P6 Mathematics SA2 2018 — Nanyang

Q: Round 1789 to the nearest hundred.

C. 1800. The tens digit of 1789 is 8, which is 5 or more, so round up the hundreds: 1789 rounds to 1800.

Q: Which digit in 31.902 is in the tenths place?

D. 9. The first digit after the decimal point is the tenths place. In 31.902 that digit is 9.

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

B. 0.55. From 0.25 to 0.45 spans 2 equal intervals, so each interval is 0.10. A is one interval beyond 0.45, giving 0.45 + 0.10 = 0.55.

Q: Find the value of 18 − 2p + 2 × 3p when p = 4.

A. 34. Substitute p = 4: 18 − 2(4) + 2 × 3(4) = 18 − 8 + 24 = 34.

Q: Which one of the following is likely to be the length of a school bus?

B. 12 m. A realistic length for a school bus is about 12 m; the other values are far too short or far too long.

Q: In the diagram below, the letters M, A, T and H are drawn on a square grid. Which letter has both parallel lines and perpendicular lines?

D. H. The letter H has two vertical strokes that are parallel to each other, and a horizontal stroke perpendicular to both, so it has both parallel and perpendicular lines.

Q: In the figure below, AOD and COE are straight lines. ∠AOB = 11° and ∠BOE = 28°. Find ∠COD.

C. 39°. ∠AOE = ∠AOB + ∠BOE = 11° + 28° = 39°. ∠COD is vertically opposite ∠AOE (since AOD and COE are straight lines), so ∠COD = 39°.

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

D. Shape (4). A rhombus has four equal sides. Shape (4) is the only one with all four sides equal in length (a slanted diamond), so it is the rhombus.

Q: The figure below shows a cube. Which of the following is not a net of the cube?

D. Net (4). Folding each arrangement of six squares, nets (1), (2) and (3) fold into a cube without overlap. Net (4) causes faces to overlap, so it is not a valid net of the cube.

Q: The pie chart below shows how Joseph spent his time on a Saturday. He spent an equal amount of time on eating and doing homework. Which bar graph best represents the information in the pie chart?

C. Graph (3). From the pie chart, Sleeping is the largest sector, Others is the next largest, and Eating and Doing homework are equal small sectors with Watching TV in between. Graph (3) shows Sleeping tallest, Others next, and equal short bars for Eating and Doing homework, matching the pie chart.

P6 Mathematics 2018 SA2 47 questions 100 marks

Source: Nanyang, 2018

This P6 Mathematics SA2 paper from Nanyang (2018) covers geometry and angles, measurement, area and perimeter, money, fractions and percentage 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 1789 to the nearest hundred.

Q1 Structured 2 marks

Farid had (4k + 6) pencils. He bought another k pencils and packed all the pencils equally into 3 boxes. How many pencils were there in each box? Give your answer in terms of k in the simplest form.

Q2 Structured 2 marks

A bicycle cost $617.10 after a discount of 15%. What was the price of the bicycle before the discount?

Q2 MCQ 1 mark

Which digit in 31.902 is in the tenths place?

Q3 Structured 2 marks

A tank is empty at first. It takes 12 minutes to fill up the tank completely with Tap A alone. It takes 8 minutes to fill up the tank completely with Tap B alone. Starting with an empty tank, how long does it take for both taps together to fill half of the tank?

Q3 MCQ 1 mark 🖼 Visual

In the number line below, what is the value of A?

Q4 MCQ 1 mark

Find the value of 18 − 2p + 2 × 3p when p = 4.

Q4 Structured 2 marks 🖼 Visual

In the figure below, WXYZ is a square. The shaded parts A and B are two squares with different areas. All the corners of squares A and B lie either on the sides of square WXYZ or on the lines WO and XZ. What fraction of the square WXYZ is shaded?

Q5 MCQ 1 mark

Which one of the following is likely to be the length of a school bus?

Q5 Structured 2 marks

A, B and C are different 2-digit numbers. Their average is 30. Find the greatest possible difference between B and C.

Q6 MCQ 1 mark 🖼 Visual

In the diagram below, the letters M, A, T and H are drawn on a square grid. Which letter has both parallel lines and perpendicular lines?

