 28, 2009

Singapore Math: RGPS Prelim 2008

I'll be sharing problem sums Brian has done and please continue to give your feedback. Posting the sums also means we are able to refer to these questions when the real exam draws near. I'm only posting the questions that I would find difficult if I had to do them and/or those that he couldn't do. These are from Raffles Girls Primary School Preliminary Exam 2008.

Q41. Tank P, a rectangular tank measuring 40cm by 35cm by 25cm was 4/5 filled with water. Tank Q, a rectangular tank measuring 30cm by 30cm by 40cm, was 3/8 filled with water. The water from Tank P was then poured into Tank Q to its brim. How much water was left in Tank P?

Volume of water in Tank P at first
--> 40 x 35 x 25 x 4/5 = 28000

Volume of water in Tank Q at first
--> 30 x 30 x 40 x 3/8 = 13500

Volume of water poured from Tank P to Tank Q
--> (30 x 30 x 40) - 13500
= 36000 - 13500
= 22500

Volume of water left in Tank P
--> 28000 - 22500 = 5500

Ans: 5500 cm3 (ans key says 5500 ml)

Q43. Some identical cubes were placed in a container as shown below. 1120cm3 of water was poured in to fill the container to its brim. Water was then drained out of the container and stopped when the water level is at the height of the bottom layer of cubes. Given that 352cm3 of water is left in the container now, find the height of the container.

Let C be the volume of each cube.

3(6C + 352) = 10C +1120
18C + 1056 = 10C +1120
8C = 64
C = 8

Side of a cube ---> 2 cm
Height of container ---> 2 x 3 = 6 cm

Q 44. There were 186 adults in an auditorium. When 7/12 of the men and 4/9 of the women left the auditorium, the total number of adults who remained became 90. How many men were there in the auditorium at first.

Let m and w be the number of men and women respectively.

m + w = 186 (1)

5/12 m + 5/9 w = 90 (2)

(2) x 36
--> 15 m +20 w = 3240 (3)

(1) x 20
--> 20 m + 20 w = 3720 (4)

(4) - (3)
--> 5 m = 480
m = 96

Ans: 96 men
Q45. A car, travelling at a constant speed, took 9 hours to travel from Town Y to Town Z. A lorry, travelling at a constant speed, took 18 hours to travel from Town Z to Town Y. Both vehicles started at the same time and they met when they were 180km from Town Z.

a) Find the distance between the two towns.
b) Find the speed of the car.

There's a little diagram in the solution so I took a picture of his working. The answers are slightly out of the camera's focus but they are (a) 540km (b) 60km/h.

Q48. Joanne had some twenty-cent coins and fifty-cent coins in a box. The percentage of the number of twenty-cent coins was 40% of the total number of coins Joanne had. Joanne took out 10 fifty-cent coins and put in twenty-cent coins of the same value. The percentage of the number of twenty-cent coins then became 50% of the total number of coins Joanne had. What was the amount of money in the box?

Let t and f be the number of twenty and fifty cent coins at first respectively.

3t = 2f ---- (1)
f - 10 = t + 25
f = t + 35
2f = 2t + 70 --- (2)

Substitute (2) into (1)

3t = 2t + 70
t = 70
f = 105

20t + 50f = 1400 + 5250 = 6650

Ans: $66.50

Brian got Q46 wrong, and the solution turned out to be relatively simple to understand.

Q46. In Box A, the ratio of the number of blue balls to the number of green balls was 4:1. In Box B, the ratio of the number of blue balls to the number of green balls was 2:3. The total number of balls in Box A was twice the total number of balls in Box B.
a) What was the ratio of the number of blue balls in Box A to the number of green balls in Box B?
b) When 40 green balls were moved from Box A to Box B, the ratio of the number of blue balls to the number of green balls in Box B became 5:8. How many green balls were there in Box B at the end?

This is the solution given in the answer key:

a) Box A --> G:B --> 1:4 --> 2:8
Box B --> G:B --> 3:2

Ans: 8:3

b) After 40 balls moved from Box A to Box B
Box B --> G:B --> 5:8 --> 16:10

Compare Before G:B --> 3:2 --> 15:10

1U --> 40
16U --> 640

Ans: 640 green balls


monlim said...

You do realise that you're just making us more kancheong, right?? When I see the words Prelim Paper, my heart just beats a little faster!!

Lilian said...

LOL! It's just me. I work with the end in mind! Preparing for PSLE right? Then do prelim lah. Don't bother with CAs and SA1, cos everything's covered in prelim paper. Easier to discover topics he's weak at this way.

breve1970 said...

Wow... seeing the both of you kancheong, I am also getting kan cheong. SA1 is next week! Felt as though we haven't done anything yet. But the only consolation is that we are at P2 so will take it nice and slow. Think I will probably go mad from P3 to P6 and beyond that!

All the best to L-A and Andre in their mid year exams! :)

Lilian said...

Ann, I was just telling a friend of mine whose girl is also in P2, same school as Hannah, to take it easy cos really, at P1 and P2, there's nothing much you can do to prep the child. Anyway, even from P3, you won't have to tear your hair out (that much) since Hannah is self-motivated and probably more gancheong than you can ever be :)

All the best to all the kiddos having SA1 next week!

breve1970 said...

Thanks Lilian. Lets hope she will continue to be gan cheong. Hannah can be quite careless in her work but I do know that most kids have this problem too. I haven't found a way to tackle this yet. Sigh.

Mon narrated an account of how one parent checks carelessness in her kids (I won't mention the method on the blog just in case) and that method frightens me. Will tell you separately.

Yes, all the very best to all the kids who are sitting for SA1! When are Brian's exams?

Lilian said...

They get better as they get older but it's inevitable that they'll still make a couple of careless mistakes here and there. Even adults will make careless mistakes, seriously. All we can tell them is to check, and re-check if there's time.

Brian has had 3 exams in the past month actually, but the only one he had to study for was the one he took in Singapore when we were back. The other two, given by the school here, one's called Measures of Academic Progress (MAP) testing Eng-Math-Science, and the other ERB (by Educational Records Bureau) testing various aspects of Language and Quantitative skills; he went without any prep. That's the thing about exams here, children aren't expected to prep so there's no stress at all, the aim is just to measure a student's progress and growth in school.

breve1970 said...

Wow... Lilian! Brian went for an exam without any prep... that sounds like my ideal school system!

Our kids should enjoy learning and not be stressed in school. I also think Han learns alot more by studying at her own pace rather than having to sit for a test for each subject every other week (that is what's happening in school right now).

Lilian said...

As long as everyone's scrambling for coveted places in 'good' schools, there has to be exams, to sieve out the good from the very good, and the very good from the crazy good; I consider most Sg students at least 'good' cos really, the amount of work kids do is just pretty mind-boggling.

Yeah, Brian went without prep, and I'm sure most, if not all, his schoolmates did the same. He's getting his MAP results today, so we'll see if the no-prep approach works or not!

breve1970 said...

All the best to Brian. Am sure he has done very well!:).

Read Mon's entry on the Math Challenge. Sounds er... really challenging. I did the RGPS P1 and P2 Math papers last year and I only scored 86/100 and 85/100. Pooh...hoooh. Am the worst in Math!

himan said...