1. Denzel, Eugene and Farhan bought a packet of marbles. Denzel received 145 marbles.Farhan received 30% less marbles than Eugene. Later,Denzel gave 68 marbles to Eugene and Farhan to share. After that, Farhan still had 30% fewer marbles than Eugene. The number of marbles Eugene had increased by 25%. How many marbles were there in the packet at first?

2. A music store collected $1 680 from the sale of headphones, CDs and DVDs. The ratio of the amount of money collected from the CDs to the amount collected from the DVDs to the amount collected from the headphones was 5 : 6 : 3. The CDs were sold at 2 for $25.
The number of CDs sold was three times the number of DVDs sold.
The number of headphones sold was 50% of the number of DVDs sold.

( a ) How many DVDs did the store sell?

( b ) If Mr Yong had $1125, how many headphones could he buy?

3. The ratio of the number of adults to the number of children in a housing estate is 3 : 8. The ratio of the number of boys to the number of girls is 2 : 5. There are 960 fewer boys than girls in the housing estate. How many more adults than boys are there in the housing estate?

4. Tan, Lim and Wong had some pens to sell. Tan had the least number of pens. Wong’s number of pens was 30% less than Lim’s. After Tan and Lim had each sold 50% of their pens, Lim had 95 more pens than Tan. If the three men had a total of 330 pens left, what was the total number of pens they had at first?

5. Anne has some $2 notes. Cindy has some $5 notes. The ratio of the number of notes Anne has to the number of notes Cindy has is 7 : 5. If Anne gives Cindy 24 notes, the ratio of the number of Anne’s notes to the number of Cindy’s notes will become 1 : 3.
(a) How many $5 notes does Cindy have at first?
(b) Find the total value of all the notes which Anne and Cindy have.

6. A rectangular tank, 56 cm long, 42cm wide and 35 cm high was 3/5 full of water. Water began to leak at a rate of 23 cm3 per second. At the same time, water was also added into the tank from a tap at the rate of 72 cm3 per second. How long would it take for the tank to become 90% full of water?
Give your answer in minutes.)

Speed!

At 9am, John was cycling from Point A to Point B. At the same time, Mary was cycling from Point B to Point A using the same route as John. Cycling at a speed 4km/h faster than Mary, John would pass Mary 300m away from the midpoint.
(a) What time did they pass each other?
(b) If John took another 3 minutes to reach Point B, what time would Mary reach Point A?

Maths - 5m

1. The Channel Boutique sold a dress for $585. This was 117% of the price of a similar dress in Chloe Boutique. During a sale, both stores offered the same percentage discount on the dress. Christine bought the dress in Chloe Boutique and found that she paid $68 less than the discounted price in Channel Boutique.

(a) Find the price of the dress in Chloe Boutique before the sale.
(b) What is the percentage discount given during the sale?

2. Van A takes 12 hours to deliver a parcel from Town X to Town Y. Van B takes 14 hours to deliver the parcel along the same route. Van A moves at a speed 14 km/h faster than Van B. Find the speed of Van A.

What in disguise???

1. Max and Roy each had some money.
If Max spent $60 each day and Roy spent $40 each day, Max would have $80 left when Roy had spent all his money.
If Max spent $30 each day and Roy spent $80 each day, Max would have $890 left when Roy had spent all his money.
How much did Roy have ?

2. Amy and Billy were given some money each. If Amy spent $25 each week and Billy spent $75 each week, Amy would still have $1350 left when Billy had spent all his money. If Amy spent $75 each week and Billy spent $25 each week, Amy would still have $150 left when Billy had spent all his money.

How much money did Amy receive?


3. 20% of Dominic’s savings was $120 more than 1/4 of Joshua’s savings.
After Dominic spent 5/6 of his savings and Joshua spent 50% of his savings, Dominic had $30 more than Joshua.
Find Dominic’s savings at first.

Apples and Oranges - Circles and Triangles

There were 225 apples and 253 oranges in Box A.
There were 260 apples and 212 oranges in Box B.
Mr Chia moved some apples and oranges from Box B to Box A.
In the end, 40% of the fruits in Box A and 70% of the fruits in Box B were apples. How many fruits did Mr Chia move from Box B to Box A?

