Primary 6 Maths Preliminary Exam 2025 – Test 5

1. Round 417 601 to the nearest thousand.

📖 REMINDER: Identify the thousands digit and look at the hundreds digit to decide whether to round up or down.

1. 417 000

2. 417 600

3. 418 000

4. 420 000

2. 90 + ³⁄₁₀ + ³⁄₁₀₀ = ?

📖 REMINDER: Convert each fraction to its decimal place value and add to the whole number.

1. 90.033

2. 90.33

3. 93.03

4. 93.3

3. Find the value of 65 - 5 × 4 + 18

📖 REMINDER: Follow the order of operations: multiplication before addition and subtraction.

1. 1300

2. 312

3. 63

4. 48

4. A concert started at 19 15 and ended at 21 35. What was the duration of the concert?

📖 REMINDER: Calculate the time difference by breaking it into hours and minutes.

1. 100 min

2. 140 min

3. 160 min

4. 180 min

5. The table shows the number of students who wear and do not wear hats.

	Wear hats	Do not wear hats
Boys	4	6
Girls	12	8

What percentage of the students do not wear hats?

📖 REMINDER: First find the total number of students, then find how many do not wear hats, then calculate the percentage.

1. 80%

2. 46.67%

3. 40%

4. 30%

6. The diagram below shows the net of a cube with faces labeled G to L

When this net is folded into a cube, which two faces will be opposite each other?

📖 REMINDER: Use mental folding: pick a base face and fold the net step-by-step to determine opposite faces.

1. G and I

2. H and L

3. J and K

4. I and J

7. In the figure below, lines AB and CD are parallel (AB ∥ CD). All other lines are straight. Which pair of angles does not add up to 180°?

📖 REMINDER: Use parallel line rules: co-interior angles sum to 180°, angles on a straight line sum to 180°.

1. ∠ a + ∠ b

2. ∠ c + ∠ d

3. ∠ c + ∠ e

4. ∠ b + ∠ e

8. Which of the following figures shows ¹⁄₄ of the figure shaded?

📖 REMINDER: The shape must be divided into equal parts, with exactly one part shaded.

1. (1) Circle divided into 3 equal sectors, 1 shaded.

2. (2) Equilateral triangle divided into 4 equal small triangles, 1 shaded.

3. (3) Hexagon divided into 6 equal triangles, 1 shaded.

4. (4) Rectangle divided into 5 equal strips, 2 shaded.

9. In the diagram below, ABC is a right-angled triangle. D is a point on the base line BC.

Find the area of the shaded triangle ADC.

📖 REMINDER: Use the perpendicular height from A to BC to find the area. DC = BC – BD.

1. 96 cm²

2. 128 cm²

3. 144 cm²

4. 160 cm²

10. The bar graph below shows the number of toy cars sold over 5 days. 72 toy cars were sold on Thursday.

(a). What was the total number of toy cars sold from Monday to Wednesday?

Answer: (a) toy cars

(b). The ratio of the number of toy cars sold on Friday to the number of toy cars sold on Saturday was 6 : 5.
How many toy cars were sold over the 6 days?

Answer: (b) toy cars

📖 REMINDER: Add the values for Q10. For Q11, use the ratio to find Saturday's sales, then sum all 6 days.

11. During a promotion, all items are sold at 25% discount. A customer gets 40% discount when she pays using the store’s mobile app.
What is the percentage increase in the discount given when a customer pays with the app?

📖 REMINDER: Compare the increase in discount percentage relative to the original discount.

1. 15%

2. 37.5%

3. 60%

4. 75%

12. In the figure below, point R is the common vertex for several shapes:

• PQR and RST are right-angled triangles with their 90° angles at vertex R.
• WRX is a 90° corner belonging to a square.
Given that ∠PRW = 38° and ∠XRT = 27°, find ∠SRQ

Answer: °

📖 REMINDER: Use the given right angles (90°) and angle sums to work step-by-step from known angles.

