Q&A - PSLE Math

[chengsmummy]

oceandeep:

//Moderator's note: Topics merged.


Pls help these 2 math questions.

1) When Mrs Lee was 40 yrs old, her son was twice her daughter age. Mrs Lee will be twice her son age when her daughter is 28 yr old. How old will Mrs Lee be when her daughter is 20 yrs old.

2) At 7am. Car A left Town X while Car B left Town Y for Town X. At 3pm, the 2 cars passed each other. 5hour later ,Car A reached Town Y but Car B was still 150 KM away from Town X. Find the distance between town X and town Y.

Thank you very much.

1) remember that the age difference among them will never change, so:
when Mrs. Lee is 40, daughter's age is x, son's age is 2x, son is x years older than daughter. and Mrs. Lee is 40-2x years older than son

when daughter is 28, son will be 28+x, Mrs. lee is 56+2x, from here, she is 28+x years older than son,

then 28+x = 40-2x, x= 4.

so when Mrs. lee is 40, her daughter is 4,
answer is when daughter is 20, Mrs. Lee will be 40+(20-4)= 56 years old

[elkniwt]

oceandeep:

//Moderator's note: Topics merged.


2) At 7am. Car A left Town X while Car B left Town Y for Town X. At 3pm, the 2 cars passed each other. 5hour later ,Car A reached Town Y but Car B was still 150 KM away from Town X. Find the distance between town X and town Y.

Give it a try.

Since Car A takes 5 hrs to complete the remaining distance which Car B took 8 hrs to complete, i.e.

Distance covered by Car A : Distance covered by Car B
8 : 5

3 units = 150 km
8 units = 400 km

Dist between X and Y is 400 km.

(Is the answer correct??)

[Cando]

James Ang:

My students are practising these common question types for the PSLE paper in 1 week's time.



1. John cycled at an average speed of 10km/h from his home to the park. On reaching the park, he cycled back home along the same route at an average speed of 8km/h. He took 1h 12 mins for the entire journey. How long did he take to cycle from the park back to his home?

2. Jack bought some pens and erasers for a total of $100.10. He spent $9.10 more on the pens than erasers. Each pen costs $3.70 more than each eraser. Jack bought 7 times as many erasers as pens. How much does a pen cost?

3. Andy sold thrice as many $5 T-shirts as $10 T-shirts. He also sold twice as many $10 T-shirts as $20 T-shirts. He collected $160 more from selling $5 T-shirts than from selling $20 T-shirts.

a)\tHow much money did he collect from selling $5 T-shirts?
b)\tHow many T-shirts did he sell altogether?

4. Tom and Jerry each has some money. If Tom spends $9 per day and Jerry spends $3 per day, Tom will have $100 left when Jerry has spent all his money. If Tom spends $3 per day and Jerry spends $9 per day, Tom will have $220 left when Jerry has spent all his money. How much did Jerry have?

5. A van travelled from Town A to Town B at an average speed of 55km/h. A car started its journey from town B to A at 90 km/h at the same time the van started. The two vehicles passed each other 70 km from the middle of the whole journey. Find the distance between the two towns.

6. 80% of marbles are red marbles and 20% of them are blue marbles. 63 red marbles and 46 blue marbles are added. The red marbles now makes up 75% of marbles and blue marbles 25% of marbles. How many red marbles are there at first?

7. Courier A takes 10 hours to deliver a parcel from Town X to Town Y. Courier B takes 12 hours to deliver the parcel along the same route. If the speed of Courier A is 9km/h faster than that of Courier B, find the speed of Courier A.

8. In a concert, 75% of the audience were female. 75 females and 5 males left the concert half way. The remaining audience were allocated seats in groups of 10. Each group has 3 males. How many people were in the audience at first?

9. On Linda’s birthday, she gave sweets to every pupil in her class. If she gave each pupil 7 sweets, she would have 4 sweets left. If she gave 2 sweets to each pupil, she would have 189 sweets left. How many pupils were there in Linda’s class?

10. The ratio of Ryan's pocket money to John's pocket money was 3 : 2. After Ryan saved $15 and John spent $8, the ratio of Ryan's pocket money to John's pocket money was 3 : 1. How much money did Ryan have at first?

11. A lorry left Town A for Town B. After travelling for 4 hours at its usual speed, the lorry stopped for 30 mins for a break. In order to reach Town B at the appointed time, the speed of the lorry was increased by 8 km/h. Given that the lorry took 3 hours to cover the remaining journey, find the distance between Town A and Town B.

12. Paul and Ray worked together to paint a house. During the job, Paul rested for 4 days and Ray took 2 days off. However, they were not absent on the same days. If they had done the same job alone, Paul would have taken 18 days and Ray 12 days. How long did the two painters take to complete painting the house?