Q6 Structured 3 marks 🖼 Visual

In the square grid below, two sides of a parallelogram have been drawn. Each side is drawn by joining dots on the square grid with a straight line. In the same way, (a) complete the drawing of the parallelogram and [1] (b) draw a trapezium in the square grid with the same perimeter as the parallelogram such that it does not overlap with the parallelogram. [1] (c) Measure and write down the size of an obtuse angle in the parallelogram.

Q7 MCQ 1 mark 🖼 Visual

In the figure below, AOD and COE are straight lines. ∠AOB = 11° and ∠BOE = 28°. Find ∠COD.

Q7 Structured 3 marks 🖼 Visual

In the figure below, ABCD is a square and ECD is an isosceles triangle. ∠DEC = 78° and ∠ABE = 38°. Find ∠BEC.

Q8 MCQ 1 mark 🖼 Visual

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

Q8 Structured 3 marks

Mr Lee has a total of 36 coins. They consist of only 20-cent, 50-cent and $1 coins. He has twice as many $1 coins as 20-cent coins. The total value of the 50-cent coins is $4.40 more than the total value of the 20-cent coins. How many $1 coins does Mr Lee have?

Q9 MCQ 1 mark 🖼 Visual

The figure below shows a cube. Which of the following is not a net of the cube?

Q9 Structured 3 marks

Town P was exactly halfway between Town M and Town N. At 08 00, Nancy started travelling from Town M to Town N while Seo Joon started travelling from Town N to Town M. Nancy travelled at 50 m/min while Seo Joon travelled at 80 m/min. They did not change their speeds throughout the journey. When they passed each other, their distance from Town P was 120 m. At what time did Seo Joon reach Town M?

Q10 MCQ 1 mark 🖼 Visual

The pie chart below shows how Joseph spent his time on a Saturday. He spent an equal amount of time on eating and doing homework. Which bar graph best represents the information in the pie chart?

Q10 Structured 3 marks

Ashley and Wei Shen have the mass of 43.3 kg each. The mass of Bernadette is 1.8 kg less than the average mass of Ashley, Wei Shen and Bernadette. Find the total mass of Ashley, Wei Shen and Bernadette.

Q11 Structured 3 marks 🖼 Visual

In the figure below, EBCD is a trapezium. ED is parallel to BC. ∠FAB = 74° and ∠EBC = 113°. Find the sum of ∠w, ∠x, ∠y and ∠z.

Q11 MCQ 2 marks

Arrange the following fractions from the largest to the smallest. 2/7, 1/5, 4/9, 2/11

Q12 Structured 4 marks 🖼 Visual

Mdm Ler, Mr Chan and Mdm Ng bought some blue and some yellow highlighters. Each blue highlighter cost $0.30 more than each yellow highlighter. The table shows the number of highlighters each of them bought for each colour (Mdm Ler: 10 blue, 17 yellow; Mr Chan: 7 blue, 20 yellow; Mdm Ng: 12 blue, 15 yellow). (a) Mdm Ng spent an equal amount of money on the blue highlighters and on the yellow highlighters. How much did each blue highlighter cost? (b) Find the difference between Mdm Ler's total spending on the highlighters and Mr Chan's total spending on the highlighters.

Q12 MCQ 2 marks

Brian and Charles had some stickers. At first, the number of stickers Brian had was 4/7 of the total number of stickers. Then, Brian sold 3/8 of his stickers. Find the ratio of the number of stickers Brian had at the end to the number of stickers Charles had at the end.

Q13 MCQ 2 marks 🖼 Visual

A thumb drive and a paper clip are placed next to a scale. Find the difference in their lengths.

Q13 Structured 4 marks

At a florist, there was a total of 3616 orchids, tulips and roses. The ratio of the number of orchids to the number of tulips was 3 : 5. After 40% of the orchids, 1/5 of the tulips and 25% of the roses were sold, there were 2644 flowers left in the end. How many orchids were there in the florist at first?

Q14 MCQ 2 marks 🖼 Visual

The square grid below shows the map of a park and its landmarks. The slide is north of the tent. Suresh is standing at a location north of the garden and south-west of the swing. He is facing the pond. Which landmark will he be facing when he turns 45° clockwise?

Q14 Structured 4 marks 🖼 Visual

Jonathan had five identical cuboids. The volume of each cuboid is 675 cm³. He stacked the five cuboids on top of one another neatly to form a big cube as shown below. He then took one of the five cuboids and dipped it into a pail of red paint. Find the area of the cuboid that was painted red.