13. Express 4⁷⁄₂₅ as a decimal.

Answer:

📖 REMINDER: Convert the fractional part to hundredths by multiplying numerator and denominator to get denominator 100.

14. Find the value of 15.4 − 9.87

Answer:

📖 REMINDER: Subtract decimals by aligning the decimal points and borrowing if needed.

15. Express 2.5% as a fraction.

Answer:

📖 REMINDER: Convert a percentage to a fraction by writing it over 100, then simplify.

16. The grid shows the layout of a Zoo with 5 animal enclosures.

Which animal enclosure is South-West of the Lion AND North-East of the Zebra?

Answer:

📖 REMINDER: Use compass directions: North = up, South = down, East = right, West = left.

17. Ali is k years old. Ben is 5 times as old as Ali. Chloe is 4 years younger than Ben.

(a) What is the total age of the three people in terms of k?

Answer: (a) k

(b) If k = 8, what is the total age of the three people?

Answer: (b) Total age:

📖 REMINDER: Write each person’s age in terms of k, then add them together for part (a). Substitute k = 8 for part (b).

18. A group of 8 adults and 9 children went to AdventureLand. What was the least amount of money the group could have paid?

AdventureLand Ticket Prices
Child ticket	$10.50
Adult ticket	$20.00
Promotion For every 2 paying adults, 1 child enters free!

Answer: $

📖 REMINDER: Maximize the use of the promotion to get as many free child tickets as possible.

19. ABCD is a straight line. The lengths of AD and AC are in the ratio 5 : 4 and the lengths of BD and AB are in the ratio 3 : 2.

What is the ratio of length AB to length CD?

Answer:

📖 REMINDER: Assign variables to segments, use the given ratios to form equations, then solve for the required ratio.

PE2,HPPS,2025,PE2HPPS2025,Ratio

20. ABCD is a rhombus. BAE and ADF are straight lines. Given ∠AED = 34° and ∠CDF = 68°, find ∠g and ∠h.

Answer: ∠g = ° ∠h = °

📖 REMINDER: In a rhombus, all sides are equal and diagonals bisect the vertex angles. Also, angles on a straight line add up to 180°.

21. A rectangular mural is made of 8 identical rectangular tiles. The top section has 5 tiles stacked horizontally,
and the bottom section has 3 tiles placed vertically side-by-side. If the length of each small tile is 30 cm,
find the perimeter of the large mural.

Answer: cm

📖 REMINDER: In this arrangement, the length of one tile equals the total width of three vertical tiles side-by-side. Use this to find the width of a tile first.

PE2,HPPS,2025,PE2HPPS2025,Geometry

22. A machine started labelling bottles at 10 a.m. at the rate of 720 bottles per hour. For every 2 hours,
the machine stops for 10 minutes. How many bottles can it label by 3.30 p.m. on the same day?

Answer: bottles

📘 REMINDER: Calculate total working time by subtracting break times from the total available time, then multiply by the rate.

23. (a) How many factors are there in 48?

Answer: (a)

(b) Write down the first common multiple of 6 and 9.

Answer: (b)

📖 REMINDER: Factors divide a number exactly. Common multiples are numbers that are multiples of both given numbers.

24. The table shows the time taken by 4 swimmers to complete a race. The time taken by Bala to complete the race is not shown.

Swimmer	Time in seconds (s)
Afiq	50.78
Bala	?
Cayden	48.12
Dai Ming	46.9

The average time taken by the 4 swimmers was 48.7 s. What was the time taken by Bala to complete the race?

Answer: s

📖 REMINDER: Average = Total sum ÷ Number of items. Use this to find the missing value.

PE2,HPPS,2025,PE2HPPS2025,Data Analysis

25. The figure below is made up of a rectangle and a semi-circle. The rectangle has a length of 24 cm and a width of 14 cm.
The semi-circle is attached to the width of the rectangle, and its diameter is equal to the width of the rectangle.
What is the total area of the figure? (Take π = 22/7)

Answer: cm²

📖 REMINDER: The figure's area is the sum of the rectangle's area and the semi-circle's area. The semi-circle's radius is half of the rectangle's width.

