Primary 6 Maths Preliminary Exam 2025 – Test 4

1. Which of the following decimals is the smallest?

📖 REMINDER: Compare the digits in each decimal place, starting from the tenths place.

1.0.21

2.0.12

3.0.201

4.0.102

2. Which of the following is the same as 3060 cm?

📖 REMINDER: Remember that 1 m = 100 cm. Convert all options to the same unit (cm) for comparison.

1.0.36 m

2.3.06 m

3.3 m 60 cm

4.30 m 60 cm

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

📖 REMINDER: For a figure to represent a fraction, the parts must be equal. Find the fraction of shaded area and simplify if needed.

1.A triangle divided into 4 parts by lines from the apex to the base, but the horizontal stripes create parts of unequal size. 1 small part at the top is shaded.

2.A circle divided into 4 equal quarters. 3 quarters are shaded.

3.A 4×4 grid of small squares. 4 of the small squares are shaded.

4.A rectangle divided vertically into 5 equal strips. 1 strip is shaded.

4. Sarah watched a movie at the cinema. The movie lasted for 2 h 30 min. After the movie ended,
she walked 20 minutes to reach her home. She reached home at 5.45 p.m. What time did the movie start?

📖 REMINDER: Work backwards from the time she reached home. Subtract the walking time and then the movie duration.

1.2.55 p.m.

2.3.25 p.m.

3.8.15 p.m.

4.10.35 p.m.

5. The square grid shows the position of 3 landmarks S, H, and T. Mina is standing at a location South of landmark S and
North-west of landmark H. In what direction is landmark T from Mina?

📖 REMINDER: Use the two conditions to pinpoint Mina's location on the grid. Then find the direction from Mina to T.

1.North-east

2.North-west

3.South-east

4.South-west

6. The pie chart shows the number of fruits sold at a stall. The same information is shown in a bar graph,
but the names of the fruits are not shown on the bar graph. The fruits are Watermelon, Orange, Apple, and Grape.

How many fruits were sold for Watermelon and Apple altogether?

📖 REMINDER: Match the tallest bar to the largest pie sector (Watermelon) and the smallest bar to the smallest sector (Grape). Use the bar heights from the graph.

1. 120

2. 130

3. 140

4. 150

7. In the figure below, FCEB and DGE are straight lines. ABC is an equilateral triangle.
Given that FC = CD = CE and ∠CFD = 50°, find ∠CGE.

📖 REMINDER: Use properties of isosceles triangles, angles on a straight line, and the angles of an equilateral triangle (60°).

1. 60°

2. 80°

3. 100°

4. 120°

8. Sam and Tom had $220 altogether at first. After Sam gave Tom $15, Sam had $50 more than Tom. How much did Tom have at first?

📖 REMINDER: Define variables for their initial amounts. Use the "after" scenario to set up an equation relating their final amounts.

WA2,CHPS,2025,PE2CHPS2025,Algebra,Primary 5

1.$40

2. $70

3. $150

4. $180

9. Arrange these volumes from the smallest to the largest:

3.5 L

3¹⁄₂ L

3 L 250 mL

📖 REMINDER: Convert all volumes to the same unit (liters) before comparing.

1.3.5 L, 3¹⁄₂ L, 3 L 250 mL

2.3¹⁄₂ L, 3.5 L, 3 L 250 mL

3.3 L 250 mL, 3¹⁄₂ L, 3.5 L

4.3.5 L, 3 L 250 mL, 3¹⁄₂ L

10. The figure below is formed by joining a quadrant (quarter circle) and a semicircle. The radius of the quadrant is 8 cm.
The diameter of the semicircle is equal to the radius of the quadrant. Find the perimeter of the figure.
Leave your answer in terms of π.

📖 REMINDER: The perimeter is the total length of the outer boundary. Find the arc lengths of the quadrant and semicircle, and include any straight edges on the outside.

1.(6π + 8) cm

2.(8π + 8) cm

3.(8π + 16) cm

4.(12π + 8) cm

11. Lily baked some strawberry muffins and blueberry muffins. She sold an equal number of strawberry muffin
s and blueberry muffins. She had ²⁄₅ of the strawberry muffins and ³⁄₈of the blueberry muffins left.
What fraction of the muffins were sold?

