P6 Mathematics SA2 2021 — Tao Nan | Singapore Past Year Paper

Q: Bob took 130 seconds to run round a track. He was 25 seconds faster than Pete. How long did Pete take to run round the track?

D. 2 min 35 s. Pete is slower by 25 seconds, so Pete's time = 130 + 25 = 155 seconds = 2 min 35 s.

Q: 8 hundreds, 5 tenths and 6 thousandths is ____.

B. 800.506. 8 hundreds = 800, 5 tenths = 0.5, 6 thousandths = 0.006. Sum = 800.506.

Q: P is 5 times of Q. Q is thrice of R. What is the ratio of R to Q to P?

B. 1 : 3 : 15. Let R = 1. Then Q = 3R = 3 and P = 5Q = 15. So R : Q : P = 1 : 3 : 15.

Q: The number of visitors who went to a flower exhibition was 70 000 when rounded to the nearest hundred. Which of the following shows a possible number of visitors?

C. 69 951. Numbers that round to 70 000 to the nearest hundred lie in 69 950 to 70 049. 70 055 and 70 051 round to 70 100; 69 949 rounds to 69 900; only 69 951 rounds to 70 000.

Q: Jenny faced south-east after turning 225° anti-clockwise. What direction was she facing at first?

A. North. To undo a 225° anti-clockwise turn, rotate 225° clockwise from south-east. South-east + 225° clockwise = north.

Q: The figure shows a semicircle of radius 21 cm. Find the perimeter of the figure. (Take π = 22/7)

C. 108 cm. Perimeter = arc + diameter = πr + 2r = (22/7)(21) + 2(21) = 66 + 42 = 108 cm.

Q: Which of the following is the same as 20 kg 8 g?

A. 20.008 kg. 1 kg = 1000 g, so 8 g = 0.008 kg. Therefore 20 kg 8 g = 20.008 kg.

Q: Find the sum of all the factors of 64.

C. 127. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Sum = 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127.

Q: Which of the following statements about the angles in the figure are true? A. ∠a = ∠r B. ∠b = ∠s C. ∠s = ∠c D. ∠s = ∠q

D. A, B and D only. By corresponding angles a = p, b = q, c = r, d = s. By vertical angles a = c, b = d, p = r, q = s. So ∠a = ∠c = ∠r (true); ∠b = ∠d = ∠s (true); ∠s = ∠d ≠ ∠c (false); ∠s = ∠q (true). Statements A, B and D are true.

Q: Study the following table carefully. Which column will the number 71 appear in?

A. A. The numbers are arranged in a 'boustrophedon' pattern that repeats every 8. Position 71 mod 8 = 7, which falls in column A (since 7 itself is in column A in the second row). So 71 is in column A.

Q1 MCQ 1 mark

Bob took 130 seconds to run round a track. He was 25 seconds faster than Pete. How long did Pete take to run round the track?

Q2 MCQ 1 mark

8 hundreds, 5 tenths and 6 thousandths is ____.

Q3 MCQ 1 mark

P is 5 times of Q. Q is thrice of R. What is the ratio of R to Q to P?

Q4 MCQ 1 mark

The number of visitors who went to a flower exhibition was 70 000 when rounded to the nearest hundred. Which of the following shows a possible number of visitors?

Q5 MCQ 1 mark

Jenny faced south-east after turning 225° anti-clockwise. What direction was she facing at first?

Q6 MCQ 1 mark 🖼 Visual

The figure shows a semicircle of radius 21 cm. Find the perimeter of the figure. (Take π = 22/7)

Q7 MCQ 1 mark

Which of the following is the same as 20 kg 8 g?

Q8 MCQ 1 mark

Find the sum of all the factors of 64.

Q9 MCQ 1 mark 🖼 Visual

Which of the following statements about the angles in the figure are true? A. ∠a = ∠r B. ∠b = ∠s C. ∠s = ∠c D. ∠s = ∠q

Q10 MCQ 1 mark 🖼 Visual

Study the following table carefully. Which column will the number 71 appear in?

Q11 MCQ 2 marks

Guan Ming has 3 empty bottles J, K and R. He poured an equal amount of milk into each of them. As a result, 50% of J was filled with milk, 25% of K was filled with milk and 75% of R was filled with milk. What is the ratio of the capacity of Bottle J to Bottle R to Bottle K?