Hi James,

Appreciate if you can at least give us the answers if not the full solutions. Thanks

[Dharma]

Hi friends.


Worked out James Ang’s Qns. Was in a hurry. Pls highlight if there are mistakes.

Cheers.

1.\tJohn cycled at an average speed of 10km/h from his home to the park. On reaching the park, he cycled back home along the same route at an average speed of 8km/h. He took 1h 12 mins for the entire journey. How long did he take to cycle from the park back to his home?

Speed ratio = 5 : 4
Time ratio = 4 : 5
9u = 72
1u = 8
Time taken to cycle back to home = 5u = 5x8 = 40 (40 mins)

2. \tJack bought some pens and erasers for a total of $100.10. He spent $9.10 more on the pens than erasers. Each pen costs $3.70 more than each eraser. Jack bought 7 times as many erasers as pens. How much does a pen cost?

\t\tQty
\t\tPen : 1u
\t\tErasers : 7u

\t\tCost
\t\tPens : 1p + $3.70
\t\tErasers : 1p

\t\tTotal cost : 1u(1p + $3.70) + 7u(1p) = $100.10
\t\t8u(1p) + 1u($3.70) = $100.10

\t\tDiff in cost : 1u(1p +$3.70) – 7u(1p) = $9.10
\t\t1u($3.70) – 6u(1p) = $9.10

\t\t14u(1p) = 91
\t\t1u(1p) = $6.50

\t\t1u($3.70) \t= $100.10 – (8x$6.50)
\t\t\t\t= $48.10
\t\t1u = 13
\t1p = $6.50/13 = $0.50
\tCost of 1 pen = $0.50 + $3.70 = $ 4.20













3. Andy sold thrice as many $5 T-shirts as $10 T-shirts. He also sold twice as many $10 T-shirts as $20 T-shirts. He collected $160 more from selling $5 T-shirts than from selling $20 T-shirts.

a) How much money did he collect from selling $5 T-shirts?
b) How many T-shirts did he sell altogether?


\tQty ratio ($5:$10:$20) = 6:2:1
\tCost ratio = 30 : 20 : 20
\t$10u = $160
\ta) Amt of money collected selling $5 T shirts = 3 x $160 = $480
\t1u = 16
b) Total T-shirts sold = 9u = 9 x 16 = 144

4. Tom and Jerry each has some money. If Tom spends $9 per day and Jerry spends $3 per day, Tom will have $100 left when Jerry has spent all his money. If Tom spends $3 per day and Jerry spends $9 per day, Tom will have $220 left when Jerry has spent all his money. How much did Jerry have?

Money at first (after N days of spending)
Tom : $100 +$9N
Jerry : $3N

Money at first (after M days of spending)
Tom : $220 + $3M
Jerry : $9M

N = 3M
$100 + $27M = $220 + $3M
$24M = $120
M = 5 days

Jerry had at first = $9 x 5 = $45

5. A van travelled from Town A to Town B at an average speed of 55km/h. A car started its journey from town B to A at 90 km/h at the same time the van started. The two vehicles passed each other 70 km from the middle of the whole journey. Find the distance between the two towns.

Speed ratio of van to car = 11:18
18u – 11u = 2 x 70 = 140
7u = 140
1u = 20
Distance between towns = 29u = 29 x 20 = 580km




6. 80% of marbles are red marbles and 20% of them are blue marbles. 63 red marbles and 46 blue marbles are added. The red marbles now makes up 75% of marbles and blue marbles 25% of marbles. How many red marbles are there at first?

Red : 4u + 63 = 3p
Blue : 1u + 46 = 1p
4u + 63 = 3u + 138
1u = 75
Nos. of red marbles at first = 4 x75 = 300

7. Courier A takes 10 hours to deliver a parcel from Town X to Town Y. Courier B takes 12 hours to deliver the parcel along the same route. If the speed of Courier A is 9km/h faster than that of Courier B, find the speed of Courier A.

Time ratio (A:B) = 5:6
Speed ratio = 6:5
1u = 9
6u = 9 x6 = 54 (54km/h)

8. In a concert, 75% of the audience were female. 75 females and 5 males left the concert half way. The remaining audience were allocated seats in groups of 10. Each group has 3 males. How many people were in the audience at first?

Female : 3u – 75 = 7p
Male : 1u – 5 = 3p

9u – 225 = 7u – 35
2u = 190
1u = 95
No. of people at first = 95 x 4 = 380

9. On Linda’s birthday, she gave sweets to every pupil in her class. If she gave each pupil 7 sweets, she would have 4 sweets left. If she gave 2 sweets to each pupil, she would have 189 sweets left. How many pupils were there in Linda’s class?