📖 REMINDER: First find the fraction sold for each type, then find the total muffins baked, then calculate the fraction sold overall.

1. ²⁷⁄₄₆

2. ¹⁹⁄₄₆

3. ³³⁄₄₆

4. ³⁷⁄₄₆

12. Write nine million, four thousand and twenty in numerals.

Answer:

📖 REMINDER: Remember the place values: millions, thousands, hundreds, tens, and ones.

13. Round 42 850 to the nearest thousand.

Answer:

📖 REMINDER: Look at the hundreds digit to determine whether to round up or down.

14. Find the value of ⁵⁄₉ + 24.
Give your answer as a fraction in the simplest form.

Answer:

📖 REMINDER: Convert the whole number to a fraction with the same denominator, then add.

15. Find the value of 5m − 12 + ^m⁄₃ when m = 9.

Answer:

📖 REMINDER: Substitute the value of m first, then follow the order of operations.

16. At a fruit stall, there were 450 fruits altogether. ¹⁄₅ of them were apples, ³⁄₅ of them were oranges and the rest were mangoes.
The fruit stall sold ²⁄₃ of the mangoes. How many mangoes did the fruit stall sell?

Answer:

📖 REMINDER: Find the fraction of mangoes first, then the number of mangoes, then how many were sold.

17. The table shows the charges to post a parcel.

Postage Rates	Rate
Mass Step	$2.50
First 600 g	$1.80
Every additional 1 kg	$1.80

Mrs. Lee posted a parcel that weighed 3.6 kg. How much did Mrs. Lee pay to post the parcel?

Answer: $

📖 REMINDER: Pay the mass step charge once, then first step charge, then additional kg charges for the remaining weight.

18. The figure below shows a rectangle WXYZ where WX = 16 cm and XY = 10 cm. Point K lies
on the line ZY such that ZK = 5 cm. Find the area of the shaded triangle WKX.

Answer: cm²

📖 REMINDER: The height of triangle WKX is the vertical distance from base WX to point K.

19. The average mass of some children is 44 kg. There is an equal number of boys and girls. The average
mass of the boys is 46 kg. Each statement below is either true, false or not possible to tell from the
information given. For each statement, select the correct answer

Statement	Answer
The total mass of the boys is heavier than the total mass of the girls.
The mass of each girl is 42 kg.

📖 REMINDER: Use average concepts: overall average is between boy and girl averages when group sizes are equal.

20. Lisa wanted to buy 14 books but found that she needed another $3. She bought 6 books and had $4.20 left.
What was the cost of a book?

Answer: $

📖 REMINDER: Set up equations with the cost per item as the unknown.

21. The figure below is made up of a Circle and a Triangle overlapping each other.

The ratio of the shaded area to the area of the Circle is 3 : 8.
The ratio of the shaded area to the area of the Triangle is 4 : 7.
What is the ratio of the area of the Circle to the area of the Triangle?

Answer:

📖 REMINDER: Make the shaded area units the same in both ratios.

22. At a parade, 95 red balloons and yellow balloons line one side of the street. There are at least 4 red balloons between any
2 yellow balloons. What is the greatest possible number of yellow balloons along the street?

Answer: yellow balloons

📖 REMINDER: Arrange balloons to maximize the yellow ones while keeping at least 4 red balloons between any two yellow ones.

23. Sarah took 120 minutes to cycle 18 km. What was her average speed in km/h?

Answer: km/h

📖 REMINDER: Convert minutes to hours before calculating speed (speed = distance ÷ time).

24. During a promotion, a television was sold for $864 after a 10% discount. How much was the usual price of the television?

Answer: $

📖 REMINDER: The sale price is 90% of the usual price (100% − 10% discount).

25. A shop sells only three types of snacks. The table shows the number of each type of snack sold in the shop.

Type of Snack	Number of snacks sold
Chips	m
Candy	3m + 6
Cookies	52

(a) Find the total number of snacks sold by the shop in terms of m.

