SMC 2023 - Grade 6

Admin dot · 2026-06-24T08:05:40Z

The figure shows the net of a cuboid with a square base of 81 $text{cm}^2$. Find the volume of the cuboid. The graph below shows the achievement levels of a game by a group of students. Each student gets 1 point at the beginner level, 3 points at the intermediate level and 5 points at expert level. The students achieve a total score of 224. How many students are at the intermediate level? $frac{3}{4}$ kg of flour was needed to bake 30 brownies. Sally baked a tray of 24 brownies. There were 24 brownies on each tray. How many trays of 24 brownies could Sally bake at most with 4 kg of flour? In the figure below, EFGH is a rhombus. HJK is an equilateral triangle. $angle$GHJ = 26º. Find $angle$HLK. An ant travelled at 75 cm/min for 2 min. A centipede travelled at 40 cm/s for 1 min. What is the difference in the distance travelled by the two animals? Give your answer in centimetres. Navin had a roll of ribbon. He used half of the roll of ribbon to cut into 12-cm strips. With the other half of the roll of ribbon, he cut them into 9-cm strips. After using up the roll of ribbon, he had 8 more strips of ribbons of length 9-cm each than of length 12-cm each. How many strips of ribbons of 12-cm length did he have? A group of students sat for a test. Their total score was 2252. The average of the highest score and the lowest score was 55. The average score for the remaining students was 63. How many students sat for the test? Jackson is a deliveryman. He had to deliver 120 parcels from 9 a.m. to 5 p.m. on a particular day. For every 10 parcels delivered, Jackson earned 30 bonus points. The line graph shows the number of parcels left undelivered by 5 p.m. on that day.How many bonus points did Jackson earn by 3 p.m.? A table with 4 columns is filled with numbers in a certain pattern. The first 6 rows of the table are shown below.In which row will the number 89 appear? The table shows the charges for CityLife taxi.Karen took a CityLife taxi from the shopping mall to her home. The taxi stopped once at a traffic light for 45 seconds. She paid $$$8.20 for the taxi ride. What was the furthest distance she could have travelled? Give your answer in metres. The pie chart and bar graph show the number of students who went to 4 different places for their Learning Journey. Each student only went for one learning journey. The bar that shows the number of students who went to the Discovery Centre has not been drawn. What percentage of the students went to the Discovery Centre? Peter had a toy car fixed on a straight track. He pushed the toy car from one end of the track to the other end of the track. Each wheel made 30 revolutions. The length of the toy car is 26 cm and the radius of each wheel is 2.5 cm. What is the length of the track? (Take $pi$ = 3.14) (Give your answer in centimetres) Andrew had 3 rods. He tied Rod A and Rod B together as shown in the figure below. When Rod A and B are tied together, they had the same length as Rod C. The ratio of the length of Rod A to the length of Rod B was 9 : 4.What was the length of Rod C? Give your answer in centimetres. The figure below shows two stacks of identical glasses. The height of the first stack of 8 glasses is 54 cm. The height of the second stack of 5 glasses is 39 cm.The height of the space in a shelf is 90 cm. What is the maximum number of glasses that one can put in a single stack to be placed in the shelf? The table below shows the number of cakes sold at a bakery for a week.82 cakes were sold on Saturday and Sunday. Find the total number of cakes sold from Monday to Sunday. Robot A can clean a hall in 6 hours. Robot B can clean the same hall in 3 hours. The two robots are used to clean the hall together. How many minutes would they take to clean the whole hall? The figure below is made up of 3 identical isosceles triangles ABC, PQR and XYZ. ∠QPR is 43º. Find the sum of ∠$m$, ∠$n$ and ∠$x$. Eunice, Fanny and Gloria shared the cost of buying a watch for their father. Eunice paid 30% of the cost of the watch while Fanny paid 35% of the remaining amount. Gloria paid the rest of the cost. There was a 20% discount when they bought the watch. Eunice paid $$$348 for her share. How much did Gloria pay for the watch? Round your answer to the nearest dollar. Liz and Alex had $$$345 altogether. Liz spent $frac{1}{7}$ of her money and Alex spent $frac{3}{4}$ of his money. In the end, Liz was left with thrice as much money as Alex. How much money did Alex have at first? Jack has 9 identical large cubes and some identical small cubes. He packs all the cubes tightly into a rectangular box such that cubes of the same size are stacked on top of each other. The box is filled to its brim exactly. The figure below shows the first layer of cubes packed in the box.The volume of the box is 14 976 $text{cm}^3$. The total volume of the 9 large cubes is $frac{4}{13}$ of the volume of the box. What is the volume of one small cube? Give your answer in $text{cm}^3$. Figure 1 is a rectangle, JKLM, with ...

