SMC 2023 - Grade 5

Admin dot · 2026-06-24T03:57:45Z

Mr Lim paid a total of $$$98 400 for his new car. He made the first payment of $$$30 000. For the remaining amount, he paid a fixed amount monthly for the next 60 months. How much did he pay each month? Edward bought some apples. $frac{3}{5}$ of the apples were rotten and were thrown away. He sold $frac{1}{4}$ of the remaining apples and had 60 apples left. How many apples did Edward have at first? In the figure below, ABC and BCD are isosceles triangles.$angle BAC=46^o$ and $angle ACD=150^o$. Find $angle BDC$. Every day, David saves $$$1.40 while his brother saves $$$2.20. David started saving 20 days earlier before his brother started saving. When David has saved $$$63, how much has his brother saved? Ali had a roll of wire measuring 1 m long. He cut 9 pieces of wire, each measuring 8 cm, from the roll of wire. The remaining wire was used to form a square. Find the area of the square. Give your answer in $text{cm}^2$. Mrs Lim baked 265 cakes and pies at first. After she sold 25 cakes and $frac{2}{7}$ of the pies, she had an equal number of cakes and pies left. How many cakes did she have at first? Study the number pattern below.The first number in Row 2 is 2 while the last number is 4.The first number in Row 3 is 5 while the last number is 9.Based on the pattern, what is the difference in value between the first number and the last number in Row 30? A group of 11 students saved an average of $$$385. When two of the students lost all their savings, the average savings of the remaining students became $$$288. What was the total amount of money lost by the two students? Mr Lim sold a total of 60 gift vouchers. 40% of the gift vouchers sold were $$$5 in value each and the rest were $$$10 in value each. How much money did Mr Lim collect from the sale of the $$$10 gift vouchers? Jerome glued a 2-cm cube and a 5-cm cube together as shown below. He then painted the whole solid blue. What was the total area of all the painted faces of the solid? Give your answer in $text{cm}^2$. At a fruit stall, the ratio of the number of apples to the number of oranges was 9 : 5.$frac{1}{2}$ of the apples and $frac{1}{2}$ of the oranges were rotten. There were 253 rotten apples and oranges. How many apples and oranges were there altogether at first? Square ABCD overlaps Triangle EFG to form Square ERCS as shown below.AB = EF = EG and R and S are the midpoints of EF and EG respectively. The area of Square ERCS is 81 cm². Find the area of the whole figure. Give your answer in cm². Mrs Lim measured and recorded the height of a group of 5 children. The table below shows the height of four of the children. Raja’s height was smudged with ink.The average height of the 5 children was 157 cm. One more child, Jack, joined the group and the average height of the six children became 159 cm. What was the average height of Jack and Raja? Give your answer in cm. Kenny and James have the same number of coins. Kenny has 20-cent coins and James has 50-cent coins. James has $$$35.70 more than Kenny. How many coins do Kenny and James have altogether? Azahar Money Changer offers an exchange rate of 0.75 US dollars for 1 Singapore dollar. At this rate, how many Singapore dollars will Mrs Lim get when she gives the money changer 675 US dollars? In January, the total expenditure of Alice, Bernice and Carol was $$$1510. In February, Alice increased her expenditure by $$$120, Bernice doubled her expenditure and Carol reduced her expenditure by $$$130. In the end, their expenditure became the same. What was Alice's expenditure in January? Sam cut out Cube Y from a larger wooden Cuboid X along the dotted line as shown below.The original volume of the Cuboid X was 6 times the volume of Cube Y. Then, Sam cut out as many 2-cm cubes as possible from the remaining Cuboid X. What was the volume of Cuboid X that was left uncut? Give your answer in $text{cm}^3$. A book costs 3 times as much as a file. John spent $frac{5}{9}$ of his money on some books. He spent $frac{3}{4}$ of the remainder on 9 files. How many books did John buy? Sharon was looking for a new laptop. During the Year End Sale, an identical laptop model was sold at Shops W and X with discounts as shown below.Shop W does not charge Goods and Services Tax (GST) while Shop X charged 8% GST on the discounted price. Sharon bought the new laptop at a lower price from one of the shops. How much did she pay for the laptop? Beatrice sold some files at $$$7.50 each and 18 bookmarks at $$$1.50 each. Jen sold the same number of files at $$$7.80 each and 18 bookmarks at $$$1.30 each. They collected the same amount of money. How many files did each girl sell? In the figure below, PQRS is a rhombus and PQTU is a trapezium.PT is a straight line.$angle$QRS is $124^circ$, $angle$ROP is $82^circ$ and $angle$STU is $18^circ$.Find the sum of $angle$SPT and $angle$RST. A group of students spent an average of 70 minutes each day for online learning. Then, 3 students who each spent 30 minutes each day joined the group. In ...

