Primary 6 Maths Preliminary Exam 2025 – Test 2

12. What is the value of 28 - (6 + 14) + 4 × 3?

Answer:

📖 REMINDER: Remember to follow the order of operations

PE2,AiTPS,2025,PE2AiTPS2025,Whole Numbers,Primary 6

13. In the figure below, AOB, COD, and EOF are straight lines. Given that ∠AOC = 35° and ∠BOF = 118°, find ∠EOC.
(Note: Figure not drawn to scale.)

Answer:   °

📖 REMINDER: Use vertically opposite angles and angle addition on a straight line.

PE2,AiTPS,2025,PE2AiTPS2025,Geometry,Primary 6

14. Find the average of 12, 18, 0 and 6.

Answer:

📖 REMINDER: To find the average, add all the numbers together, then divide by how many numbers there are.

PE2,AiTPS,2025,PE2AiTPS2025,Averages,Primary 6

15. A ribbon was cut into two pieces in the ratio 2 : 7. The length of the longer piece was 42 cm.
What was the length of the ribbon at first?

Answer:   cm

📖 REMINDER: Use the given ratio and the length of the longer part to find the total length.

PE2,AiTPS,2025,PE2AiTPS2025,Ratio,Primary 5

16. The bar graph below shows the time taken by 5 students to complete a 100-meter swimming race.
(Note: Graph not drawn to exact scale here, but similar to original.)

(a) Who was the fastest swimmer?

Answer:

(b) How much longer did David take than Esha to complete the race?

Answer:   s

📖 REMINDER: The fastest swimmer has the shortest time. Subtract Esha’s time from David’s time to find how much longer David took.

PE2,AiTPS,2025,PE2AiTPS2025,Data Analysis,Primary 6

17. A solid cuboid of height 15 cm has a square base of side 8 cm. What is its volume?

Answer:   cm³

📖 REMINDER: Volume of a cuboid = base area × height. 

PE2,AiTPS,2025,PE2AiTPS2025,Measurement,Primary 6

18. In the figure below, rectangle PQRS is made up of 12 identical rectangles.
What fraction of rectangle PQRS is shaded? Express your answer in the simplest form.
(Note: Figure not drawn to scale.)

Answer:

📖 REMINDER: Find the area of each shaded triangle, add them, then divide by the total area of the large rectangle. Simplify the fraction.

PE2,AiTPS,2025,PE2AiTPS2025,Fractions,Primary 6

19.  Tom wants to spend the least amount of money to buy 18 doughnuts.
Each doughnut is sold at $m.  How much will he pay for the doughnuts?
Express your answer in terms of m.

Answer:   m

📖 REMINDER: For every 4 doughnuts, Tom pays for 3. Find how many full sets of 4 fit into 18, then pay full price for any extra doughnuts.

PE2,AiTPS,2025,PE2AiTPS2025,Algebra,Primary 6

20. What is the total volume of water in the three beakers combined? Give your answer in milliliters (ml).
(Note: Diagram not drawn to scale.)

Answer:   ml

📖 REMINDER: Find the value per marking for each beaker, then multiply by the water level mark to find each volume in ml.

PE2,AiTPS,2025,PE2AiTPS2025,Measurement,Primary 6

21. In the figure below , ABCD is a trapezium where AD ∥ BC. Triangle BCF is an isosceles triangle (BF = CF), and
EFC is a straight line. If ∠DAB = 114° and ∠EFB = 80°, find the value of ∠ABF.
(Note: Figure not drawn to scale.)

Answer:   °

📖 REMINDER: Use properties of parallel lines, isosceles triangles, and angles on a straight line to solve step by step.

PE2,AiTPS,2025,PE2AiTPS2025,Geometry,Primary 6

22. The figure is made up of two identical right-angled triangles overlapping each other.
Total height of each triangle = 10 cm and XY = 2 cm. PQ is a straight line.
Find the area of the shaded part. (Note: Figure not drawn to scale.)

