P6 Mathematics SA2 2012 — Nanyang

Q: Arrange the following numbers from the largest to the smallest. 34 899, 34 989, 34 909, 34 999

D. 34 999, 34 989, 34 909, 34 899. Ordering from largest to smallest: 34 999 > 34 989 > 34 909 > 34 899, which is option D.

Q: 248 + 303 = 999 − [ ? ] The missing number in the box is __________.

A. 448. 248 + 303 = 551. So 999 − ? = 551, giving ? = 999 − 551 = 448.

Q: Which one of the following pairs of numbers has 8 as a common factor?

D. 16 and 24. 16 = 8 × 2 and 24 = 8 × 3, so 8 divides both. Hence 16 and 24 share 8 as a common factor.

Q: In 934.825, what does the digit 2 stand for?

B. 0.2 tenths. The digit 2 is in the hundredths place, so it stands for 2 hundredths = 0.02, which equals 0.2 tenths (0.2 × 0.1 = 0.02).

Q: Which one of the following is the closest estimate of 69.2 × 48.7?

D. 3 500. Rounding, 69.2 ≈ 70 and 48.7 ≈ 50, so 70 × 50 = 3 500.

Q: A group of children was asked to name their favourite type of cake. The pie chart below shows their preferences. The number of children who liked chocolate cakes was 6 times the number of children who liked mango cakes. How many children liked cheesecakes?

A. 45. Chocolate = 6 × mango = 6 × 15 = 90 children, which is 60% of the total, so total = 90 ÷ 0.6 = 150. Cheese = 150 − 90 − 15 = 45.

Q: In the figure below, XU, WZ, YO and VO are straight lines. ∠YOX = ∠VOW = 90°. Which of the following 2 angles will not always add up to 90°?

B. ∠a and ∠c. With ∠YOX = ∠VOW = 90°, angles a and b sum to 90° (within ∠YOX), c and d sum to 90° (within ∠VOW), and a and d also sum to 90°. However ∠a and ∠c are not constrained to add up to 90°.

Q: The figure below shows a cube with 3 printed sides. All faces are unshaded. Which one of the following is a net of the cube?

D. net option 4. Only option D folds into the cube with the printed/dotted edges lining up correctly to match the three shown faces.

Q: Simplify the following algebraic expression: 4h + 3 × 12 + (12h + 3h) ÷ 5h

C. 16h + 3. (12h + 3h) ÷ 5h = 15h ÷ 5h = 3, and combining the h-terms gives 16h, so the expression simplifies to 16h + 3.

Q: Anna paid $963, inclusive of a 7% GST, for a washing machine. What was the amount of GST that she paid?

B. $63. $963 represents 107% of the pre-GST price. GST = 963 × 7/107 = $63.

P6 Mathematics 2012 SA2 48 questions 100 marks

Source: Nanyang, 2012

This P6 Mathematics SA2 paper from Nanyang (2012) covers measurement, money, patterns and algebra, ratio, percentage and geometry and angles across 48 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

Arrange the following numbers from the largest to the smallest. 34 899, 34 989, 34 909, 34 999

Q1 Open-ended 2 marks

Aisha bought 12 mangoes which were sold at 3 for $10. She then used her remaining amount of money to buy 12 oranges which were sold at 4 for $5. How much money did she have at first?

Q2 Open-ended 2 marks 🖼 Visual

In the figure below, the area of the square ABDE is 100 cm². Line FC is parallel to Line AB. The ratio of the shaded parts to the unshaded part is 1 : 3. Find the area of the unshaded part.

Q2 MCQ 1 mark

248 + 303 = 999 − [ ? ] The missing number in the box is __________.

Q3 Open-ended 2 marks

For every pack of 5 sweets, you get p sweets free. The sweets cost $3 for a pack. The sweets are only sold in packets. How many sweets can you get with $20?

Q3 MCQ 1 mark

Which one of the following pairs of numbers has 8 as a common factor?

Q4 MCQ 1 mark

In 934.825, what does the digit 2 stand for?

Q4 Open-ended 2 marks

Due to the rise in the cost of fuel, an airline has raised the price of the air tickets from $395 to $440. What was the percentage increase in the price of the air ticket? Give your answer correct to the nearest percent.

Q5 MCQ 1 mark

Which one of the following is the closest estimate of 69.2 × 48.7?

Q5 Open-ended 2 marks

The average of 5 odd numbers is 19. The average between the largest and the smallest number is also 19. What is the sum of the remaining 3 numbers?

Q6 MCQ 1 mark 🖼 Visual

A group of children was asked to name their favourite type of cake. The pie chart below shows their preferences. The number of children who liked chocolate cakes was 6 times the number of children who liked mango cakes. How many children liked cheesecakes?