SMC

Last Post by Admin dot 2 minggu ago

1 Posts

1 Users

0 Reactions

14 Views

RSS

Admin dot

(@edukasidot)

Posts: 120

Member Admin

Topic starter

The figure shows the net of a cuboid with a square base of 81 $\text{cm}^2$. Find the volume of the cuboid.

The graph below shows the achievement levels of a game by a group of students. Each student gets 1 point at the beginner level, 3 points at the intermediate level and 5 points at expert level. The students achieve a total score of 224. How many students are at the intermediate level?

$\frac{3}{4}$ kg of flour was needed to bake 30 brownies. Sally baked a tray of 24 brownies. There were 24 brownies on each tray. How many trays of 24 brownies could Sally bake at most with 4 kg of flour?

In the figure below, EFGH is a rhombus. HJK is an equilateral triangle. $\angle$GHJ = 26º. Find $\angle$HLK.

An ant travelled at 75 cm/min for 2 min. A centipede travelled at 40 cm/s for 1 min. What is the difference in the distance travelled by the two animals? Give your answer in centimetres.

Navin had a roll of ribbon. He used half of the roll of ribbon to cut into 12-cm strips. With the other half of the roll of ribbon, he cut them into 9-cm strips. After using up the roll of ribbon, he had 8 more strips of ribbons of length 9-cm each than of length 12-cm each. How many strips of ribbons of 12-cm length did he have?

A group of students sat for a test. Their total score was 2252. The average of the highest score and the lowest score was 55. The average score for the remaining students was 63. How many students sat for the test?

Jackson is a deliveryman. He had to deliver 120 parcels from 9 a.m. to 5 p.m. on a particular day. For every 10 parcels delivered, Jackson earned 30 bonus points. The line graph shows the number of parcels left undelivered by 5 p.m. on that day.

How many bonus points did Jackson earn by 3 p.m.?

A table with 4 columns is filled with numbers in a certain pattern. The first 6 rows of the table are shown below.

In which row will the number 89 appear?

The table shows the charges for CityLife taxi.

Karen took a CityLife taxi from the shopping mall to her home. The taxi stopped once at a traffic light for 45 seconds. She paid $\$$8.20 for the taxi ride. What was the furthest distance she could have travelled? Give your answer in metres.

The pie chart and bar graph show the number of students who went to 4 different places for their Learning Journey. Each student only went for one learning journey. The bar that shows the number of students who went to the Discovery Centre has not been drawn. What percentage of the students went to the Discovery Centre?

Peter had a toy car fixed on a straight track. He pushed the toy car from one end of the track to the other end of the track. Each wheel made 30 revolutions. The length of the toy car is 26 cm and the radius of each wheel is 2.5 cm. What is the length of the track? (Take $\pi$ = 3.14) (Give your answer in centimetres)

Andrew had 3 rods. He tied Rod A and Rod B together as shown in the figure below. When Rod A and B are tied together, they had the same length as Rod C. The ratio of the length of Rod A to the length of Rod B was 9 : 4.

What was the length of Rod C? Give your answer in centimetres.

The figure below shows two stacks of identical glasses.
The height of the first stack of 8 glasses is 54 cm. The height of the second stack of 5 glasses is 39 cm.

The height of the space in a shelf is 90 cm. What is the maximum number of glasses that one can put in a single stack to be placed in the shelf?

The table below shows the number of cakes sold at a bakery for a week.

82 cakes were sold on Saturday and Sunday. Find the total number of cakes sold from Monday to Sunday.

Robot A can clean a hall in 6 hours. Robot B can clean the same hall in 3 hours. The two robots are used to clean the hall together. How many minutes would they take to clean the whole hall?

The figure below is made up of 3 identical isosceles triangles ABC, PQR and XYZ.
∠QPR is 43º. Find the sum of ∠$m$, ∠$n$ and ∠$x$.