Answer:   cm²

📖 REMINDER: When two identical triangles overlap, the shaded area equals the area of the unshaded trapezoid on the left.

PE2,AiTPS,2025,PE2AiTPS2025,Measurement,Primary 6

23. A shop had some bags for sale. After selling 36 bags in the morning and ⁵⁄₈ of the remaining bags in the afternoon,
¹⁄₄ of the bags were left unsold. How many bags were sold altogether?

Answer:   bags

📖 REMINDER: Work backwards from the fraction left to find the original total, then calculate how many were sold.

PE2,AiTPS,2025,PE2AiTPS2025,Fractions,Primary 6

25. Deena had 3.25 kg of flour at first. She used 780 g of it. How many kilograms of flour was left?

Answer:   kg

📖 REMINDER: Convert either both to kilograms or both to grams before subtracting, then give answer in kilograms.

PE2,AiTPS,2025,PE2AiTPS2025,Decimals,Primary 6

26. The line graph below shows the growth of a plant over 4 weeks.

What was the percentage increase in the height of the plant from Week 1 to Week 3?
(Note: Graph not drawn to scale.)

Answer:   %

📖 REMINDER: Percentage increase = [(new height − original height) ÷ original height] × 100%.

PE2,AiTPS,2025,PE2AiTPS2025,Percentage,Primary 6

27. The figure is made of a rectangle (14 cm wide, 20 cm tall) and a semicircle on top (diameter = 14 cm).
An isosceles triangle ABC is inscribed with base BC on the bottom of the rectangle and vertex A at the top of the semicircle.
Find the area of the shaded region (area inside the composite shape but outside the triangle).(Use π = ²²⁄₇)

Answer:   cm²

📖 REMINDER: Find total area of rectangle + semicircle, then subtract area of triangle to get shaded area.

PE2,AiTPS,2025,PE2AiTPS2025,Measurement

28. The figure is formed using 3 identical squares and 2 identical equilateral triangles. The three squares are joined in
a straight row,and the two triangles are attached to the top and bottom sides of the middle square. The total perimeter
of the figure is 160 cm.If XY is a straight line connecting the leftmost vertex to the rightmost vertex, what is the length
of XY?(Note: Figure not drawn to scale.)

Answer:   cm

📖 REMINDER: Find side length by dividing perimeter by number of exterior sides, then XY spans 3 squares horizontally.

PE2,AiTPS,2025,PE2AiTPS2025,Measurement,Primary 6

29. A group of students were asked to choose their favorite after-school club in a survey. The results are represented in the
pie chart below.Half of the students surveyed chose Chess Club or Sports Club as their favorite.
(Note: Pie chart not drawn to scale.) 

(a) What fraction of the students chose Science Club as their favorite? Express your answer in its simplest form.

Answer: 3/10³⁄₁₀

(b) Each of the statements below is either true, false, or not possible to tell from the information given. Select the correct answer.

📖 REMINDER: Use pie chart percentages to find missing fraction. For True/False statements, compare percentages and consider effect of adding new data.

PE2,AiTPS,2025,PE2AiTPS2025,Data Analysis,Primary 6

30. Figure 1 shows an empty tiered container with total height 18 cm. Figure 2 shows it filled with 300 ml of water;
water level is 10 cm high when upright.Figure 3 shows it turned upside down; water level is 14 cm from the ground.
What is the capacity of the container? (1 ml = 1 cm³) (Note: Figures not drawn to scale.)

Answer:   ml

📖 REMINDER: Find base area from upright water volume, then find air gap volume when inverted, and add to water volume for total capacity.

PE2,AiTPS,2025,PE2AiTPS2025,Measurement,Primary 6

31. PQRS is a rhombus. PQU is an isosceles triangle where PQ = QU. S, P, U lie on a straight line. TQR is an equilateral triangle.
Given that ∠SPQ = 124°, find ∠PQU. (Note: Figure not drawn to scale.)

Answer:   °

📖 REMINDER: Use supplementary angles on a straight line and isosceles triangle properties to find the unknown angle.

