P6 Mathematics SA2 2019 — Nanyang

Q: Round 895 547 to the nearest thousand.

C. 896 000. The hundreds digit is 5, so round up: 895 547 rounds to 896 000.

Q: 2 tenths and 6 thousandths is ____.

A. 0.206. 2 tenths = 0.2 and 6 thousandths = 0.006, so 0.2 + 0.006 = 0.206.

Q: In the scale below, what is the value of A?

B. 7.96. Between 7.9 and 8.0 there are 5 equal intervals of 0.02 each. Arrow A points to the 3rd mark past 7.9, which is 7.9 + 0.06 = 7.96.

Q: Which two lines in the square grid are perpendicular to each other?

C. CD and DE. On the square grid, lines CD and DE meet at D at a right angle (a small right-angle square is marked at D), so they are perpendicular.

Q: In the figure below, AOB, COD and EOF are straight lines. ∠DOF = 42° and ∠BOE = 73°. Find ∠AOC.

B. 65°. ∠AOC is vertically opposite ∠BOD. ∠BOD = 180° − ∠DOF − ∠BOE = 180° − 42° − 73° = 65°. So ∠AOC = 65°.

Q: In the square grid below, which shape is a trapezium?

A. (Shape 1). A trapezium has exactly one pair of parallel sides. Shape (1) is the figure with exactly one pair of parallel sides, so it is the trapezium.

Q: The figure below shows a cube. Which of the following is a net of the cube?

A. (Net 1). Net (1) folds up into a closed cube with six faces and no overlapping faces, so it is a valid net of the cube.

Q: Find the value of r such that 4r − r = 24.

C. 8. 4r − r = 3r, so 3r = 24, giving r = 24 ÷ 3 = 8.

Q: The pie chart below shows the volume of water in containers A, B, C, D and E. Which bar graph best represents the information in the pie chart?

C. (Bar graph 3). In the pie chart C is the largest sector, B is the next largest, A is slightly smaller than B, and D and E are small slivers (C > B > A, with D and E small). Bar graph (3) matches this with C tallest, B next, A a little shorter, and D and E short.

Q: Which one of the following is likely to be the height of a vending machine in the school canteen?

B. 2 m. A vending machine is a tall appliance about adult height; 2 m is the only realistic value (20 m is far too tall, 20 cm and 2 cm far too short).

P6 Mathematics 2019 SA2 47 questions 100 marks

Source: Nanyang, 2019

This P6 Mathematics SA2 paper from Nanyang (2019) covers measurement, geometry and angles, average, rate and speed, whole numbers and place value, fractions and ratio across 47 questions worth 100 marks. Practise Mathematics the way it's tested at P6 level in Singapore, with step-by-step answers on LearnBuddy.

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Q1 MCQ 1 mark

Round 895 547 to the nearest thousand.

Q1 Open-ended 2 marks

Adele has n albums. Benjamin has 5n albums. Adele has 8 fewer albums than Benjamin. How many albums does Adele have?

Q2 Open-ended 2 marks

Tap A takes 36 minutes to fill a tank completely. Tap B takes 72 minutes to fill the same tank completely. How many minutes will Tap A and Tap B take to fill the tank completely when they are turned on at the same time?

Q2 MCQ 1 mark

2 tenths and 6 thousandths is ____.

Q3 Open-ended 2 marks

The average number of books that Ada, Baba and Cindy have is 17. Cindy has 21 books. Baba has more books than Ada. At most, how many books does Ada have?

Q3 MCQ 1 mark 🖼 Visual

In the scale below, what is the value of A?

Q4 MCQ 1 mark 🖼 Visual

Which two lines in the square grid are perpendicular to each other?

Q4 Open-ended 2 marks

Susan deposits $50 000 in a bank for one year. The interest rate is 1.8% per year. How much will she have in the bank at the end of one year?

Q5 MCQ 1 mark 🖼 Visual

In the figure below, AOB, COD and EOF are straight lines. ∠DOF = 42° and ∠BOE = 73°. Find ∠AOC.

Q5 Open-ended 2 marks 🖼 Visual

In the figure below, PQRS is a trapezium. TUQ and TSR are straight lines. PQ // SR. ∠PUQ = 80° and ∠QPU = 76°. Find ∠STU.