Eunice, Fanny and Gloria shared the cost of buying a watch for their father. Eunice paid 30% of the cost of the watch while Fanny paid 35% of the remaining amount. Gloria paid the rest of the cost. There was a 20% discount when they bought the watch. Eunice paid $\$$348 for her share. How much did Gloria pay for the watch? Round your answer to the nearest dollar.

Liz and Alex had $\$$345 altogether. Liz spent $\frac{1}{7}$ of her money and Alex spent $\frac{3}{4}$ of his money. In the end, Liz was left with thrice as much money as Alex. How much money did Alex have at first?

Jack has 9 identical large cubes and some identical small cubes. He packs all the cubes tightly into a rectangular box such that cubes of the same size are stacked on top of each other. The box is filled to its brim exactly. The figure below shows the first layer of cubes packed in the box.

The volume of the box is 14 976 $\text{cm}^3$. The total volume of the 9 large cubes is $\frac{4}{13}$ of the volume of the box. What is the volume of one small cube? Give your answer in $\text{cm}^3$.

Figure 1 is a rectangle, JKLM, with a perimeter of 42 cm.
Figure 2 is made up of four such rectangles and a shaded square, QRST, in the centre.
The area of Square QRST is 169 $\text{cm}^2$. Find the length of JM in centimetres.

The ratio of the number of men to the number of women was 3 : 4. There were 12 more women than children. After $\frac{1}{3}$ of the men, $\frac{1}{2}$ of the women and $\frac{1}{4}$ of the children left, there were 425 people remaining. How many people were there at first?

The first 4 figures of a pattern are shown below. The length of each side of a cube in Pattern 1 is 3 cm.

What is the difference in the volume of the cubes in Pattern 11 and Pattern 12? (Give your answer in cubic centimetres.)

The ratio of the number of teachers to students in Sunshine School is 1:12. Aunty Lisa baked 1800 cookies for all the students and teachers during Children’s Day. She gave each teacher 4 more cookies than each student. The students received 4 times as many cookies as the teachers. How many teachers were there in Sunshine School?

Mr Wu earned $\$$8500 in January. He spent 60% of his earnings and saved the rest. In February, his earnings decreased. He reduced his spending by 15% and saved the rest. In the end, he saved 25% of his earnings in February. What was Mr Wu’s earnings in February?

Kenneth stacked two 50-cent coins and four 10-cent coins as shown in Figure 1. He found that the two stacks of coins have the same height. He then stacked an unknown number of such 50-cent coins, 10-cent coins and 20-cent coins to the same height as shown in Figure 2. The total value of all the 50-cent and 10-cent coins in Figure 2 is $\$$25.20.

The height of each 20-cent coin is $\frac{3}{5}$ of the height of each 50-cent coin. Find the value of all the 20-cent coins.

George drew 13 identical squares of sides 5 cm and arranged them as shown. He then drew 4 quadrants in such a way that when he shaded some areas within the 13 squares, he created a pattern.

What is the area of the shaded part? Take 𝜋 = 3.14.

In the figure below, not drawn to scale, JKLM, LNOP and QRSK are squares.
∠NKO = 110° and ∠SOP = 130°. Find ∠LNK.

On Monday, Tina jogged around a park once along the jogging track at an average speed of 12 km/h for 20 min and 10 km/h for 1 h 15 min.

On Tuesday, Tina and her brother jogged around the same park along the jogging track. They started at the same point but in the opposite directions. Tina jogged at an average speed of 14 km/h while her brother jogged at an average speed of 16 km/h. At what time would they meet if they started jogging at 06 45? Give your answer in 24-hour clock.

A rectangular tank was completely filled with water. The tank was fixed in the position shown. A partition was placed in the tank. There was an outlet at the base of the tank as shown. When the outlet was unplugged at 4.00 p.m., water flowed out at a rate of 6 ℓ/min. At what time did the water stop draining out of the tank? (Give your answer in 24-hour format.)

The figure below shows a square ABCD. The length of ED is $\frac{2}{3}$ of the length of AD. The area of triangle BCF is 27 $\text{cm}^2$ and this is $\frac{3}{5}$ the area of triangle AEF. What is the length of AB?

The figure is made up of a quadrant and a semi-circle. C is the mid-point of the arc of the semi-circle. The ratio of the length of BC to the length of CD is 2 : 3. Using the  value of the calculator, find the area of the shaded parts of the figure. Give your answer correct to the nearest whole number.