WA2,MBSP,2024,TestMBSPWA22024,Geometry,Primary 5

32. Ravi read part of a magazine in the morning. The ratio of the number of pages he read to the number of pages that were
unread was 7 : 3.After reading another 120 pages of the magazine in the afternoon, Ravi still had 25% of the magazine
unread. How many pages were there in the magazine?

📖 REMINDER: Start by expressing morning read and unread in terms of total pages using the ratio. Then set up an equation for the afternoon situation.

WA2,AiTPS,2025,PE2AiTPS2025,Ratio,Primary 6

33. Town A and Town B were 360 km apart. Tim left Town A for Town B at 60 km/h. At the same time, Dana left
Town B for Town A at 90 km/h along the same route. How long had they travelled when they met each other?
Express your answer in h and min.

Answer:     h     min

📖 REMINDER: Add their speeds to find how quickly they close the distance, then divide total distance by combined speed to find time.

WA2,AiTPS,2025,PE2AiTPS2025,Speed,Primary 5

34. TA fruit seller had some mangoes. He sold 2⁄5 of them and donated 104 of them. He was left with 1⁄3 of the mangoes and
packed them into 24 bags. Some bags contained 4 mangoes each while the rest contained 6 mangoes each.

(a) How many mangoes were packed?

Answer (a):   mangoes

(b) How many bags contained 6 mangoes each?

Answer (b):   bags

📖 REMINDER: First find the total mangoes using fractions, then the packed quantity, then use simple algebra to find the bag distribution.

WA2,AiTPS,2025,PE2AiTPS2025,Fractions,Primary 5

35. The figure below is composed of a central rectangle with a length of 25 cm and a width of 10 cm. Attached to its left and
right ends are two identical squares with sides of 10 cm. Four identical quarter circles, each with a radius of 10 cm,
round the outer corners of the squares.Two identical shaded circles, each with a diameter of 6 cm, are located inside
the squares.

(a) Find the perimeter of the unshaded part. (Take π = 3.14)

Answer: (a)   cm

(b) Find the total area of the unshaded parts. (Take π = 3.14)

Answer:  (b)   cm²

📖 REMINDER: Carefully identify which lines and curves form the boundary of the unshaded region. For area, sum the areas of the simple shapes that make up the whole figure first.

PE2,AiTPS,2025,PE2AiTPS2025,Measurement,Primary 5

36. Three sisters, Ava, Bella, and Chloe, had the same number of coins. Ava had only fifty-cent coins.
Bella and Chloe each had a mix of fifty-cent and one-dollar coins. Bella had 24 one-dollar coins while
Chloe had 8 one-dollar coins.

(a) Of the three sisters, who had the least and who had the most amount of money?

Answer: (a) Least:      ,     Most: 

(b) Bella used half of her one-dollar coins and some of her fifty-cent coins to buy a dress that cost $22.00. How many fifty-cent coins did Bella use?

Answer:  (b)   fifty-cent coins

(c) What was the difference in the total value of Ava and Chloe's coins?

Answer: (c) $ 

📖 REMINDER: All three start with an equal number of coins. To compare their total money, consider that converting a 50-cent coin to a one-dollar coin increases its value by $0.50.

PE2,AiTPS,2025,PE2AiTPS2025,Money,Primary 5

37. Two rectangular tanks, Tank C and Tank D, are shown below.At first, Tank C was ¹⁄₄ filled with water and Tank D was empty.

(a) What was the volume of water in Tank C at first?

Answer: (a)   cm³

(b) Both taps were turned on at the same time. Water from both taps flowed at the same rate of 3.6 litres per minute.
How long did it take for the height of the water in both tanks to be the same?

Answer:  (b)   minutes

📖 REMINDER: Convert flow rate to consistent units (cm³/min). The rate of water level rise depends on the base area of each tank. Set up an equation where the final water heights are equal.

PE2,AiTPS,2025,PE2AiTPS2025,Rates and Volume,Primary 5