If she gives 5 less sweets per pupil = she has (189 – 4) = 185 sweets extra left
No. of pupils = 185 /5 = 37


10. The ratio of Ryan’s pocket money to John’s pocket money was 3 : 2. After Ryan saved $15 and John spent $8, the ratio of Ryan’s pocket money to John’s pocket money was 3 : 1. How much money did Ryan have at first?

Ryan : 3u + $15 = 3p
John : 2u - $8 = 1p
3u + $15 = 6u - $24
3u = $39
1u = $13
Amt Ryan had at first = 3 x $13 = $39

11. A lorry left Town A for Town B. After travelling for 4 hours at its usual speed, the lorry stopped for 30 mins for a break. In order to reach Town B at the appointed time, the speed of the lorry was increased by 8 km/h. Given that the lorry took 3 hours to cover the remaining journey, find the distance between Town A and Town B.

Total distance = 1u(4) + (1u+8 )(3) = 7u + 24 = 1u (7.5)
0.5u = 24
1u = 48
Total distance = 7.5 x 48 = 360km


12. Paul and Ray worked together to paint a house. During the job, Paul rested for 4 days and Ray took 2 days off. However, they were not absent on the same days. If they had done the same job alone, Paul would have taken 18 days and Ray 12 days. How long did the two painters take to complete painting the house?

Paul can paint 1/18 of house in 1 day
Ray can paint 1/12 of the house in 1 day

Paul and Ray can paint (1/18 + 1/12) = 30/216 = 5/36 of house in 1 day.

Paul work 2 days alone : Complete 1/9 of house
Ray work 4 days alone : Complete 1/3 of house

When they work alone; complete 1/9 + 1/3 = 12/27 of the house

Balance 15/27 of house painted together.

No. of days working together = (15/27)/(5/36) = 4 days

No. of days to complete = 4 + 4 + 2 = 10 days

[Dharma]

fxchow:

Hi,


Can someone help. TIA

After a Mathematics quiz, Mr Li gave the three prize winners a box of pencils to share.
The 1st winner received 2/3 of the pencils plus 1/3 of a pencil.
The 2nd winner received 2/3 of the remainder plus 1/3 of a pencil.
The 3rd winner received 2/3 of the new remainder plus 1/3 of a pencil.
But there were no more pencils left.
How many pencils were there in all?
Ans: 13 pencils

3rd winner gets : 2/3 of remainder + 1/3 of pencil = 1/3 x 3 = 1 pencil

2nd winner gets : [(1+1/3) x 3] - 1 = 3 pencils

1st winner gets : [(4 + 1/3) x 3] – 4 = 9 pencils

Total no. of pencils at first = 1 + 3 + 9 = 13

[k1ndan]

http://i300.photobucket.com/albums/nn19/k1ndan/Maths3.jpg\">

[k1ndan]

Dharma:

Hi friends.


Worked out James Ang's Qns. Was in a hurry. Pls highlight if there are mistakes.
...

Thanks, Dharma for the detailed working.

[James Ang]

picked out several questions from student’s schoolwork for parents to try before PSLE;


1. In a classroom, when a boy stands up, the number of boys sitting becomes 4/5 of the number of girls sitting. On the other hand, when a girl stands up, the number of girls sitting becomes 8/7 of the number of boys sitting. How many boys and girls are there in the class?

(Ans: 21 boys and 25 girls)

2. A box containted some twenty-cent coins and some fifty-cent coins in the ratio 3:4. When 26 fifty cent coins were taken out and replaced by the same value of twenty-cents coins, the ratio becomes 4:1. Find the sum of money in the box.

(Ans: $33.80)

3. The masses of copper and zinc in an alloy are in the ratio 2:3. If 12g of zinc is added to the alloy, the total mass of the alloy will become 36g. What is the new ratio of the mass of copper to that of zinc in the alloy?

(Ans: 4:11)

[MdmKS]

k1ndan:

http://i300.photobucket.com/albums/nn19/k1ndan/Maths3.jpg\">

a) height of a bowl = 4.5 - (5 - 4.5) = 4 cm

b) 42 - 22 = 20 cm
22 - 20 = 2 cm
height of a flower pot = 20 - 2 = 18 cm

correct?

[James Ang]

I have observed that P6 students who do PSLE Maths P2 (Story sums) normally fall into two major categories; those who know and those who don't. The ability gap will be further widened with the use of scientific calculators allowed for PSLE 2009. One example I can give is the SCGS prelims paper 2009, when neighbourhood/average school (generally schools that do not expose students to challenging sums in exams) student does that paper, many cannot do Paper 2 well while those students who are strong in models and heuristics can get every question right.


If Paper 2 is made up of all questions of those challenging models and heuristic types shown in this thread, more than half of students will do badly. Of course \"Tianzhu\" and \"Dharma\" type of students will score perfectly and even have time to draw beautiful diagrams too. Such ace students will never get Maths fatigue.