Q15 MCQ 2 marks

A and B are whole numbers. A has exactly 2 factors. B has exactly 4 factors. C is the product of A and B. At least how many factors does C have?

Q15 Structured 5 marks 🖼 Visual

The line graph below shows the number of pens sold in a bookstore each month from July to December in 2017. (a) In which two months were the number of pens sold the same? (b) Find the total number of pens sold from August to November. (c) Each statement below is either true, false or not possible to tell from the information given in the line graph. For each statement, put a (✓) in the correct column. Statement 1: The increase in the number of pens sold from June to July was less than the increase in the number of pens sold from August to September. Statement 2: The number of pens sold in July was three times the number of pens sold in May.

Q16 Open-ended 1 mark

Ze Hui had 24 marbles at first. He gave 6 marbles to his brother. What fraction of his marbles did he give to his brother? Express your answer as a fraction in its simplest form.

Q16 Structured 5 marks 🖼 Visual

The perimeter of rectangle ABCD is 12 cm more than that of rectangle AMND. The area of rectangle MBCN is 54 cm². (a) Find the length of AD. (b) The perimeter of square EFGH is 12 times the length of AD. Use the calculator value of π to find the area of the circle which touches the 4 sides of square EFGH, correct to 1 decimal place.

Q17 Open-ended 1 mark

The distance between two points is 267 cm. Express this distance in metres.

Q17 Structured 5 marks

Rectangular tanks A and B contained some water. The height of the water level in tank A was equal to that in tank B at first. Tank A had a base area of 3400 cm² and Tank B had a base area of 850 cm². 8500 cm³ of water was poured out from Tank B and the height of the water level decreased by 40% of Tank B. Some water was added into Tank A and the height of the water level increased by 80% in Tank A. (a) Find the total amount of water in the two tanks in the end. (b) Some water was then transferred from Tank A to Tank B without spilling until the height of the water level in both tanks was the same again. What was the height of the new water level in each tank?

Q18 Open-ended 1 mark 🖼 Visual

There are 8 shaded squares in the figure below. Shade 2 more squares to form a symmetric figure with AB as the line of symmetry.

Q19 Open-ended 1 mark 🖼 Visual

The figure below is made up of identical cubes. How many cubes are there in the figure?

Q20 Open-ended 1 mark 🖼 Visual

In which of the following can the area of the shaded face of the cuboid be found?

Q21 Structured 2 marks

How many common factors do 16 and 20 have?

Q22 Structured 2 marks

Jane has $31.70. She has $0.50 less than Bala. Mr Tan has 10 times as much money as Jane. (a) How much money does Bala have? (b) How much money does Mr Tan have?

Q23 Structured 2 marks

This year, ABC Sports Club had 150 members. Last year, it had 120 members. Find the percentage increase in the number of members this year.

Q24 Structured 2 marks 🖼 Visual

The table below shows the carpark charges for a shopping mall. CARPARK CHARGES: 7 a.m. to 6 p.m. — $0.60 for every 30 min. Mr Raj parked his car from 8.30 a.m. to 12 noon in the shopping mall. How much did he pay?

Q25 Structured 2 marks

Jerry had 110 buns. He ate 2 buns and packed the remaining buns equally into 6 packets. How many buns were there in each packet?

Q26 Structured 2 marks

Mrs Tay baked some cupcakes. 1/4 of the cupcakes that she had baked were vanilla cupcakes, 1/5 of the remaining cupcakes were lychee cupcakes and the rest were chocolate cupcakes. She baked 36 chocolate cupcakes. How many cupcakes did she bake in total?

Q27 Structured 2 marks 🖼 Visual

Find the perimeter of the isosceles triangle shown below.

Q28 Structured 2 marks

Jake has $y. Kyra has $(y + 14) more than Jake. Kyra has $68. How much money does Jake have?

Q29 Structured 2 marks 🖼 Visual

In the figure below, WZY and XYZ are triangles. ∠YWZ = 74°, ∠XYZ = 90° and WY = YZ. Find ∠WYX.

Q30 Structured 2 marks 🖼 Visual

In the figure below, WXYZ is a trapezium. WZ is parallel to XY. ∠XWY = 52°, ∠WYZ = 66° and ∠WZY = 55°. Find ∠WXY.

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