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Mr Lim paid a total of $\$$98 400 for his new car. He made the first payment of $\$$30 000. For the remaining amount, he paid a fixed amount monthly for the next 60 months. How much did he pay each month?

Edward bought some apples. $\frac{3}{5}$ of the apples were rotten and were thrown away. He sold $\frac{1}{4}$ of the remaining apples and had 60 apples left. How many apples did Edward have at first?

In the figure below, ABC and BCD are isosceles triangles.
$\angle BAC=46^o$ and $\angle ACD=150^o$. Find $\angle BDC$.

Every day, David saves $\$$1.40 while his brother saves $\$$2.20. David started saving 20 days earlier before his brother started saving. When David has saved $\$$63, how much has his brother saved?

Ali had a roll of wire measuring 1 m long. He cut 9 pieces of wire, each measuring 8 cm, from the roll of wire. The remaining wire was used to form a square. Find the area of the square. Give your answer in $\text{cm}^2$.

Mrs Lim baked 265 cakes and pies at first. After she sold 25 cakes and $\frac{2}{7}$ of the pies, she had an equal number of cakes and pies left. How many cakes did she have at first?

Study the number pattern below.
The first number in Row 2 is 2 while the last number is 4.
The first number in Row 3 is 5 while the last number is 9.

Based on the pattern, what is the difference in value between the first number and the last number in Row 30?

A group of 11 students saved an average of $\$$385. When two of the students lost all their savings, the average savings of the remaining students became $\$$288. What was the total amount of money lost by the two students?

Mr Lim sold a total of 60 gift vouchers. 40% of the gift vouchers sold were $\$$5 in value each and the rest were $\$$10 in value each. How much money did Mr Lim collect from the sale of the $\$$10 gift vouchers?

Jerome glued a 2-cm cube and a 5-cm cube together as shown below. He then painted the whole solid blue. What was the total area of all the painted faces of the solid? Give your answer in $\text{cm}^2$.

At a fruit stall, the ratio of the number of apples to the number of oranges was 9 : 5.
$\frac{1}{2}$ of the apples and $\frac{1}{2}$ of the oranges were rotten. There were 253 rotten apples and oranges. How many apples and oranges were there altogether at first?

Square ABCD overlaps Triangle EFG to form Square ERCS as shown below.
AB = EF = EG and R and S are the midpoints of EF and EG respectively. The area of Square ERCS is 81 cm². Find the area of the whole figure. Give your answer in cm².

Mrs Lim measured and recorded the height of a group of 5 children. The table below shows the height of four of the children. Raja’s height was smudged with ink.

The average height of the 5 children was 157 cm. One more child, Jack, joined the group and the average height of the six children became 159 cm. What was the average height of Jack and Raja? Give your answer in cm.

Kenny and James have the same number of coins. Kenny has 20-cent coins and James has 50-cent coins. James has $\$$35.70 more than Kenny. How many coins do Kenny and James have altogether?

Azahar Money Changer offers an exchange rate of 0.75 US dollars for 1 Singapore dollar. At this rate, how many Singapore dollars will Mrs Lim get when she gives the money changer 675 US dollars?

In January, the total expenditure of Alice, Bernice and Carol was $\$$1510. In February, Alice increased her expenditure by $\$$120, Bernice doubled her expenditure and Carol reduced her expenditure by $\$$130. In the end, their expenditure became the same. What was Alice's expenditure in January?

Sam cut out Cube Y from a larger wooden Cuboid X along the dotted line as shown below.

The original volume of the Cuboid X was 6 times the volume of Cube Y. Then, Sam cut out as many 2-cm cubes as possible from the remaining Cuboid X. What was the volume of Cuboid X that was left uncut? Give your answer in $\text{cm}^3$.

A book costs 3 times as much as a file. John spent $\frac{5}{9}$ of his money on some books. He spent $\frac{3}{4}$ of the remainder on 9 files. How many books did John buy?

