Primary 6 Maths Preliminary Exam 2025 – Test 3

1. What is ninety-eight thousand and seven in numerals?

📖 REMINDER: Write the number in words clearly, then identify the place value for each part (thousands, hundreds, tens, ones).

1. 987

2. 9807

3. 98 007

4. 980 007

2. Which one of the following fractions is smaller than ²⁄₅?

📖 REMINDER: Compare each fraction to the given fraction by finding a common denominator or converting to decimals.

1. ¹⁄₂

2. ³⁄₈

3. ⁴⁄₉

4. ³⁄₇

3. Maria had 250 stamps. She used 40 stamps for her collection.
What percentage of her stamps did she use for her collection?

📖 REMINDER: Percentage = (Part / Whole) × 100%.

1. 82%

2. 62%

3. 16%

4. 84%

4. ABCD is a square and AC is a diagonal. Point P lies on the side BC. Given that ∠PAC = 26°, find ∠PAB.

📖 REMINDER: The diagonal of a square bisects the right angles at its corners.

1.15°

2.19°

3.26°

4.45°

5. ABCD is a rectangle. BD is a diagonal, and line AE is drawn such that it intersects the diagonal at point F.
Given that ∠BAE = 35° and ∠ADB = 28°, find ∠x (which is ∠AFD).

📖 REMINDER: Use properties of rectangles (parallel sides, 90° angles) and triangle angle sum.

1.62°

2.83°

3.97°

4.118°

6. Arrange these distances from the shortest to the longest.
3.08 km , 3 km 60 m , 3¹⁄₄ km

📖 REMINDER: Convert all distances to the same unit (kilometers) before comparing.

1. 3.08 km, 3¹⁄₄ km, 3 km 60 m

2. 3 km 60 m, 3.08 km, 3¹⁄₄ km

3. 3 km 60 m, 3¹⁄₄ km, 3.08 km

4. 3¹⁄₄ km, 3 km 60 m, 3.08 km

7. Benjamin went hiking from 7.20 a.m. to 5.35 p.m. How long was his hike?

📖 REMINDER: Calculate the duration by finding the time difference.

1. 9 h 15 min

2. 10 h 15 min

3. 9 h 45 min

4. 10 h 45 min

8. The pie chart below shows the number of visitors at a science center over 4 days. 120 visitors were there on Wednesday.
How many visitors were there on Thursday?

📖 REMINDER: A right angle (90°) is 1/4 of a full circle (360°), which corresponds to 25%.

1. 85

2. 48

3. 72

4. 15

9. The figure below shows a shaded "curved frame."
- The outer boundary is a large semicircle with a radius of 18 cm.
- The inner boundary is a medium semicircle with a radius of 12 cm.
- The two ends are closed by two identical small semicircles.

Find the perimeter of the shaded figure. (Take π = 3.14)

📖 REMINDER: The perimeter consists of three curved parts: the outer semicircle arc, the inner semicircle arc, and the two small semicircular ends (which together form one full circle).

1. 75.36 cm

2. 94.20 cm

3. 103.62 cm

4. 113.04 cm

10. In the figure below, PQRS is a parallelogram and TUV is a triangle. SRV is a straight line.
Line PS is parallel to line TU (PS ∥ TU).Given that ∠UTV = 68° and ∠QRV = 57°, find the value of ∠n.

📖 REMINDER: Use properties of parallel lines and angles in triangles and parallelograms.

1. 120°

2. 123°

3. 125°

4. 127°

11. Leo had $360 and Mia had $120 at first. After both of them spent an equal amount of money on a game,
the amount of Leo's money left was 4 times the amount of Mia's money left. How much money did Leo have left?

📖 REMINDER: Both spend the same amount. The relationship between what's left is given.

1. $320

2. $280

3. $240

4. $200

12. Emily packed 90 apples and 108 oranges into as many baskets as possible with no fruits left unpacked.
She packed the same number of fruits in each basket. The number of each type of fruit in each basket
was the same. How many baskets of fruits did Emily pack?

📖 REMINDER: Find the greatest common divisor (GCD) of the two fruit quantities to determine the maximum number of baskets.

1. 7

2. 9

3. 12

4. 18

13. Round 23.157 to the nearest tenth.

Answer:

📖 REMINDER: Look at the hundredths digit to decide whether to round the tenths digit up or leave it unchanged.

14. Find the value of ⁸⁄₉ ÷ 12. Give your answer as a fraction in the simplest form.

Answer:

📖 REMINDER: Dividing by a whole number is the same as multiplying by its reciprocal.

15. Liam used blue ribbons and yellow ribbons to decorate a gift box. For every 3 blue ribbons Liam used,
he used 2 yellow ribbons. Liam used a total of 60 ribbons. How many yellow ribbons did Liam use for the gift box?

Answer: {{{24}}} yellow ribbons

📖 REMINDER: Find the total number of parts in the ratio first, then find the fraction that represents the yellow ribbons.

