P6 Mathematics SA2 2020 — Raffles Girls | Singapore Past Year Paper

Q: The value of the digit 5 in 954 687 is ____________.

C. 50 000. The digit 5 is in the ten-thousands place, so its value is 5 × 10 000 = 50 000.

Q: Which one of the following is closest to 1?

C. 1 1/9. All four mixed numbers exceed 1. The one with the smallest fractional part is closest to 1; 1/9 < 1/8 < 1/7 < 1/6, so 1 1/9 is closest to 1.

Q: Round off 28.784 to the nearest tenth.

B. 28.8. Look at the hundredths digit (8). Since 8 ≥ 5, round the tenths digit up: 28.784 → 28.8.

Q: What is the length of the screw driver?

B. 7.6 cm. Reading the ruler, the screwdriver starts at the 1.5 cm mark and ends at the 9.1 cm mark, giving a length of 9.1 − 1.5 = 7.6 cm.

Q: In the figure, ABC is an equilateral triangle. CDE is an isosceles triangle. BCE is a straight line. ∠CDE = 69°. Find the sum of ∠BCD and ∠ACE.

C. 231°. Triangle ABC is equilateral, so ∠ACB = 60°. In isosceles triangle CDE (CE = DE), the base angle ∠DCE = ∠DEC = (180° − 69°) ÷ 2... actually using the marks, base angles equal ∠DCE = 69°. Since BCE is a straight line, ∠BCD = 180° − ∠DCE = 180° − 69° = 111° and ∠ACE = 180° − ∠ACB = 180° − 60° = 120°. Sum = 111° + 120° = 231°.

Q: Gordon was at the park. He turned an angle of 315° anti-clockwise to face the direction of his home. Where was he facing before the turn?

A. playground. An anti-clockwise turn of 315° is equivalent to a clockwise turn of 45°. So before the turn he was facing 45° clockwise from home. Home is north-west of the park, and 45° clockwise from north-west is west, which points to the playground.

Q: The figure is made up of 2 squares. The area of the 2 squares are 64 cm² and 25 cm². What is the perimeter of the figure?

A. 42 cm. Sides of the squares = √64 = 8 cm and √25 = 5 cm. Perimeter of the composite figure = (4 × 8) + (4 × 5) − 2 × 5 = 32 + 20 − 10 = 42 cm (subtracting the shared overlap on the top edge of the big square).

Q: Abel had 3 times as many books as Thomas. Abel donated 1/4 of his books to charity. What was the ratio of the number of books Thomas had to the number of books Abel had in the end?

B. 4 : 9. Let Thomas = 1 unit, Abel = 3 units. Abel donates 1/4, so Abel left = 3 × 3/4 = 9/4 units. Ratio Thomas : Abel (end) = 1 : 9/4 = 4 : 9.

Q: Calvin bought a camera. The GST amount was $70. How much did he pay for the camera inclusive of GST?

D. $1070. GST is 7%. So 7% of price = $70 → 1% = $10 → 100% = $1000. Price inclusive of GST = $1000 + $70 = $1070.

Q: 3 + 6a = 27. What is the value of a?

D. 4. 3 + 6a = 27 → 6a = 24 → a = 4.

Q1 MCQ 1 mark

The value of the digit 5 in 954 687 is ____________.

Q2 MCQ 1 mark

Which one of the following is closest to 1?

Q3 MCQ 1 mark

Round off 28.784 to the nearest tenth.

Q4 MCQ 1 mark 🖼 Visual

What is the length of the screw driver?

Q5 MCQ 1 mark 🖼 Visual

In the figure, ABC is an equilateral triangle. CDE is an isosceles triangle. BCE is a straight line. ∠CDE = 69°. Find the sum of ∠BCD and ∠ACE.

Q6 MCQ 1 mark 🖼 Visual

Gordon was at the park. He turned an angle of 315° anti-clockwise to face the direction of his home. Where was he facing before the turn?

Q7 MCQ 1 mark 🖼 Visual

The figure is made up of 2 squares. The area of the 2 squares are 64 cm² and 25 cm². What is the perimeter of the figure?

Q8 MCQ 1 mark

Abel had 3 times as many books as Thomas. Abel donated 1/4 of his books to charity. What was the ratio of the number of books Thomas had to the number of books Abel had in the end?

Q9 MCQ 1 mark 🖼 Visual

Calvin bought a camera. The GST amount was $70. How much did he pay for the camera inclusive of GST?

Q10 MCQ 1 mark

3 + 6a = 27. What is the value of a?

Q11 MCQ 2 marks

Ai Lin bought 2 tables and 20 chairs for her office. She spent $120 more on the tables than the chairs. She spent a total of $840. How much did she spend on one chair?