Spring answers

Q1	3	Q6	1	Q11	1
Q2	4	Q7	3	Q12	3
Q3	1	Q8	3	Q13	2
Q4	4	Q9	4	Q14	2
Q5	2	Q10	4	Q15	4

Q16	1600
Q17	65
Q18	9
Q19	0.5
Q20	0.17
Q21	135
Q22	60
Q23	January and February or June and July
Q24
Q25 Q26 Q27 Q28 Q29      Q30	8y 1170 Northwest 75 3 : 2 2x

Maths Questions (4m)

1. Mr Yeo bought 4 times as many spoons as bowls and spent $495 in total.

He spent $15 more on the bowls than on the spoons.

If a bowl cost $6.50 more than a spoon, what was the cost of a spoon ?

2. A car took 5 hours to travel from Town A to Town B while a bus took

4 hours longer to travel from Town B to Town A. 

Both vehicles set off at the same time and moved towards each other.

Two hours later, they were 255 km apart. What was the speed of the bus ?

To do list

You need to do the following for today.

1. Draft 2 of your latest CW (Please ensure there's significamt improvement from Draft 1)

2.  Get your parent(s) to sign Maths Prelim papers.

3. Check MConline email for Casuarina answers.

4. Check MConline email for Spring Paper 1.

5. Complete S and T 10.

6. The answers for all Maths posts (1m to 5m math problems) are released as comments. Please check. Let me know the questions that we have to discuss in class here.

7. Get parent(s) to acknowledge letter on PSLE Matters. Return the form tomorrow.

Do you agree with this parent?

Hey all, this letter written by a parent to the Straits Times forum concerns you!

Do you agree with him?

Are you able to solve the Maths problem he mentioned in the letter?

I am interested to hear from you.

5m Maths Questions

1.         A rectangular tank with a base area of 500 cm² and a height of 12 cm contains some water. When some identical cubes are put into it, it becomes 5/6  filled. Each identical cube has sides of 5 cm. He then removes all the cubes and the tank is 2/3 filled with water only.

(a)               What is the volume of water in the tank? (1m)

(b)               How many cubes has he put into the tank at first? (4m)

2.         Jason, Edward and Sam had a total of $837. Jason had the least amount of money. The ratio of Edward’s money to Sam’s money was 4 : 3 at first. Jason and Edward each spent 1/3 of their money. Given that the three boys had $648 left, how much did Jason have at first?

3.         In a village, 2/7 of the men and 80% of the women keep long hair.  The number of people with short hair is 5600 and 12.5% of the people with short hair are women.

            (a)  How many people in the village keep long hair?  (4m)

            (b)  What percentage of the people in the village keep long hair? 

      (Give your answer correct to 1 decimal place.) (1m)

4.         At 8.30 a.m., Hassan left Town X for Town Y driving at a speed of 70 km/h throughout his journey.  At 10.00 a.m., Wong left Town X and drove at a constant speed along the same route as Hassan.  Wong took 6 hours to catch up with Hassan.  Wong reached Town Y at 6 p.m.

(a)  What was Wong’s driving speed? (3m)

(b)  Find the distance between Town X and Town Y. (1m)

(c)  At what time did Hassan reach Town Y? (1m)

4m Maths Questions

1.         The price of one egg tart is $0.90 from Delicious Bakery. For every 3 egg tarts a customer buys, he can buy the fourth one at half the price.

What is the greatest number of egg tarts that a customer can buy with $72?

2.         In a hall, there are 16 rows of 19 chairs each. Mr Wong wishes to rearrange these chairs into a square with the same number of chairs on each side. There are no chairs inside the square. How many chairs will there be on each side of the square?

3.         The distance between Town A and Town B was 520 km. At 8.30 a.m., a van left Town A for Town B travelling at a constant speed. At the same time, a car travelling at a constant speed set off from Town B towards Town A. The two vehicles met each other at 12.30 p.m. The car was travelling at 20 km/h faster than the van.  What was the speed of the car?