Q6 Structured 4 marks 🖼 Visual

Mdm Ler has 4 boxes of fruits, Box A, Box B, Box C and Box D. The bar graph below shows the number of fruits in each box. The bar representing Box D has not been drawn. (a) How many more fruits are there in Box C than Box A? (b) Box B contains only pears and oranges. There are 4 more pears than oranges in Box B. How many oranges are there in Box B? (c) The total number of fruits in the 4 boxes is 360. Find the number of fruits in Box D.

Q6 MCQ 1 mark 🖼 Visual

In the square grid below, which shape is a trapezium?

Q7 Structured 4 marks 🖼 Visual

In the figure below, BDEF is a rhombus. ACE is a triangle. ∠ABF = 76° and ∠DBC = 29°. (a) Find ∠BED. (b) Find ∠EAC.

Q7 MCQ 1 mark 🖼 Visual

The figure below shows a cube. Which of the following is a net of the cube?

Q8 Structured 5 marks 🖼 Visual

The figure below shows a large circle and two identical small semicircles. The diameter of the large circle, POQ, is 24 cm. (a) Find the perimeter of the shaded part. Take π = 3.14. (b) Find the total area of the unshaded parts. Take π = 3.14.

Q8 MCQ 1 mark

Find the value of r such that 4r − r = 24.

Q9 MCQ 1 mark 🖼 Visual

The pie chart below shows the volume of water in containers A, B, C, D and E. Which bar graph best represents the information in the pie chart?

Q9 Structured 3 marks 🖼 Visual

In the square grid below, AB and BC form two sides of a parallelogram ABCD. Each side is drawn by joining dots on the square grid with a straight line. In the same way, (a) complete the drawing of parallelogram ABCD. (b) Using the given line BC, complete the drawing of square BCEF such that it does not overlap parallelogram ABCD.

Q10 MCQ 1 mark 🖼 Visual

Which one of the following is likely to be the height of a vending machine in the school canteen?

Q10 Open-ended 3 marks

At a sports shop, each basketball cost $23.60 and each football cost $36.40. Mr Chong bought 3 times as many basketballs as footballs. He spent $550.40 more on the basketballs than the footballs. How many footballs did Mr Chong buy?

Q11 Open-ended 3 marks

There are some children in a hall. 5/9 of them are boys. The girls are divided equally into 11 groups. The total number of girls is fewer than 60. There are 6 boys who wear spectacles. How many boys do not wear spectacles?

Q11 MCQ 2 marks

Which one of the following fractions is nearest to 1?

Q12 Open-ended 3 marks

Da Ren has 10 candies. Elijah has 30 candies. Faith has 4 fewer candies than the average number of candies that Da Ren, Elijah and Faith have. How many candies do they have altogether?

Q12 MCQ 2 marks 🖼 Visual

The square grid below shows the positions of points P, Q, R, S and T. Which of the following statements is true?

Q13 Open-ended 3 marks

At 7 a.m., Cyclist A left Town M for Town N. At 8 a.m., Cyclist B left Town M for Town N. Cyclist A travelled at a constant speed of 15 km/h and Cyclist B travelled at a constant speed of 10 km/h. Both cyclists did not change their speeds throughout. After arriving at Town N, Cyclist A immediately left Town N for Town M. Cyclist A and Cyclist B passed each other at 11 a.m. At what time did Cyclist B arrive at Town N?

Q13 MCQ 2 marks 🖼 Visual

What is the reading shown on the weighing scale below?

Q14 MCQ 2 marks

The height of Ashley is 2/3 of the height of Zheng Xin. The ratio of the height of Zheng Xin to that of Chloe is 4 : 5. Find the ratio of the height of Chloe to the total height of Zheng Xin and Ashley.

Q14 Structured 4 marks 🖼 Visual

In the figure below, X and Y are identical rectangular tanks. X has a square base of side 16 cm and a height of 64 cm. At first, X was completely filled with water and Y was empty. John poured the water from X to Y, without spilling, until the height of the water level in X became 22 cm. (a) How much water was there in Y in the end? (b) Find the height of water in Y in the end.

Q15 MCQ 2 marks

The first 22 numbers of a number pattern are given below. 2, 2, 0, 1, 4, 2, 2, 2, 0, 1, 4, 2, 2, 2, 0, 1, 4, 2, 2, 2, 0, 1, ... Find the sum of the first 48 numbers in the number pattern.