Answer: (a) snacks

(b) The shop sold a total of 200 snacks. How many packs of chips did the shop sell?

Answer: (b) packs of chips

📖 REMINDER: Add all expressions for part (a), then solve the equation for part (b).

26. In the figure below, PQR is an isosceles triangle where PQ = QR. QSTU is a parallelogram. PVU is a straight line.
Given that ∠QPR = 50° and ∠RQS = 135°, find ∠SUP.

Answer: °

📖 REMINDER: Use properties of isosceles triangles and parallelograms to find unknown angles.

27. A vendor sold some packs of chips and drinks. Each pack of chips costs $2.80 and each drink costs $4.20.
The vendor sold twice as many packs of chips as drinks. He earned a total of $1176. How many packs of chips did he sell?

Answer: packs of chips

📖 REMINDER: Let the number of drinks be x, then chips = 2x. Set up equation from total earnings.

28. Jack and Sam started cycling from the same place in opposite directions along a straight path. Jack’s speed
was 30 m/min faster than Sam’s speed. Both did not change their speeds.They were 18.72 km apart after they
finished cycling. Jack cycled 2.4 km morethan Sam. What was Sam’s speed in m/min?

Answer: m/min

📖 REMINDER: Use total distance apart and distance difference to find time, then speed.

29. At first, ¹⁄₁₂ of a water tank was filled. A tap was turned on at 08:00 for more water to flow into the tank.
It was turned off at 08:20. The graph below shows the volume of water in the tank over these 20 minutes.

(a) How many litres of water flowed from the tap in 1 minute?

Answer: (a) L/min

(b) At 08:30, the tap was turned on again to fill the tank to the brim at the same rate as before. At what time will the tank be filled to the brim with water?

Answer: (b) am

📖 REMINDER: Use volume increase over time to find flow rate, then find tank capacity from initial fraction full.

30. A sports club designed a metal badge in the shape of a stadium (a rectangle with two semi-circular ends).
The badge has a shaded outer border and an unshaded inner section.

- The outer shape is a rectangle with two identical large semi-circles on the ends.
- The inner section (white) is a smaller rectangle with two identical small semi-circles on the ends.
- The length of the straight part of the badge is 40 cm.
- The total length of the entire badge is 80 cm.
- The radius of the inner (small) semi-circles is 12 cm.
- (Take π = 3.14)

(a) What is the radius of the large outer semi-circles?

Answer: (a) cm

(b) What is the total area of the shaded part of the badge?

Answer: (b) cm²

📖 REMINDER: The total length includes both outer semi-circle radii plus the straight part. Shaded area = area of outer shape − area of inner shape.

31. Mr. Tan and Ms. Lee bought pens at the prices shown below.

(a) Mr. Tan bought an equal number of red pens and blue pens. He spent $6 more on the red pens than on the blue pens. How many pens did he buy altogether?

Answer: (a) pens

(b) Ms. Lee spent an equal amount of money on red pens and blue pens. What fraction of the pens she bought were red? Leave your answer in its simplest form.

Answer: (b)

📖 REMINDER: Use the concept of common multiples to compare costs for equal numbers or equal spending.

32. Liam spent ³⁄₅ of his money on 4 identical pens and 6 identical notebooks. The cost of each pen was twice the cost of each notebook.
He bought some more notebooks with ⁷⁄₈ of his remaining money and had $6 left. How much did Liam spend on the notebooks altogether?

Answer: $

📖 REMINDER: Work step-by-step with fractions of total money and the relationship between pen and notebook prices.

33. Three boys Adam, Ben, and Carl had the same number of coins. Adam and Ben each had a mix of fifty-cent and ten-cent coins.
Adam had 9 ten-cent coins, while Ben had 10 ten-cent coins. Carl had only fifty-cent coins.

(a) How much more money did Adam have than Ben?

Answer: $

(b) Ben used all his fifty-cent coins to buy some food. He then had $6 less in coins than Carl. How many fifty-cent coins did Carl have?

Answer: (b) fifty-cent coins

📖 REMINDER: Let each boy's total coins be N. Use coin counts to compare values, and then form equations in part (b).

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