4.         A vase and a bottle had a total of 810 mℓ of water.  Susan tripled the amount of water in the vase and added 30 mℓ of water into the bottle.  The ratio of the amount of water in the vase and bottle is now  9 : 4.  How much more water was there in the bottle than in the vase at first?

3m maths Questions

1.         Tim and Jonathan can paint a room in 2 h together. If Tim is painting the room alone, he can only complete the task in 6 h. How long will Jonathan take to paint a room all by himself?

2.         Lu Lu Garments imported T-shirts from overseas and sorted them into 3 different colours. 3/7 of the T-shirts were red and 2/5 of the T-shirts were green. The rest of the T-shirts were yellow. There were 912 more green T-shirts than yellow T-shirts. How many green T-shirts were imported?

3.         Mr Lee bought some T-shirts for $425. If he was given a discount of 15%, he would be able to buy 5 more identical T-shirts for the same amount of money. What was the original price of each T-shirt?

4.                  The price of one tuna bun from Sunshine Bakery is 70 cents.  When a customer buys 5 tuna buns, he can buy one more at 30 cents.  What is the greatest number of tuna buns that a customer can buy with $28?        

2m Maths Questions (Calculators allowed)

1. Fatimah bought a book and 5 identical pens for  $7r.  The book cost $5 more than a pen. 

(a) Express the price of a pen in terms of r.

(b) If  r = 2, find the cost of 2 such pens.

2. 63% of the students in a school were boys.  When 23 more girls joined the school, the number of girls became 356.  How many students were there at first?

3. The ratio of the length of a rectangle to its breadth is  4 : 1.  If the area of the rectangle is 196 cm², what is its length?

4. The area of a rectangle is 162 m². The breadth of the rectangle is more than 6 m. The length is twice of the breadth. Both the length and the breadth are whole numbers. What is the length of the rectangle?

5. Mr Han bought 34 belts. He sold half of them at $23 each and the rest at $21.50 each. What was the average price of the 34 belts?

1m and 2m Maths questions (Calculators not allowed)

Questions 1 to 10 carry 1 mark each.
Questions 11 to 15 carry 2 mark each.

1. What is the value of the digit ‘2’ in 19.826?

2. A packet containing less than 80 pens can be shared equally among 4 boys or 8 girls. What is the maximum number of pens the packet could contain?

3. The mass of a parcel was recorded as 3.4 kg, rounded off to 1 decimal place. If it weighed less than 3.4 kg and has 2 decimal places, write down a possible mass of the parcel.

4. Find the sum of all the factors of 26.

5. A movie marathon started at 10.30 p.m. and ended at 6.35 a.m. the next day. How long was the movie marathon in hours and minutes?

6. Irfan has thrice as much money as Don. If Irfan gives Don $45, he will have the same amount of money as Don. How much money does Irfan have?
 
7. A cuboid measuring 12 cm by 9 cm by 2 cm has the same volume as a cube. Find the length of the cube.

8. The average of 4 numbers is 15. If the average of 3 of them is 18,

what is the fourth number?

9. The sum of the page numbers of two facing pages in a magazine is 73.  What are these two page numbers?                           

10. What is the smallest number that can be divided by both 5 and 17 without any remainder?         

11. Kaiwei has 7 litres of paint to paint 10 doors. 3/4 ℓ  of paint is needed to paint a door completely.  What fraction of a door will not be painted?

12. 4 similar cups and 3 similar teapots cost $71 altogether. Each cup cost $5 less than each teapot. What was the cost of each teapot?

13. At first Alvin had twice as many trading cards as Steven. After Alvin had given away 285 of his trading cards, Steven had twice as many trading cards as Alvin. How many trading cards did they have altogether at first?

14. Paula baked 18 more fruit cakes than chocolate cakes. After giving away 35 cakes of each type, the number of chocolate cakes became 75% of the number of fruit cakes. How many chocolate cakes had she left?  

15. Mrs Young drove at 60 km/h for 45 minutes.  She rested for 15 minutes and continued  the rest of the journey for another hour at 80 km/h.  What was her average speed for the whole journey?