Q12 MCQ 2 marks 🖼 Visual

The figure is made up of a square and an oval. The ratio of the area of the square to the area of the oval is 2 : 3. The shaded area is 1/6 the area of the oval. The shaded area is 36 cm². Find the area of the figure.

Q13 MCQ 2 marks

The original price of a box of cookies was $m. Aunty Loh bought a dozen such boxes of cookies. She was given a discount of 50 cents for every 2 boxes bought. How much did she pay for the boxes of cookies altogether?

Q14 MCQ 2 marks

Jonathan read 3 books in 2 hours. He spent 15 minutes longer to read the first book than the second book. He spent the same amount of time to read the last 2 books. How many minutes did he take to read the first book?

Q15 MCQ 2 marks

Which of the following fractions is closest to 3/4?

Q16 Open-ended 1 mark

Find the value of 49.14 ÷ 7.

Q17 Open-ended 1 mark

Express 0.5% as a fraction in the simplest form.

Q18 Open-ended 1 mark 🖼 Visual

The table below shows the number of books read by each pupil in a class of 28 pupils. One of the numbers in the table is covered by an ink stain. The average number of books read by the pupils in the class is 10. What is the number covered by the ink stain?

Q19 Open-ended 1 mark

A bottle contains 1.05 litres of water. Wendy pours 300 ml of water from it into a cup. How much water is left in the bottle?

Q20 Structured 1 mark 🖼 Visual

In the square grid, (a) Point ____ is West of Point D. (b) Point ____ is South-West of Point E.

Q21 Open-ended 2 marks

What is the missing number in the box? □ ÷ 2 × 30 + (200 − 90) = 320

Q22 Open-ended 2 marks

3/5 of Christy's spending is equal to 7/12 of Kelvin's spending. What is the ratio of Kelvin's spending to Christy's spending?

Q23 Open-ended 2 marks 🖼 Visual

The figure below shows 2 semicircles. EG is 34 cm. Find the perimeter of the figure. Leave your answer in terms of π.

Q24 Open-ended 2 marks 🖼 Visual

The bar graph below shows the number of cakes produced by ABC Bakery in 5 months. In which month did the bakery produce 1/4 of the total number of cakes produced in the 5 months?

Q25 Open-ended 2 marks 🖼 Visual

Ming Lei drew three rectangles to form a figure. The areas of the rectangles were in the ratio 3 : 5 : 18. She then shaded some parts of the figure as shown. What fraction of the figure was shaded? Express your answer in the simplest term.

Q26 Open-ended 2 marks

16 students were assigned to line up in a row from one end to the other end of a corridor to welcome parents to a school event. They had to stand at an equal spacing of 1.2 m apart. On the day of the event, 5 of the students did not turn up. As a result, the remaining students had to line up from one end to the other end of the corridor at a new equal spacing. What was the new spacing between 2 students?

Q27 Open-ended 2 marks

A school bus can carry 24 adults or 32 children. There are already 9 adults and 11 children on the bus. How many more children can the bus carry?

Q28 Open-ended 2 marks 🖼 Visual

The following figure, not drawn to scale, is made up of a square, a rectangle and 2 identical triangles. AB and CD are straight lines. Find the area of the figure.

Q29 Open-ended 2 marks

Mr Tao saved 40% of his salary. When he increased his savings by 20%, he would have $400 less to spend. How much was his salary?

Q30 Open-ended 2 marks

Nora bought a packet of milk for $0.85 and a banana muffin for $1.40. She gave the cashier a $5 note. She received her change all in coins. What is the least number of coins Nora would have received?

Q31 Open-ended 2 marks

Peter and James were usually given $58 altogether for their weekly pocket money. As James needed money for new books next week, he asked for $19 more. As a result, he would have 3/4 as much money as Peter. How much was Peter's pocket money?

Q32 Open-ended 2 marks

There were 34 red candies and 18 yellow candies in a jar. An equal number of red and yellow candies were removed from the jar. The ratio of the number of red candies to the number of yellow candies became 5 : 1. How many red candies were there in the end?

Q33 Open-ended 2 marks

Melissa is able to type 45 words per minute. She was tasked to type a document of 30 pages. Given that the average number of words on each page was 450 words, how many hours will she take to complete her task?

Q34 Open-ended 2 marks

Mr Wong is 46 years old now. His son is n years younger than him. Find, in terms of n, their total age in 3 years' time.

