Primary 6 Maths Preliminary Exam 2025 – Test 6

1. In 6 417 295, the digit 2 stands for ______.

📖 REMINDER: Identify the place value of the digit 2 in the given number.

1. 200

2. 2 000

3. 20 000

4. 200 000

2. Which one of the following numbers is the smallest?

📖 REMINDER: Compare the digits after the decimal point from left to right to find the smallest value.

1. 0.402

2. 0.042

3. 0.204

4. 0.024

3. Express 3³⁄₁₂ as a decimal.

📖 REMINDER: Convert the mixed number to an improper fraction or convert the fraction part to a decimal, then add to the whole number.

1. 3.32

2. 3.25

3. 3.14

4. 3.3

4. The line graph below shows the total amount of money collected in a donation jar from Monday to Friday.
On which day did the amount of money in the jar increase the most?

📖 REMINDER: Read the vertical axis carefully to find the value for each day, then calculate the difference from one day to the next.

1. Monday to Tuesday

2. Tuesday to Wednesday

3. Wednesday to Thursday

4. Thursday to Friday

5. The figure below is made up of 5 identical squares. The total width is 24 cm. Find the perimeter of the figure.

📖 REMINDER: The total width is made up of 3 squares placed side-by-side.

1. 64 cm

2. 72 cm

3. 96 cm

4. 108 cm

6. A number line with points P, Q, R, and S is shown. Which point represents ¹⁄₂?

📖 REMINDER: Identify the value of each interval by comparing two known values.

1. P

Q

R

S

2. Q

3. R

4. S

7. Express 40¢ as a percentage of $8.

📖 REMINDER: Convert both amounts to the same unit (cents) before calculating the percentage.

1. 4%

2. 25%

3. 400%

4. 2500%

8. The figure shows a circle that fits perfectly inside a square. The perimeter of the square is 112 cm.
Find the area of the circle. (Take π = ²²⁄₇)

📖 REMINDER: The side of the square is equal to the diameter of the circle.

1. 154 cm²

2. 616 cm²

3. 2464 cm²

4. 176 cm²

9. The pie chart shows the flavours of ice cream sold at a shop. Vanilla is a right angle (90°) at the centre.
Mint represents ¹⁄₁₆ of the total. The rest are Chocolate and Strawberry. There are 480 ice creams in total
and there are twice as many Chocolate ice creams as Vanilla ice creams. How many Strawberry ice creams are there?

📖 REMINDER: A right angle (90°) is one-quarter of a full circle (360°).

1. 60

2. 90

3. 120

4. 150

10. The figure below shows an 8-point compass. Mary was facing South-East (SE) at first.
She turned 135° anti-clockwise. Which direction is she facing now?

📖 REMINDER: On an 8-point compass, the angle between any two adjacent points is 45°.

1. North (N)

>

2. West (W)

3. East (E)

4. North-East (NE)

11. Calvin had 20 more stamps than Devi at first. After Devi gave 16 of her stamps to Calvin,
Calvin now has 3 times as many stamps as Devi. How many stamps did Calvin have at first?

📖 REMINDER: Use a model drawing or work backwards from the final ratio to find the initial amounts.

1. 18

2. 26

3. 34

4. 42

12. The table shows the number of puzzles solved by students in a math club. Each student solved a whole number of puzzles.
The total number of puzzles solved was 92. How many students solved exactly 2 puzzles?

Puzzles solved per student	0	1	2	3	4
Number of students	4	8	?	6	5

📖 REMINDER: Calculate the total from known values first, then find the missing group's contribution.

1. 15

2. 18

3. 20

4. 22

13. A video game costs $25 after a discount of 30%. Sarah was given a further discount of $4 because of a holiday promotion.
What is the total percentage discount for the video game?

📖 REMINDER: First find the original price, then calculate the total discount amount and percentage.

1. 20 %

2. 25 %

3. 40 %

4. 60 %

14. A solid wooden block measuring 12 cm by 9 cm by 7 cm is placed on a table. The exposed surfaces
(the top and the four sides) are painted blue.The bottom surface, which is touching the table, is not painted.
The block is then cut into 1-cm cubes.How many of the cubes have NONE of their surfaces painted blue?

📖 REMINDER: Only remove layers from the painted sides to find the unpainted core.

1. 192

2. 240

3. 288

4. 320

15. In the figure, ABCD is a square. Points B, C, and E form an equilateral triangle inside the square. Find ∠DEC.

📖 REMINDER: Identify equal sides from the square and equilateral triangle properties to find an isosceles triangle.

1. 15°

2. 30°

3. 45°

4. 75°

16. Find the value of 5604 + 30

Answer:

📖 REMINDER: Add the ones digits first, then the tens, and finally combine the results.