Check MConline for Maths Paper 2

Solution to 5m question 1

1. John had $700 in his bank. With this money, he donated $4 a day to charity. His sister, Mary, too donated 1/5 of her $5 daily allowance to the charity and she saved the rest. If both of them started the donation drive on the same day, how long would it be before John had 2/3 as much money as the amount Mary saved?

Part 1
Part 2
Part 3
Part 4
Part 5

5m qns

1. John had $700 in his bank. With this money, he donated $4 a day to charity. His sister, Mary, too donated 1/5 of her $5 daily allowance to the charity and she saved the rest. If both of them started the donation drive on the same day, how long would it be before John had 2/3 as much money as the amount Mary saved?


2. Mrs Lim’s son helped her to type the page numbers of her new story book. He noticed that different pages required different numbers of digits. He counted that there were a total of 675 digits. How many pages were there in the story book?


3.  Citrine bought twice as many pencils as notebooks and spent a total of $53.60. She spent $2.40 more on the notebooks than the pencils. Given that a notebook costs $1.90 more than a pencil, find the cost of a pencil.


4. Candle A and candle B are of the same length. Candle A , which is broader, can burn for 5 h while Candle B, the thinner candle , can burn for 4 h. If both candles are lighted at the same time, how long does it take for Candle A to be twice as long left as Candle B?

4m qns

1.There were 192 oranges and melons in a box. Mr Liu removed 2/5 of the oranges from the box and he added 24 melons into the box. As a result, there was an equal number of oranges and melons left in the box.
How many more oranges than melons were there in the box at first ?

2. There are some yellow and green balls in a basket.
The sum of 3/8 of the number of yellow balls and all the green balls is 430. The sum of 1/2 of the number of yellow balls and 1/4 of the number of green balls is 192. How many green balls are there in the basket ?

3. Starting from the same position on a straight road, Timothy and Michael jogged in the opposite direction. With Timothy jogging at an average speed of 1.6 km/h slower than Michael, the two men were 4.2 km apart after jogging for 45 minutes. Find the average speed of Michael. (Give your answer in km/h).

4. Mrs Tan had 98 pieces of $10 notes and $50 notes in her piggy bank.
She took out 3/4 of the $50 notes and put in another ten $10 notes.
As a result, the number of $10 notes was five times the number of $50 notes.
What was the total value of money she had in her piggy bank at first?

3m qn

1. Alice bought some candies. She ate the same number of candies everyday. After 4 days, she had 5/6 of the candies left. After another 5 days,
she had 30 candies left. How many candies did she have at first ?

2. During a school assembly, the ratio of the number of girls to the number of boys was 6 : 7. If 63 girls left the school hall, the new ratio of the number of girls to the number of boys became 9 : 14. How many pupils were there in the school hall at first ?

3. Tap A can fill up an empty tank in 20 minutes.

Tap B can empty the same tank completely filled with water in 12 minutes.

Both taps are turned on at the same time when the tank is half-filled with water.

How long will it take for the tank to be totally emptied?

4. A cuboid has a rectangular base of perimeter of 64 cm. The ratio of its length to its breadth of the base is 5:3. The volume of the cuboid is 2400 cm³.

Find its height.

5. Raju earns a monthly salary of $ 4 500. He spends 1/5  on food and gives 2/3 of the remainder to his mother. He will save the remaining sum of his salary. How much will he save after 1 year?

2 mark qns

1. 5 oranges and 4 pears cost $3.10. 4 pears and 3 apples cost $2.50. If an apple costs as much as an orange, how much does 1 apple cost?

2. Marilyn has a mass of 45.5 kg. She is 3.8 kg heavier than Nicole. What is their total mass ?

3. Find the maximum number of 4-cm cubes that can fill a box measuring 29 cm by 18 cm by 15 cm.

4. The cost of renting a car is $70 per day. In addition, there is a 5% GST charge on the total rent. How much must Faizal pay if he rents a car for 2 weeks ?

5. The table shows the taxi charges:

 

Taxi charges	Amount
First  2 km	$3.20
For every additional 100 m	$0.10

Mr Poh took a taxi to work. The taxi travelled a distance of 6.8 km. How much did he pay for the taxi fare?