PE2,HPPS,2025,PE2HPPS2025,Measurement

26. The table shows the number of boys and girls, and teachers in Schools X and Y. Some information is missing.

	Boys	Girls	Teachers	Total
School X	845	?	?	?
School Y	?	882	?	?
Total	?	1470	?	8670

(a) The total number of people in both schools is 8670. If School Y has 1655 boys, how many boys are there in total in both schools?

Answer: (a) boys

(b) The number of girls in School X is 2/3 of the number of girls in School Y. Find the total number of students in School X.

Answer: (b) students

📖 REMINDER: Part (a): Add boys from School X and School Y. Part (b): Use the ratio to find girls in School X before calculating total students.

PE2,HPPS,2025,PE2HPPS2025,Data Analysis

27. For every laptop that Jenny sells, she earns a sum of money as shown:

Swimmer	Time in seconds (s)
Afiq	50.78
Bala	?
Cayden	48.12
Dai Ming	46.9

Jenny sold a laptop and earned $80. What was the selling price of the laptop?

Answer:

📖 REMINDER: Break the selling price into two parts: the first $200 and the remainder. Calculate earnings from each part using the given percentages.

28. At a shop, erasers were sold in packets of 3 and pens were sold in packets of 5.
Bella paid with a $50-note for 12 erasers and 15 pens. How much change did Bella receive?
Give your answer in terms of q.

	Cost per packet
Erasers	$q
Pens	$2q

Answer: .

📖 REMINDER: First find how many packets of erasers and pens Bella bought, then calculate the total cost in terms of q. Subtract from $50 to find the change.

29. Lisa’s coin box contained 20-cent and 50-cent coins. In the coin box, there were 9 more 50-cent coins than 20-cent coins.
The total amount of money in the coin box was $25.50.

(a) How many coins were in the coin box?

Answer: (a) coins

(b) How much money does Lisa have left in the coin box after spending all her 20-cent coins on snacks?

Answer: $

📖 REMINDER: Let the number of 20-cent coins be x. Then 50-cent coins = x + 9. Write an equation for the total value and solve.

30. Sam cut a rope into 3 pieces. The first piece was 2 m longer than ¹⁄₅ of the original length of the rope.
The second piece was 1 m longer than ¹⁄₂ of the remaining rope after the first cut. The third piece was 10 m.
What was the original length of the rope?

Answer: m

📖 REMINDER: Let the original length = L. Express each piece in terms of L, then form an equation where the sum of all pieces equals L.

31. Mrs Lee bought ³⁄₇ as many muffins as tarts for a party. She spent ⁵⁄₆ as much on each muffin as each tart.
Each muffin cost $7.00. She paid $453.60 more on the tarts than the muffins.

(a) How much did she pay for each tart?

Answer: (a) $

(b) How many tarts did she buy?

Answer: (b) tarts

📖 REMINDER: Let number of tarts = T, number of muffins = (3/7)T. Let price per tart = P, then price per muffin = (5/6)P. Use the cost difference to solve.

32. There were some apples and oranges in a crate. In the morning, when 30 apples were added to the crate,
the ratio of apples to oranges became 4 : 3. Then 40 oranges were removed from the crate and the ratio became 3 : 1.

(a) How many apples were there in the crate at first?

Answer: (a) apples

(b) In the afternoon, more apples and oranges were added. The number of apples increased by 50% and the number of oranges increased by 100%.
Find the total number of apples and oranges added in the afternoon.

Answer: (b) apples and oranges

📖 REMINDER: Let original apples = A, oranges = O. Use the two ratios to set up equations, solve for A and O, then calculate the afternoon increases.

PE2,HPPS,2025,PE2HPPS2025,Ratio

Primary 6 Maths Preliminary Exam 2025 – Test 5

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