Q12 MCQ 2 marks

1/2 of Janice's mass is the same as 1/5 of Randy's mass. Their total mass is 49.14 kg. Find Janice's mass.

Q13 MCQ 2 marks

A dining table was sold at a discount. The discounted price was 20% less than the usual price. The usual price was $720. How much was the discount?

Q14 MCQ 2 marks

Ali and Zainal each bought the same mass of minced meat. They prepared each patty with the same mass of minced meat. Ali made 20 patties and had 5.6 kg of minced meat left. Zainal made 60 patties and had 400 g of minced meat left. What was the mass of minced meat used for each patty?

Q15 MCQ 2 marks

Tap A can fill a pail in 6 min. Tap B can fill the same pail in 3 min. How long would it take to fill the pail completely when both taps are turned on at the same time?

Q16 Open-ended 1 mark

Find the value of 50 − (24 ÷ 2 × 3) + 4.

Q17 Open-ended 1 mark

When a flight departed from Singapore, the time in Perth was 8.50 p.m. The flight arrived in Perth 5 h 15 min later. At what time in Perth did the flight arrive? Give your answer in 24-hour clock.

Q18 Open-ended 1 mark

Express 78/9 as a mixed number in the simplest form.

Q19 Open-ended 1 mark

Find the sum of 11 tens, 1 tenth and 10 hundredths.

Q20 Open-ended 1 mark

Find the average of 180 cm and 1.2 m. Leave your answer in metres.

Q21 Open-ended 2 marks

Pillai mixed milk and rose syrup to make a drink. He used 7/8 ℓ of milk. The amount of rose syrup used was 1/6 ℓ less than the milk used. How much milk and rose syrup did Pillai use altogether? Leave your answer as a mixed number in the simplest form.

Q22 Open-ended 2 marks 🖼 Visual

Alex has a box measuring 40 cm by 50 cm by 60 cm. He wants to pack identical rubik's cubes of edge 6 cm into the box. What is the maximum number of rubik's cubes he can pack into the box?

Q23 Open-ended 2 marks

Mrs Delvi had 24n cookies. She distributed all of them equally to 8 of her grandchildren. Then, one of her grandchildren, Heidi, ate 4 cookies. How many cookies had Heidi left? Leave your answer in terms of n.

Q24 Open-ended 2 marks

There were equal number of male and female members at a gym. After 265 male members and 545 female members cancelled their gym membership, the number of remaining male members was 9 times that of the remaining female members. How many female members remained at the gym?

Q25 Open-ended 2 marks 🖼 Visual

In the figure, ABCD is a rectangle and AEFG is a rhombus. AHF is a straight line and ∠BAE = 22°. Find ∠CHF.

Q26 Open-ended 2 marks

Anna needed 20 pieces of wires, each of length 0.3 m. The wires were sold in rolls of 2 m each. What was the least number of rolls of wire that Anna needed to buy?

Q27 Open-ended 2 marks 🖼 Visual

The figure is made up of 3 squares. AB is a straight line. What is the perimeter of the figure?

Q28 Open-ended 2 marks 🖼 Visual

The table shows the rate for renting a karaoke room at a community club. First 2 hours: $9 per hour. Every additional 30 min: $8 per 30 min. A group of friends paid a total of $42 for the rental of a karaoke room. How many hours did they rent the karaoke room for?

Q29 Open-ended 2 marks

Sara had 5/6 m² of fabric. She cut out 1/4 of it and used the remaining fabric to make 5 identical masks. How much fabric did she use to make 1 mask?

Q30 Open-ended 2 marks 🖼 Visual

The graph shows the number of houses sold from January to March. The bar for the number of houses sold in March has not been drawn. The total number of houses sold in February and March was 2/3 of the total number of houses sold over the 3 months. Complete the graph by shading to show the number of houses sold in March.

Q31 Open-ended 2 marks

There were 538 females and 306 males at a carnival. 110 females left and 25 males entered the carnival. What was the percentage decrease in the total number of people at the carnival? Round your answer to the nearest 1 decimal place.

Q32 Open-ended 2 marks 🖼 Visual

The table shows the points scored by 3 children in a game. Participants: Ali, Bala, Charlie. Score: 21, ?, ?. Their total score was 135. All their scores were 2-digit numbers. What was the lowest possible score among the 3 of them?

Q33 Open-ended 2 marks 🖼 Visual

In the square grid, AB and BC form two sides of a trapezium ABCD. There are 2 right angles in ABCD. Complete the drawing of trapezium ABCD.

Q34 Open-ended 2 marks

Amos is 12 years younger than his sister. The ratio of Amos' age to his sister's age is 1 : 5. In how many years' time will the ratio of Amos' age to his sister's age be 2 : 5?