PE2,MGPS,2025,PE2MGPS2025,Whole Numbers

17. Find the value of 84 + (12 - 8) + 5 × 15

Answer:

📖 REMINDER: Remember the order of operations: Brackets first, then multiplication/division, then addition/subtraction.

18. Find the value of ⁵⁄₉ + 7. Give your answer as a fraction in the simplest form.

Answer:

📖 REMINDER: Convert the whole number to a fraction with the same denominator before adding.

PE2,MGPS,2025,PE2MGPS2025,Fractions

19. A group of students were surveyed on their favorite sport. The results are displayed in the pie chart below.
Soccer: ¹⁄₂, Basketball: ¹⁄₅, Badminton: The remaining 12 students. How many students were surveyed in total?

Answer: students

📖 REMINDER: The whole pie chart represents 1 (or 100%). Find the fraction for the 'remaining' part first.

20. The table shows the hourly rate of work done at a grocery store.

Day	Hourly rate
Weekdays (Monday to Friday)	$9
Weekend (Saturday and Sunday)	$12

Nathan works at the store for 8 hours daily on weekdays and 6 hours on Saturdays. How much does he earn in a week?

Answer: $

📖 REMINDER: Calculate weekday and weekend earnings separately, then add them together.

21. The solid below is made up of identical cubes joined together in a “staircase” shape. The area of the shaded front
face is 96 cm². Find the total volume of the solid. (The figure is not drawn to scale.)

Answer: cm³

📖 REMINDER: Use the shaded front face to find the size of one cube before finding the total volume.

PE2,MGPS,2025,PE2MGPS2025

22. A bag contains marbles of three different colours. ²⁄₅ of the marbles are blue. The ratio of the number of
red marbles to green marbles is 3 : 4. Find the ratio of the number of blue marbles to that of the green marbles.

Answer:

📖 REMINDER: Represent all marbles using the same total number of equal parts.

MGPS,2025,PE2MGPS2025,Ratio

23. A long bookshelf can hold a maximum of 80 books.A librarian arranges Comic books and Math books on the shelf.
There must be at least 6 Math books placed between any 2 Comic books. What is the greatest number of Comic books
that can be placed on the shelf?

Answer: comic books

📖 REMINDER: To maximise the number of Comic books, use the minimum number of Math books require between them.

MGPS,2025,PE2MGPS2025,Model Drawing

24. Lily had $6a. After buying some notebooks at $3 each, she had $a left. How many notebooks did she buy?
Give your answer in terms of a.

Answer:

📖 REMINDER: Find the amount spent first, then divide by the cost of one item.

MGPS,2025,PE2MGPS2025,Algebra,Primary 5

25. In the figure below, ABCD is a rectangle and DMEF is a square. M is the midpoint of line AB.
Given that AB = 24 cm and BC = 5 cm, find the perimeter of the square DMEF.
(The figure is not drawn to scale.)

Answer: cm

📖 REMINDER: Use the midpoint and right-angled triangle to find the side length of the square.

26. A table with 4 columns is filled with numbers in a pattern as shown below.

Column A	Column B	Column C	Column D
3	4	5	6
10	9	8	7
11	12	13	14
18	17	16	15
…	…	…	…

In which column will the number 268 appear?

Answer:

📖 REMINDER: Look for how the numbers increase row by row and how the order changes.

27. The usual price of a pair of running shoes is $150. During a storewide sale,
Sarah bought the shoes at a discount of 30%. How much did Sarah pay for the shoes?

Answer: $

📖 REMINDER: You may either find the discount first or find the percentage of the price paid.

MGPS,2025,PE2MGPS2025,Percentage

28. The usual price of a basketball is $160.During a sale, Laura bought the basketball at a discount of 25%.
How much did Laura pay for the basketball?

Answer: $

📖 REMINDER: You can either find the discount amount first or find the percentage of the price paid.

MGPS,2025,PE2MGPS2025,Percentage

29. Tom had a 1.5-m long metal wire. He used some of it to form an equilateral triangle with sides of (3p + 5) cm.
He had 99 cm of wire left. What is the value of p?

Answer:

📖 REMINDER: Make sure all units are the same before forming the equation.

MGPS,2025,PE2MGPS2025,Algebra,Primary 6

30. The sum of three different 3-digit numbers is 405. Of the three numbers, find the largest possible number.

Answer:

📖 REMINDER: To maximise one number, make the other numbers as small as possible.

31. Participants of a shooting contest must obtain at least a certain score in the first round to qualify for the second round.
There were 200 participants in the first round and the table below shows the number of participants for each score.

Score	Number of participants
0	40
1	38
2	36
3	34
4	32
5 or more	20

65% of the participants did not qualify for the second round.
From the table, what was the lowest score of a participant who qualified for the second round?