16. The total mass of 8 boxes is 9.68 kg. Each box has the same mass. What is the mass of 12 such boxes?

Answer: kg

📖 REMINDER: Find the mass of one item first, then multiply by the required number of items.

17. The graph below shows the number of books read by a group of students during their school holidays.

(a) How many students read at least 3 books?

Answer: books

📖 REMINDER: "At least 3 books" means 3 books or more (3 and 4 books in this case). Read the values from the graph carefully.

18. James bought 4 packs of cards. Each pack contained n cards. He kept 4 cards for himself and gave the rest of
the cards equally to his 8 friends.

(a) How many cards did each friend receive in terms of n?

Answer: (a) cards

(b) Each friend received 7 cards from James. Find the value of n.

Answer: (b) n =

📖 REMINDER: First find the total cards, subtract what James kept, then divide equally among friends.

19. The square grid below shows the positions of Points A, B, C, D, E, and F.

(a) Tom walked directly from Point C to Point B in a straight line. In which direction did Tom walk?

Answer: (a)

(b) Lisa stood at Point B at first. After she turned 90° anti-clockwise, she faced Point F. Which point was Lisa facing at first?

Answer: (b) Point

📖 REMINDER: Use the grid positions and compass directions. For turning problems, reverse the rotation to find the original direction.

20. In the figure below, XOY is a straight line. The reflex angle ∠XOZ is 215° and the reflex angle ∠ZOW is 245°. Find ∠XOW.

📖 REMINDER: Add the reflex angles for total rotation, then subtract 360° if needed to find the final angle.

1. 80°

2. 90°

3. 100°

4. 110°

21. Benjamin traveled from City P to City Q. He traveled at an average speed of 75 km/h for a total distance of 225 km.
He reached City Q at 5:30 p.m. What time did Benjamin leave City P?

Answer: p.m.

📖 REMINDER: Use the formula: Time = Distance ÷ Speed, then subtract the travel time from the arrival time.

22. A rectangular block is formed by joining a cube and a cuboid as shown.

What is the length (L) of the cuboid part of the block?

Answer: cm

📖 REMINDER: Find the cube's volume first, then subtract from total volume to get cuboid volume. Use the shared dimensions to find the missing length.

23. This figure is made up of 4 identical squares, an equilateral triangle, and a semicircle.

Find the perimeter of the figure. Leave your answer in terms of π.

📖 REMINDER: Find the side length of each square first, then calculate each component's perimeter contribution separately.

1. (99 + 4π) cm

2. (99 + 4.5π) cm

3. (108 + 4.5π) cm

4. (108 + 5π) cm

24. Jamie baked some cookies. He gave ¹⁄₆ of the cookies to his neighbors and ¹⁄₄ of the cookies to his friends.
He sold ¹⁄₂ of the remaining cookies. At the end of the day, he was left with 42 cookies. How many cookies
did Jamie give to his neighbors?

Answer: cookies

📖 REMINDER: Work backwards from the final amount using fractions. Find the original total first, then calculate what was given away.

25. The figure shows the amount of liquid in two identical small beakers and one large measuring jug at first.
All the liquid from both beakers was poured into the jug without any spilling over. What would be the total
volume of the liquid in the jug in the end? Give your answer in millilitres (ml).

Answer: ml

📖 REMINDER: First find the volume in each container by reading the scale markings, then add all volumes together.

26. ABCD is a rhombus and BEFD is a rectangle. Given that ∠BCD = 68°, find the value of ∠ADF.

Answer: °

📖 REMINDER: Use properties of rhombus (diagonals bisect angles) and rectangle (all angles are 90°).

27. At first, the bottles in a warehouse were placed on 80 shelves with an equal number of bottles on each shelf. 8 shelves were removed and the bottles on these shelves were placed on the remaining 72 shelves. The number of bottles on each remaining shelf was 50. How many bottles were removed from the 8 shelves?

Answer: bottles

📖 REMINDER: Find the total number of bottles first, then work out how many were on the removed shelves.

28. David had five fewer $1 coins than 20¢ coins. He used all his $1 coins and three 20¢ coins. The total value of the 20¢ coins left was $2.40. How much money did David use?

Answer: $

📖 REMINDER: Set up equations based on the coin quantities, then calculate the total value used.

29. In a stationery shop, erasers are sold in packs of 6 for $5 and pencils are sold in packs of 9 for $12.

Sarah bought the same number of erasers and pencils. She spent $156 altogether. How many pencils did Sarah buy?

Answer: pencils

📖 REMINDER: Find the LCM to create a combined set, then calculate how many sets were bought.

30. The figure below is made up of two identical parallelograms, ABDH and HDEG, and a triangle EFG. ABC and DEF are straight lines.
Triangle EFG is an isosceles triangle where GE = EF.

(a) Find ∠AHG.

Answer: (a) °

(b) Find ∠EFG.

Answer: (b) °

📖 REMINDER: Use parallelogram properties (opposite angles equal, adjacent angles supplementary) and isosceles triangle properties.