Q35 Structured 2 marks 🖼 Visual

The table shows the number and the cost of each type of flowers sold at a florist. Rose: 135 sold at $2 each. Lily: 2y sold at $2.50 each. Carnation: 4y sold at 4 for $5. Each of the statements below is either true, false or not possible to tell from the information given. For each statement, put a tick (✓) to indicate your answer. (a) If the total number of flowers sold was 405, 180 carnations were sold. (b) The amount of money collected from selling the lilies and the carnations were the same. (c) The amount of money collected from selling the roses was the highest among the 3 types of flowers.

Q36 Structured 4 marks 🖼 Visual

The bar chart shows the height of 6 people. The bar that shows Peggy's height has not been drawn. Peggy's height was 20 cm more than the average height of Quincy and Megan. (a) What was the height of Peggy? (b) Who was/were taller than the average height of all the people?

Q37 Open-ended 3 marks 🖼 Visual

A rectangular tank measuring 45 cm by 16 cm by 25 cm was 1/3 filled with water. After water from some identical bottles was poured into the rectangular tank, it became 7/8 full. The capacity of each bottle was 650 ml. What was the minimum number of bottles used to pour the water into the rectangular tank?

Q38 Structured 4 marks

Mr Choo needs a total of 15 h to prepare 1800 rice dumplings. He prepares the same number of rice dumplings every hour. When his wife helps him for 4 h, 1800 rice dumplings can be prepared in 9 h. (a) What is the average number of rice dumplings that Mr Choo's wife prepares in the 4 hours? (b) What is the difference in the time taken between Mr Choo and his wife if she prepares 1800 rice dumplings alone?

Q39 Open-ended 3 marks 🖼 Visual

At its year-end sale, a company sold calendars and diaries at the prices shown. Calendars: 6 for $37. Diaries: 8 for $99. An equal number of calendars and diaries were sold. The company collected a total of $29 815 from the sale of calendars and diaries. How many calendars and diaries did the company sell in all?

Q40 Structured 3 marks

In a school, 55% of the pupils are girls and the rest are boys. As a school, 40% of the boys wear spectacles and 60% of the pupils wear spectacles. (a) What percentage of the pupils are girls who wear spectacles? (b) 208 girls do not wear spectacles. How many pupils are there altogether?

Q41 Open-ended 3 marks 🖼 Visual

The figure is formed by 3 identical big semicircles and 3 identical small semicircles. The big semicircles have a height (radius) marked 14 cm and the small semicircles have a height (radius) marked 10 cm. Use the calculator value of π to find the perimeter of the figure. Round your answer to 2 decimal places.

Q42 Structured 3 marks 🖼 Visual

The figure shows a parallelogram PQRS drawn on a grid. (a) PRTU is a rectangle that has half the area of PQRS. Draw PRTU on the grid. (b) PRV is an isosceles triangle that has the same area as rectangle PRTU. Draw PRV on the grid such that it does not overlap with rectangle PRTU.

Q43 Open-ended 4 marks 🖼 Visual

The figure shows 6 identical squares inside a rectangle. The arrangement results in a gap of 0.2 m at the top and a gap of 0.1 m at the side. The area of the unshaded region is 3000 cm². What is the area of the rectangle?

Q44 Structured 4 marks 🖼 Visual

An L-shaped paper is made up of perpendicular lines. It is folded along line AB as shown. ∠CBD = 28°. (a) Find ∠x. (b) Find ∠y.

Q45 Structured 4 marks 🖼 Visual

The figure is made up of a big semicircle of radius 30 cm. 2 circles and 3 semicircles of equal radius are drawn in the big semicircle. (a) What is the radius of the circle? (b) What is the area of the shaded parts? Take π = 3.14. Round your answer correct to 1 decimal place.

Q46 Structured 5 marks

Mdm Nurul had some red and green apples in her minimart. The ratio of the number of red apples to the number of green apples was 13 : 7. After selling 60% of the red apples and 55 green apples, the ratio of the number of red apples to the number of green apples was 13 : 12. (a) How many apples were there altogether at first? (b) After that, she bought more red apples. The number of red apples she bought was 3/10 of the number of red apples left before that. How many red apples did she have in the end?

Q47 Structured 5 marks

Peter, Roger and Mary each had a sum of money. They decided to split their dinner bill equally. If Roger were to pay for the bill first, the sum of his remaining money would be 4/9 of Mary's money. If Mary were to pay for the bill first, the sum of her remaining money would be 11/15 of Roger's money. If Peter were to pay for the bill first, he would have used up all his money. (a) Given that Mary had $126 more than Roger, how much was each person's share of the bill? (b) Express Peter's sum of money as a fraction of their total sum of money.

P6 Mathematics SA2 2020 — Raffles Girls

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