P6 Mathematics SA2 2020 — Tao Nan | Singapore Past Year Paper

Q: Farmer Brown harvested 109 436 oranges last year. Express this number to the nearest hundred thousand.

A. 100 000. 109 436 is closer to 100 000 than to 200 000 when rounded to the nearest hundred thousand, since the ten-thousands digit (0) is less than 5. Answer: 100 000.

Q: 20 + 7/10 + 7/1000 = ____.

C. 20.707. 7/10 = 0.7 (tenths place) and 7/1000 = 0.007 (thousandths place). 20 + 0.7 + 0.007 = 20.707.

Q: There are 70 adults and children in a hall. 56 are adults. What is the ratio of the number of children to the total number of people in the hall?

B. 1 : 5. Children = 70 − 56 = 14. Ratio of children to total = 14 : 70 = 1 : 5.

Q: 3 : 9 = 4 : □. What is the missing number in the box?

B. 12. 3 : 9 simplifies to 1 : 3. So 4 : □ must also be 1 : 3, giving □ = 4 × 3 = 12.

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

C. AE and CE. From the figure, lines AE and CE meet at point E forming a right angle (90°), so they are perpendicular to each other.

Q: My teacher paid $25 for 50 notepads. How much did each notepad cost?

C. 50 cents. Cost per notepad = $25 ÷ 50 = $0.50 = 50 cents.

Q: Round each of the numbers to the nearest whole number. What is the estimated value? 32.6 + 40.4 x 9.51

B. 433. Round each number: 32.6 → 33, 40.4 → 40, 9.51 → 10. Then apply order of operations: 33 + 40 × 10 = 33 + 400 = 433.

Q: Find the perimeter of the semicircle. (Take π = 22/7)

B. 36 cm. Diameter = 14 cm so radius = 7 cm. Perimeter of semicircle = ½ × π × diameter + diameter = ½ × (22/7) × 14 + 14 = 22 + 14 = 36 cm.

Q: In the figure, BCDE is a square and BEF is an equilateral triangle. Find ∠BFC.

A. 15°. Triangle BEF is equilateral so BF = BE = side of square = BC, and ∠FBE = 60°. ∠FBC = ∠FBE + ∠EBC = 60° + 90° = 150°. Triangle FBC is isosceles (BF = BC), so ∠BFC = ∠BCF = (180° − 150°) ÷ 2 = 15°.

Q: The mass of Box A is 6 kg. The total mass of Box B and Box C is also 6 kg. What is the average mass of the 3 boxes?

D. 4 kg. Total mass of 3 boxes = 6 + 6 = 12 kg. Average = 12 ÷ 3 = 4 kg.

Q1 MCQ 1 mark

Farmer Brown harvested 109 436 oranges last year. Express this number to the nearest hundred thousand.

Q2 MCQ 1 mark

20 + 7/10 + 7/1000 = ____.

Q3 MCQ 1 mark

There are 70 adults and children in a hall. 56 are adults. What is the ratio of the number of children to the total number of people in the hall?

Q4 MCQ 1 mark

3 : 9 = 4 : □. What is the missing number in the box?

Q5 MCQ 1 mark 🖼 Visual

Which two lines in the figure are perpendicular to each other?

Q6 MCQ 1 mark

My teacher paid $25 for 50 notepads. How much did each notepad cost?

Q7 MCQ 1 mark

Round each of the numbers to the nearest whole number. What is the estimated value? 32.6 + 40.4 x 9.51

Q8 MCQ 1 mark 🖼 Visual

Find the perimeter of the semicircle. (Take π = 22/7)

Q9 MCQ 1 mark 🖼 Visual

In the figure, BCDE is a square and BEF is an equilateral triangle. Find ∠BFC.

Q10 MCQ 1 mark

The mass of Box A is 6 kg. The total mass of Box B and Box C is also 6 kg. What is the average mass of the 3 boxes?

Q11 MCQ 2 marks 🖼 Visual

What percentage of the triangle is unshaded?

Q12 MCQ 2 marks 🖼 Visual

A small square is placed over a large square. The length of each square is a whole number. The area of the large square that is not covered by the small square is 56 cm². What is the perimeter of the large square?

Q13 MCQ 2 marks

A wire is cut into 2 pieces. One piece is made into an equilateral triangle of sides y cm long. The other piece is made into a square of sides 8 cm long. What is the length of the wire before it is cut?

Q14 MCQ 2 marks

A supermarket gave a discount of $3 for every $40 spent. Mr Lim bought some groceries and paid $119. What was the price of the groceries before the discount?

Q15 MCQ 2 marks 🖼 Visual

In the figure, ABCD is a square, CE = CD and ∠EDC = 68°. Find ∠CBE.

Q16 Open-ended 1 mark

Find the value of 40.04 ÷ 8.

Q17 Open-ended 1 mark

Janet completed a race in 148 seconds. She was 15 seconds slower than Stella. How long did Stella take to complete the race? (Give answer in min and s.)

Q18 Open-ended 1 mark 🖼 Visual

The table below shows the charges for a cleaning service. First 2 hours: $100. Every additional hour: $30. Mdm Lee paid the shop $160 to clean her house. How many hours of cleaning did she pay for?

Q19 Open-ended 1 mark

Express 0.5% as a fraction in the simplest form.

Q20 Open-ended 1 mark 🖼 Visual

In the figure, PQ is the line of symmetry. Shade a unit square to make the figure symmetrical.

Q21 Structured 2 marks

Alan is less than 50 years old. His age is a multiple of 5. Next year, his age is a multiple of 7. How old is he now?

Q22 Structured 2 marks

At a party, there were 25% more men than women. There were 180 adults at the party. How many men were there?