Answer:

📖 REMINDER: Find how many participants did not qualify, then use cumulative totals from the lowest score.

32. A school needs 30 strips of decorative paper, each of length 45 cm, for an art activity.The decorative paper is sold in
rolls of 4 m each. What is the least number of rolls of decorative paper the school needs to buy?

Answer: rolls

📖 REMINDER: Find the total length needed first, then divide by the length of one roll.

MGPS,2025,PE2MGPS2025,Measurement

33. The figure below is made up of 5 identical rectangles.The total height of the figure is 24 cm.
The breadth (width) of one rectangle is 6 cm.Find the area of the figure.

Answer: cm²

📖 REMINDER: Find the dimensions of one rectangle first before finding the total area.

MGPS,2025,PE2MGPS2025,Measurement

34. The graph below shows the number of visitors to a Science Centre from January to May.

(a) What was the average number of visitors per month from January to May?

(a) visitors

(b) What was the percentage increase in the number of visitors from January to February?

(b) %

📖 REMINDER: Average = Total ÷ Number of months . Percentage increase = Increase ÷ Original × 100%

MGPS,2025,PE2MGPS2025,Data Analysis

35. A bar graph shows the number of four different flavors of cupcakes (A, B, C, D) sold at a bakery.
300 cupcakes were sold altogether.Flavor A sold 120 cupcakes. The number of Flavor C cupcakes
sold was ²⁄₃the number of Flavor D cupcakes sold. The total amount collected from the sales of
Flavor C and Flavor D was $240.

(a) How many Flavor C cupcakes were sold?

Answer: (a) Flavor C cupcakes

(b) How many Flavor B cupcakes were sold?

Answer: (b) Flavor B cupcakes

📖 REMINDER: Use the ratio C:D = 2:3. Set up a money equation for C and D to find the unit value.

36. Two friends, Liam and Noah, completed a 12 km hike. They started together. Liam reached the end 10 minutes before Noah,
who was 2 km behind him at that moment. Noah hiked at a steady pace and finished at 11:00 a.m.

(a) At what time did they start hiking?

Answer: (a) a.m.

(b) What was Liam's average speed for the hike in m/min?

Answer: (b) m/min

📖 REMINDER: Find Noah's speed from the final 2 km he covered in 10 minutes after Liam finished.

MBSP,2024,PE2MBSPWA22024,Measurement

37. The graph shows the cost of using data for two mobile plans, Plan X and Plan Y.

(a) How much does it cost to use the first 3 GB of data when using Plan X's service?

Answer: (a) $

(b) Mark used Plan Y's service and paid $12.00 for his data. How much data did he use?

Answer: (b) GB

(c) Anna and Ben each used 8.5 GB of data. Anna used Plan X while Ben used Plan Y.
What is the difference in the amounts they paid?

Answer: (c) $

📖 REMINDER: Read the graph carefully. Note where the cost lines change slope or become flat.

PE2,MGPS,2025,PE2MGPS2025,Data Analysis

38. At a school concert, 30 performers invited either 1, 2, or 3 friends. The ratio of performers who invited 1 friend to those
who invited 2 friends was 2:1. There were 50 friends altogether. Find the number of performers who invited 3 friends.

Answer: performers

📖 REMINDER: Use the ratio to define the groups. The total number of performers and the total number of guests create two equations.

39. Bala had 120 more stamps than Charles at first. Each of them gave Ali some of their stamps.
The number of stamps Charles gave Ali was ²⁄₅ of the stamps Bala had at first. The number of
stamps Bala gave to Ali was ³⁄₅ of the number of stamps Charles had at first. After giving,Bala
and Charles had an equal number of stamps left.

How many stamps did Bala have at first?

Answer: stamps

📖 REMINDER: Let Bala's initial stamps be B and Charles's be C. Set up equations based on the given fractions and the final equal amounts.

40. Tom built a garden path using 3 rectangular blocks and 2 identical curved blocks.
A curved block is a quarter-circle corner piece as shown in Figure 1. The width of the path is 7 m.

- The curved piece has an inner radius equal to the width of the path (7 m).
- The total vertical height of the path layout is 50 m.
- The top and bottom rectangular pieces are each 10 m long.
- The middle vertical rectangular piece has length x.

(a) Find the length of x.

Answer: (a) m

(b) Find the area of the entire path. (Take π = ²²⁄₇)

Answer: (b) m²

📖 REMINDER: The outer radius of the curved piece is the inner radius plus the width. The total height is the sum of the two outer radii and the middle vertical piece x.

PE2,HPPS,2025,PE2HPPS2025,Measuremen

Primary 6 Maths Preliminary Exam 2025 – Test 6

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