Q6 Open-ended 3 marks

In a quiz, Wei Liang had to answer 20 multiple choice questions. For every correct answer, he would be awarded 3 marks but for every wrong answer, 1 mark would be deducted. Wei Liang answered all the questions and was awarded 36 marks. How many questions did he answer wrongly?

Q7 Open-ended 3 marks 🖼 Visual

Richard went to the money changer to exchange 900 Singapore Dollars for Hong Kong Dollars. At the counter, he saw the table shown below: 1 Singapore Dollar = 0.79 US Dollar 1 Hong Kong Dollar = 0.13 US Dollar What was the amount of Hong Kong Dollars that he exchanged for, correct to the nearest dollar?

Q7 MCQ 1 mark 🖼 Visual

In the figure below, XU, WZ, YO and VO are straight lines. ∠YOX = ∠VOW = 90°. Which of the following 2 angles will not always add up to 90°?

Q8 Open-ended 3 marks 🖼 Visual

Construct a rhombus ABCD below such that ∠ADC is 65° and AD is 6 cm.

Q8 MCQ 1 mark 🖼 Visual

The figure below shows a cube with 3 printed sides. All faces are unshaded. Which one of the following is a net of the cube?

Q9 MCQ 1 mark

Simplify the following algebraic expression: 4h + 3 × 12 + (12h + 3h) ÷ 5h

Q9 Structured 3 marks 🖼 Visual

Keegan drew up a bar graph based on the amount of time he spent on each of the activities in 1 week. a) After totalling up the number of hours that he had recorded in the graph for that week, he realised that he had recorded the time spent on one of the activities wrongly. The time recorded was 10% more than the actual time for that activity. Which activity did he record wrongly? b) What was the actual time taken for the activity that was recorded wrongly in (a)?

Q10 MCQ 1 mark

Anna paid $963, inclusive of a 7% GST, for a washing machine. What was the amount of GST that she paid?

Q10 Open-ended 3 marks 🖼 Visual

Tom started running from Point X in a clockwise direction and John started running from Point Y in an anti-clockwise direction on a 400 m track as shown in the figure below. They started running from directly opposite ends of the track at the same time. Tom ran at an average speed of 160 m/min while John ran at an average speed of 200 m/min. How far would Tom have run by the time they passed each other the second time on the track? Give your answer as a mixed number in the simplest form.

Q11 Open-ended 4 marks 🖼 Visual

The figure below shows an empty open-top metal tank. The external dimensions of the tank are 62 cm by 25 cm by 41 cm. There is an equal thickness of the metal 1.5 cm all around the tank. Water flows from a tap into the tank at a rate of 34 cm³/s for half an hour. Find the volume of water that overflowed.

Q11 MCQ 2 marks

A rope 14.56 m long was first cut into two pieces in the ratio of 2 : 5. The longer piece was then cut into two pieces in the ratio of 2 : 3. Find the length of the longest piece after the two cuts.

Q12 Structured 4 marks 🖼 Visual

In the figure below, ABCD is a square, CDF is an equilateral triangle and AF is a straight line. Find a) ∠AFC b) ∠BEC

Q12 MCQ 2 marks 🖼 Visual

The areas of three faces of the cuboid below are 24 cm², 16 cm² and 6 cm². Find the volume of the cuboid.

Q13 MCQ 2 marks

How many cubes of volume 8 cm³ are needed to build a cuboid measuring 24 cm by 8 cm by 16 cm?

Q13 Structured 4 marks

Both shops, ABC and XYZ, offered a 15% discount for the same type of mattress. If Mr Muthu were to buy from Shop XYZ, he would have paid $38.25 less than the discounted price in Shop ABC. a) What was the difference in the original price of the mattress between the two shops? b) The original price of the mattress in Shop ABC was $1510. What was the minimum percentage discount it must offer so that the discounted price in Shop ABC would be lower than the discounted price in Shop XYZ? Give your answer correct to the nearest percent.

Q14 MCQ 2 marks

Gerry has more stickers than Mary. The ratio of the total number of stickers both have to the difference between the number of stickers each of them have is 13 : 3. Express the number of stickers Gerry has as a fraction of the number of stickers Mary has.

Q14 Open-ended 4 marks 🖼 Visual

Figures A and B below are each formed by overlapping 7 circular rings of radius 10 m each. The ring in the middle in both figures passes through the centres of the 6 outer rings. Use the calculator value of π to find the total area of the shaded regions in both figures, correct to 2 decimal places.