Q23 Structured 2 marks 🖼 Visual

The figure below is not drawn to scale. EF, CG and CH are straight lines. ∠GAB is 117° and ∠FBH is 69°. Find ∠ACB.

Q24 Structured 2 marks

Sally had 2 boxes of beads. After transferring 1/7 of the beads from Box A to Box B, the ratio of the number of beads in Box A to the number of beads in Box B becomes 3 : 7. What is the ratio of the number of beads in Box A to the number of beads in Box B at first?

Q25 Structured 2 marks

4 people can sit at a square table, one at each side of the table. 6 people can sit at two square tables joined together. How many tables are needed to form a long table for 50 people?

Q26 Structured 2 marks

Alan spent 1/3 of his pocket money on a shirt and 15% of the remainder on a book. What fraction of his allowance did he spend in all?

Q27 Structured 2 marks 🖼 Visual

The figure is made up of a square and a semicircle. Find the shaded area.

Q30 Structured 2 marks 🖼 Visual

The length of HG is thrice the length of AB. The shaded triangle is 13 cm². Find the area of Rectangle EFGH.

Q31 Open-ended 2 marks

Paper 2 Question 1. What is the missing number in the box? 140 ÷ 20 x □ + (180 − 120) = 270.

Q32 Open-ended 2 marks

Paper 2 Question 2. 3/5 of Lily's savings is equal to 7/12 of Janet's savings. What is the ratio of Janet's savings to Lily's savings?

Q33 Open-ended 2 marks

Paper 2 Question 3. At first, Aaron and Ben were facing the same direction. Aaron then turned 225° clockwise to face North-West while Ben turned 90° clockwise. What direction did Ben face in the end?

Q34 Open-ended 2 marks

Paper 2 Question 4. Alice is 5v years old. Beatty is 18 years younger than Cally. Alice is 2v years older than Beatty. Find, in terms of v, the total age of the 3 children in 2 years' time.

Q35 Open-ended 2 marks 🖼 Visual

Paper 2 Question 5. X, Y and Z are squares in the big square, ABCD. AF = FD. The length of Y is half the length of X. The length of Y is twice the length of Z. What fraction of the figure is shaded?

Q36 Structured 3 marks 🖼 Visual

Paper 2 Question 6. The length of AE is 3.3 m. B is the midpoint of AC. C is the midpoint of BD and D is the midpoint of BE. What is the length of DE in centimetres?

Q37 Structured 3 marks 🖼 Visual

Paper 2 Question 7. The figure below shows two identical right-angled triangles overlapping each other. Find the shaded area.

Q38 Structured 3 marks

Paper 2 Question 8. Denise bought 9 more 26-cent stickers than 32-cent stickers from an online shopping website. She spent a total of $12.78 on these stickers. How many 26-cent stickers did Denise buy?

Q39 Structured 3 marks

Paper 2 Question 9. Mrs Lee went to a sale and paid a total of $600 for a watch and a necklace. The watch was sold to her at a 20% discount. The total discount given for these 2 items was $140. Mrs Lee paid $120 more for the necklace than the watch. What was the original price of the necklace?

Q40 Structured 3 marks

Paper 2 Question 10. Frank had to make 200 toy cars. He made 8 toy cars each day from Monday to Friday and 15 each day on Saturday and Sunday. Starting on a Thursday, on which day of the week did Frank complete making all the toy cars?

Q41 Structured 4 marks 🖼 Visual

Paper 2 Question 11. The figure shows a rectangular aquarium with no matter at first. It is then filled with water up to 3/5 its height. How many litres of water is needed?

Q42 Structured 4 marks 🖼 Visual

Paper 2 Question 12. ABCD is a 5 m by 5 m square house built in a field. The field is 50 m long and 35 m wide. A dog is tied to Corner D of this house with a rope of length 10 m long. Find the maximum area in the field that this dog can move within. (Take π = 3.14)

Q43 Structured 4 marks 🖼 Visual

Paper 2 Question 13. The figure is made up of identical triangles. (a) How many triangles are there in the 10th layer? (b) How many shaded triangles are there in the 100th layer? (c) In which layer will you find 109 triangles?

Q44 Structured 4 marks 🖼 Visual

Paper 2 Question 14. The bar graph shows the number of people in the different age groups. The table below shows the percentage of people in the different age groups who are online food delivery users. (a) Which age group has the most number of people? (b) Which age group has the least number of online food delivery users? (c) The amount of money spent by online food delivery users aged 15 to 24 years old is $115 000 000. What is the average amount of money spent by each of the users in this age group? Give your answer to the nearest whole number.

Q45 Structured 4 marks 🖼 Visual

Paper 2 Question 15. A semicircle is drawn on a square grid. (a) Measure and write down the length of the radius of the semicircle. (b) Draw a rectangle ABCD such that the length of BC is equal to the length of the radius. (c) Join BD and measure ∠ABD.

Q46 Structured 4 marks 🖼 Visual

Paper 2 Question 16. Mr and Mrs Tan lived with their four children in a 5-room flat. The line graph showed the total water usage each week for Mr Tan's family. (a) There was a sharp increase in water usage from Week ____ to Week ____. (b) Find the average water usage for each week. (c) Each statement below is either true, false or not possible to tell from the information given. For each statement, put a tick (✓) in the correct column. (i) The average water usage for each member in a week was 700 litres. (ii) The reason that the water usage increased from Week 1 to Week 2 was due to a leak in the water pipe.

Q47 Structured 5 marks 🖼 Visual

Paper 2 Question 17. The figure below is made up of 3 different rectangles with identical breadth. The length of Rectangle E is 5/11 the length of Rectangle F. The length of Rectangle G is 1/2 of the total length of Rectangle E and Rectangle F. Find the length AB of the figure.

P6 Mathematics SA2 2020 — Tao Nan

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