Q15 Structured 4 marks 🖼 Visual

The figure below shows a grey cube and a white cube. The length of each edge of the grey cube is twice that of the white cube. Xin Neng wants to use 5 grey cubes and the least number of white cubes to build a new cube. (a) How many white cubes does Xin Neng need to build the new cube? (b) Given that the volume of the new cube is 1728 cm³, find the length of the edge of the white cube.

Q16 Structured 4 marks 🖼 Visual

The table below shows the number of pens in each type of bag (Red 40, Blue 50, Green 60). (a) Mdm Ng has a total of 8 red and green bags. Find the smallest possible difference between the total number of pens in Mdm Ng's red bags and the total number of pens in her green bags. (b) Mr Lee has some red and some blue bags. The ratio of the total number of pens in Mr Lee's red bags to the total number of pens in his blue bags is 6 : 5. Express the number of his blue bags as a fraction of the total number of his bags.

Q16 Open-ended 1 mark

Amanda had 2 m of ribbon at first. She used 80 cm of the ribbon. What fraction of the ribbon did she use?

Q17 Open-ended 1 mark

Express 6.04 kilograms in grams.

Q17 Structured 5 marks 🖼 Visual

Joong Ki, Minho and Ali have some green and some red buttons. Joong Ki has 9 more buttons than Minho. Minho has 5 more green buttons than Joong Ki. The ratio of the number of red buttons that Joong Ki has to the number of red buttons that Minho has is 5 : 3. The ratio of the number of green buttons to red buttons Ali has is 3 : 1. (a) How many red buttons do Joong Ki and Minho have altogether? (b) Each statement below is either true, false or not possible to tell from the information given. For each statement, put a tick (✔) to indicate your answer. Statement 1: Ali has 11 more green buttons than red buttons. Statement 2: The total number of buttons that Joong Ki, Minho and Ali have is an odd number.

Q18 Open-ended 1 mark 🖼 Visual

The figure is made up of identical squares. Shade two more squares so that the figure has exactly one line of symmetry.

Q19 Open-ended 1 mark 🖼 Visual

Johnson stacked 13 unit cubes and glued them together to form the solid below. Draw the side view of the solid on the grid below.

Q20 Open-ended 1 mark 🖼 Visual

The solid below is formed by unit cubes. How many unit cubes are there?

Q21 Open-ended 2 marks

Write down the common multiple of 3 and 5 that is nearest to 27.

Q22 Structured 2 marks

A wallet costs $30.40. A belt costs $16.60 less than the wallet. (a) Find the cost of the belt. (b) Find the cost of 40 such wallets.

Q23 Open-ended 2 marks 🖼 Visual

The opening hours of a shop are shown below. How long is the shop open each day? Give your answer in hours and minutes. (Sign: The Precious Bear Shop, Open Daily 10.30 a.m. to 5.45 p.m.)

Q24 Open-ended 2 marks

There were 500 people at a food fair on Monday. On Tuesday, there were 400 people at the food fair. What was the percentage decrease in the number of people who went to the food fair from Monday to Tuesday?

Q25 Open-ended 2 marks

Mrs Tham bought 2780 beads to make some necklaces. She used 9 beads for each necklace. What was the greatest number of such necklaces made by Mrs Tham?

Q26 Open-ended 2 marks

Andy has 1/2 ℓ of oil. He has 1/5 ℓ less oil than Mei Yan. How much oil does Mei Yan have?

Q27 Open-ended 2 marks

Mr Chan packs 3/4 kg of curry powder into small packets. Each small packet contains 1/8 kg of curry powder. How many small packets of curry powder are there?

Q28 Open-ended 2 marks 🖼 Visual

In the figure below, WXY and WZY are isosceles triangles. WX = YX and WZ = YZ. ∠WXY = 70° and ∠YWZ = 35°. Find ∠XYZ.

Q29 Open-ended 2 marks 🖼 Visual

In the figure below, STUV is a parallelogram. ∠STU = 107° and ∠TSW = 53°. Find ∠VSW.

Q30 Open-ended 2 marks

The length and breadth of a rectangle are 3y metres and (y + 1) metres respectively. Find its perimeter given that y = 5.