Q15 MCQ 2 marks 🖼 Visual

The picture below shows the landmarks of the Botanic Gardens. From where John was standing as he was reading his map, he realised that the Orchid Garden was on his northeast and the Plant Museum was on his southwest. What landmark was on his southeast?

Q15 Structured 4 marks 🖼 Visual

A photo album was made up of single sheets of plastic which were folded into half to create four pages of the album. Each page was able to hold 2 photos. To make an album for 16 photos, we would need 2 sheets of plastic folded as shown in Figure 1 above. The middle of this album held photos with photo number 7, 8, 9 and 10. a) What were the photo numbers of the photos found in the middle of an album made from 3 sheets of plastic? b) A sheet of plastic was removed from an album, X, which was made up the same way as the photo album above. Photos with photo numbers 23, 24, 49 and 50 were found on the front left and right pages as shown in Figure 2. i) What were the photo numbers of the photos found at the back of this sheet of plastic? ii) How many photos were there in Album X at first?

Q16 Open-ended 1 mark

Kathy mixed 1.5 ℓ of syrup with 6 ℓ of water. She then poured the mixture equally into 25 glasses. How much mixture was there in each glass? Express your answer in millilitres.

Q16 Structured 5 marks

Last month, May spent 1/4 of her income on transport, 9/20 on food and saved the rest. Her income was increased by 1/10 in this month. She spent the same amount on transport but increased her savings by 30%. She saved $780 this month. a) How much did she spend on transport? b) How much did she spend on food this month?

Q17 Open-ended 5 marks 🖼 Visual

Four children decided to find out their total mass. As they did not want their friends to know their individual mass, the children decided to weigh themselves 3 persons at a time. Although the children tried all possible ways of grouping themselves into threes for weighing, only four different readings were repeatedly recorded on the weighing scale: 99.5 kg, 108.1 kg, 111.7 kg, 116.3 kg. Find the combined mass of the heaviest child and the lightest child.

Q17 Open-ended 1 mark

Find the value of 8 2/7 − 2 5/14. Express the answer in the simplest form.

Q18 Open-ended 5 marks

At a swimming meet, School A had 18 more representatives than School B and 6 fewer representatives than School C. The ratio of the number of boys to girls from the three schools was 1 : 3. The ratios of the number of boys to the number of girls in Schools A, B and C were 1 : 3, 1 : 5 and 2 : 5 respectively. How many representatives from the three schools were there in all?

Q18 Open-ended 1 mark

Find the value of 18 × 7 2/9.

Q19 Open-ended 1 mark

Find the value of 12.24 ÷ 6. Leave your answer as a decimal.

Q20 Open-ended 1 mark 🖼 Visual

Chilli Crab Seafood Restaurant opens every day during the time shown in the table below. Opening hours — Lunch: 11.30 a.m. to 3.00 p.m.; Dinner: 6.30 p.m. to 3.30 a.m. How many hours and minutes does the restaurant open each day?

Q21 Open-ended 1 mark

What is 20.04 litres in millilitres?

Q22 Open-ended 1 mark 🖼 Visual

In the figure below, BCDE is a rhombus and DEA is a straight line. Find the value of ∠b.

Q23 Open-ended 1 mark 🖼 Visual

The figure below is made up of equilateral triangles. Shade 2 more triangles so that the figure has three lines of symmetry.

Q24 Open-ended 1 mark

During a recent Science Test, the ratio of Julia's marks to Lynn's marks is 6 : 7. Lynn scored 5 marks more than Julia. What was Julia's marks?

Q25 Open-ended 1 mark

Lee Hui swam a total of 1 km when she was training for a competition. She took 1250 s to cover 1 km. What was her average speed? Give your answer in m/s.

Q26 Open-ended 2 marks

Ali ate 1/4 of a cake. He cut the remaining cake into a number of equal pieces. Each piece was 1/12 of the cake. How many equal pieces did Ali cut the remaining cake into?

Q27 Open-ended 2 marks

The ratio of the length to the breadth of a rectangle is 3 : 2. The area of the rectangle is 600 cm². Find its length.

Q28 Open-ended 2 marks 🖼 Visual

The pattern in the box shows part of a tessellation. Extend the tessellation by drawing two more unit shapes in the space provided within the box.

Q29 Open-ended 2 marks 🖼 Visual

The table below shows the number of each type of coins that Debbie has in her piggy bank. Type of coins: 10¢ = 69, 20¢ = ?, 50¢ = 45. She has a total of $36.60 in her piggy bank. How many 20¢ coins does she have?

Q30 Open-ended 2 marks

Mary made (20y + 2) rice dumplings. She gave 4 rice dumplings to each of her sisters and had 4y rice dumplings left. How many sisters did Mary have?

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