Sharon was looking for a new laptop. During the Year End Sale, an identical laptop model was sold at Shops W and X with discounts as shown below.

Shop W does not charge Goods and Services Tax (GST) while Shop X charged 8% GST on the discounted price. Sharon bought the new laptop at a lower price from one of the shops. How much did she pay for the laptop?

Beatrice sold some files at $\$$7.50 each and 18 bookmarks at $\$$1.50 each. Jen sold the same number of files at $\$$7.80 each and 18 bookmarks at $\$$1.30 each. They collected the same amount of money. How many files did each girl sell?

In the figure below, PQRS is a rhombus and PQTU is a trapezium.
PT is a straight line.
$\angle$QRS is $124^\circ$, $\angle$ROP is $82^\circ$ and $\angle$STU is $18^\circ$.

Find the sum of $\angle$SPT and $\angle$RST.

A group of students spent an average of 70 minutes each day for online learning. Then, 3 students who each spent 30 minutes each day joined the group. In the end, the average time spent online learning for the whole group of students became 55 minutes. How many students were there in total in the end?

Green and red flags are tied to a rope in the pattern as shown below. The widths of the green flags are 14 cm and the red flags are 11 cm. The first and the last flag is tied 12 cm from each end of the rope. The gap between each green and red flag is 6 cm. There is a total of 97 flags tied to the rope. What is the length of the rope in centimetres?

Joshua spent $\frac{1}{8}$ of his monthly salary and an additional $\$$50 on food. He spent $\frac{2}{5}$ of the remainder and an additional $\$$70 on household expenses. He was left with $\$$2630. How much was Joshua’s monthly salary?

Rectangular Tank A measuring 20 cm by 7 cm by 23 cm is filled with water to the brim. Rectangular Tank B measuring 8 cm by 11 cm by 13 cm is filled with some water. After $\frac{1}{5}$ of the water from Tank A is poured into Tank B, Tank B is $\frac{5}{8}$ filled with water. How much water was in Tank B at first? Give your answer in $\text{cm}^3$.

The table below shows the rates for a cruise to Penang.

Mr Potter, his wife and 3 children aged 8, 10 and 15 years old were planning to go on a cruise to Penang. Mr Potter chose the Ocean View package and he received an early bird discount of 15% off his total cost. He also needed to pay additional 8% GST on the discounted price. How much did he have to pay in all? Round your answer to the nearest dollar.

1000 concert tickets were on sale over a week. Each ticket was sold for $\$$25. The graph below shows the number of tickets that were left unsold at the end of each day.

On Sunday, the concert organiser held a special promotion to sell all the remaining tickets. For every 5 tickets bought, the 6th ticket was given free. Sunshine School bought all the remaining tickets with this special promotion. How much did the concert organiser collect from the sale of the remaining tickets on Sunday?

During a sale, a discount of 10% was given to every 12 chocolate bars bought. Each chocolate bar cost $\$$8. Dan paid a total of $\$$331.20 for some chocolate bars. How many chocolate bars did he buy?

Eggs were only sold in trays of 30 eggs at a shop.

Mr Lee bought some such trays of eggs and re-packed them into carton boxes of 12 eggs as shown below.

He needed 6 more eggs to have exact carton boxes of 12 eggs. He also needed 26 more carton boxes than the number of trays he had bought. How many eggs did Mr Lee buy from the shop?

The ratio of the number of female members to the number of male members in a chess club was 4 : 3. When 38 male members left the club and 28 new female members joined the club, the number of male members to the number of female members became 1 : 2. How many male members were there in the chess club in the end?

A tank measuring 60 cm by 10 cm by 24 cm was empty at first. Water from a tap started to fill the tank at the rate of 600 $\text{cm}^3$ per minute. When the tank was $\frac{1}{4}$ filled with water, a crack appeared at the base of the tank. Water began to leak from the crack at the rate of 150 $\text{cm}^3$ per minute. What was the total time taken for the whole tank to be completely filled with water? Give your answer in minutes.

The table below showed the price of grapes and cherries at a fruit stall.
Grapes: $\$$1.55 per 100 g
Cherries: $\$$2.60 per 100 g
Mrs Kim bought some grapes and cherries to make fruit salad. She bought twice as heavy cherries as grapes. She used $\frac{2}{5}$ of the grapes and $\frac{3}{4}$ of the cherries. She was then left with 120 g more grapes than cherries. How much did she pay for the grapes and cherries?