Q35 Open-ended 2 marks 🖼 Visual

In the figure below, ABC is an equilateral triangle with AB = BC = CA. Given ∠ABD = 21° and ∠ADE = 44°, find ∠BDE.

Q36 Structured 3 marks 🖼 Visual

In the figure below, not drawn to scale, ABCF is a rhombus and BCD is an isosceles triangle. ∠ABE = 39° and ∠BCF = 128°. (a) Find ∠AFC. (b) Find ∠FCD.

Q37 Structured 3 marks 🖼 Visual

The bar graph shows the number of cars owned by families in a neighbourhood. (a) How many families have less than 2 cars? (b) From the families who own at least 3 cars, what fraction of them have 4 cars? Give your answer in the simplest form.

Q38 Open-ended 3 marks

In a school, 60% of the boys and 40% of the girls wear spectacles. The number of boys and girls who wear spectacles is the same. For the boys and girls who do not wear spectacles, the number of girls outnumbered the number of boys by 50. How many girls are there?

Q39 Structured 4 marks 🖼 Visual

In the diagram below, PQR is an equilateral triangle and PTR is an isosceles triangle. QS is a straight line. QS ⊥ PR and ∠QTR = 121°. Find (a) ∠TRP (b) ∠QPT

Q40 Open-ended 3 marks

At first, the number of strawberries that Roger and Darren had was in the ratio 5 : 7 respectively. Roger gave 1/5 of his strawberries to his sister and Darren ate 35 of his strawberries. In the end, Roger had twice as many strawberries as Darren. Find the number of strawberries Darren had at first.

Q41 Structured 4 marks

In his demonstration on the art of tea making, John first poured some tea from a pot into an empty cup. The amount of tea in the cup is 1/4 of the amount of tea left in the pot. For the second step, he poured 20 ml of milk into the cup. Finally, he poured 50 ml of tea from the pot into the cup. The final amount of liquids in the cup was 1/3 of that left in the pot. (a) Find the total amount of milk and tea added from the second and final steps. (b) Find the original amount of tea in the pot.

Q42 Structured 4 marks 🖼 Visual

Triangle T is drawn by joining dots on the square grid below. (a) Draw a right-angled triangle with the same area as Triangle T. Label the triangle R. (b) Draw a parallelogram with twice the perimeter as Triangle T. Label the parallelogram P. (c) The following statement is either true, false or not possible to tell. Put a ✓ in the correct column. 'The area of P is twice the area of T.'

Q43 Structured 4 marks 🖼 Visual

Study the following figure. ABCD is a square and the area of the circle is 200.96 cm². (Take π = 3.14) (a) Find the radius of the circle. (b) Find the length of the arc AB. (c) Find the area of the shaded triangle BCD.

Q44 Structured 4 marks 🖼 Visual

The line graph below shows the number of residents in Town A and Town B who are involved in a recycling project from Year 2000 to Year 2020. (a) In which year(s), were there more residents involved in the recycling project in Town B than in Town A? (b) For Year 2025, the number of residents in Town A who are to be involved in the recycling project are expected to increase by 25%. Find the number of residents in Town A who are expected to be involved in Year 2025. (c) What is the percentage increase in the number of residents in Town B who are involved in the recycling project from Year 2000 to Year 2020?

Q45 Open-ended 3 marks

The total age of workers in a restaurant is 256 years. The average age of the oldest worker and youngest worker is 41 years. The average age of the rest of the workers is 29 years. Find the total number of workers in the restaurant.

Q46 Structured 5 marks 🖼 Visual

Aaron uses circles and triangles to form figures that follow a pattern. The first four figures are shown below. (a) Complete the table for Figure 5 and Figure 20. (b) Find the Figure Number of the pattern that has a total of 729 triangles and circles. (c) Find the Figure Number of the pattern with 840 triangles.

Q47 Structured 5 marks 🖼 Visual

The following solid figure was formed using ten 2-cm cubes. The exterior of the solid figure (including the base of the solid) was painted. (a) Find the total painted surface area of the solid figure. (b) If the 2-cm cubes were taken apart, how many faces of the cubes were not painted? (c) More cubes were added to form a big cube. What is the least number of 2-cm cubes added?

P6 Mathematics SA2 2021 — Tao Nan

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