31. The table shows the number of cookies sold at a bakery last week.

Day	Number of cookies sold
Monday to Friday	3p per day
Saturday	p + 20
Sunday	6p + 2

(a) How many cookies were sold altogether last week? Express your answer in terms of p in the simplest form.

Answer: (a) p +

(b) Each statement below is either true, false or not possible to tell from the information given.

Statement	Answer
More cookies were sold on Saturday than on Monday.
Each cookie cost $1.50. The amount of money collected on Monday was $4.5p.

📖 REMINDER: For part (a), sum all the expressions. For part (b), analyze each statement logically based on the algebraic expressions.

32. The table shows how much an electrical company charges for electricity. The charges are before GST.

Usage	Charges
First 180 units	$0.25 per unit
Any usage above 180 units	$0.35 per unit

(a) In January, the Wang family used 260 units of electricity. How much did the Wang family pay for their usage after including a 9% GST?

Answer: (a) $

(b) In February, the charges of electricity for the Wang family was $60.05 before GST. How many units of electricity did the Wang family use in February?

Answer: (b) units

📖 REMINDER: Calculate in two tiers for part (a), then work backwards for part (b).

33. X and Y are two rectangular tanks. At first, X was filled with some water and Y was empty. The base area of Y is 135 cm².
Some water was poured from X to Y without spilling. In the end,the amount of water in Y was 2430 cm³. The height of
water in X was ³⁄₄ the height of water in Y.The amount of water then left in X was ²⁄₃ the amount of water in Y.
What is the base area of X?

Answer: cm²

📖 REMINDER: Remember the formulas: Volume = Base Area × Height. Work step-by-step to find the missing height and volume for Tank X.

34. A book costs $3.80 more than a notebook. Lisa bought twice as many notebooks as books. She spent a total of $102.40.
She spent $6.40 more on the books than on the notebooks. Find the total cost of one notebook and one book.

Answer: $

📖 REMINDER: Define variables for the costs and use the given relationships about total spending and spending differences to set up equations.

35. At first, ²⁄₅ of a fish tank was filled with water. A tap was turned on for more water to flow into the tank.
It was then turned off after 20 minutes. The line graph below shows the amount of water in the tank over the 20 minutes.
(Note: The graph shows that at Time = 0 min, there are 60 litres of water. At Time = 20 min, there are 120 litres of water.)

(a) How many litres of water flowed into the tank in one minute?

Answer : (a) litres/min

(b) At the end of 20 minutes, what fraction of the tank was not filled with water?

Answer : (B)

(c) The tap was turned on again at the same rate as before. How many more minutes did it take to fill the tank completely?

Answer : (c) minutes

📖 REMINDER: Use the graph data to find the flow rate. Relate the initial volume to the fraction of the tank filled to find the total capacity.

36. A sports club had 400 members in 2023. 30% of the members were females and the rest were males.
In 2024, the number of male members increased by 20% and the female members dropped to 84 members.

(a) Find the percentage decrease in the number of female members from 2023 to 2024.

Answer: (a) %

(b) What was the total number of members in the sports club in 2024?

Answer: (b) members

📖 REMINDER: Work step-by-step: first find the initial numbers of males and females, then apply the given percentage changes.

37. Jack bought two gadgets at this sale.

(a) Jack paid a total of $39.00 for the two gadgets. He paid $9.00 less for the second gadget than the first one. How much did he pay for the first gadget?

Answer: (a) $

(b) Find the original price of the first gadget.

Answer: (b) $ (c)

(c) Jack saved a total of $11.00. Find the percentage discount given for the second gadget.

Answer: (c) %

📖 REMINDER: For (a), set up an equation using the total paid and the price difference. For (b) and (c), use the relationship between discount percentage, amount saved, and original price.

38. Sam and Leo went out together with a total of $86. Sam spent 4 times as much money as Leo.
The amount of money Leo had left was $10 more than ¹⁄₂ of what Sam spent. The amount of
money Sam had left was ¹⁄₅ of what Leo had left.

(a) How much money did Leo spend?

Answer: (a) $

(b) How much money did Sam have at first?

Answer: (b) $

📖 REMINDER: Define variables for the amounts spent and left. Use the given relationships to form equations and solve step by step.

39. A garden walkway of length 36 m and width 60 cm is paved using a repeating pattern of circular stepping stones
and rectangular bricks as shown below.

- Section A: A single large circular stone with a diameter equal to the width of the walkway.
- Section B: Four identical rectangular bricks laid side-by-side to fill a square area.

The pattern alternates: Section A – Section B – Section A – Section B… until the end of the walkway. (Take π = 3.14)

(a) How many circular stones and rectangular bricks are used for the entire walkway?

Answer: (a) stones and bricks

(b) The area not covered by the stones or bricks is filled with decorative pebbles. Find the total area covered by pebbles in square meters (m²).

Answer: (b) m²

📖 REMINDER: Ensure all units are consistent (convert meters to centimeters). Calculate the area of circles using πr².

Primary 6 Maths Preliminary Exam 2025 – Test 3

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