P6 Mathematics SA2 2020 — Nanyang | Singapore Past Year Paper

Q: Which of the following numbers is 12 000 when rounded to the nearest hundred?

B. 11 950. Rounding to the nearest hundred: 11 908 → 11 900; 11 950 → 12 000 (rounds up); 12 089 → 12 100; 12 095 → 12 100. Only 11 950 rounds to 12 000.

Q: 4 tens and 28 hundredths is ____.

A. 40.28. 4 tens = 40; 28 hundredths = 0.28. Sum: 40 + 0.28 = 40.28.

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

C. 36.055. The scale runs from 36.03 to 36.09, a range of 0.06 divided into 6 equal intervals of 0.01 each. The arrow labelled A points midway between the 2nd and 3rd marks (between 36.05 and 36.06), giving 36.055.

Q: Which pair of lines is parallel?

C. AB and CD. On the grid, segments AB and CD slope down at the same gradient (both go down 2 units for every 2 units across), so they are parallel.

Q: In the figure below, ∠BCD = 183°, ∠ECD = 117° and ∠ACE = 45°. Find ∠BCA.

A. 15°. Angles around point C sum to 360°. ∠BCA = 360° − ∠BCD − ∠ECD − ∠ACE = 360° − 183° − 117° − 45° = 15°.

Q: In the figure below, PQRS is a rhombus. Which of the following statements is false?

D. ∠x + ∠z = 180°. In rhombus PQRS, opposite angles are equal so ∠w = ∠y (true) and ∠x = ∠z. All four sides are equal so PQ = PS (true). Opposite sides are parallel so PQ // SR (true). However adjacent angles (not opposite angles) are supplementary; ∠x and ∠z are opposite angles, so ∠x + ∠z ≠ 180° in general (it equals 2∠x). Hence statement D is false.

Q: A wheel of radius 14 cm made 10 complete turns. Find the distance covered. Take π = 22/7.

B. 880 cm. Circumference = 2πr = 2 × 22/7 × 14 = 88 cm. Distance covered in 10 turns = 88 × 10 = 880 cm.

Q: Mrs Field sold (6n + 1) coconuts on Monday. She sold n more coconuts on Tuesday than on Monday. How many coconuts did she sell altogether?

D. 13n + 2. Tuesday sales = (6n + 1) + n = 7n + 1. Total = (6n + 1) + (7n + 1) = 13n + 2.

Q: The table below shows how Megan spent her money. Which of the following bar graph best represents Megan's spending?

C. Bar graph (3). From the table: Magazine $6, Story Book $10, Eraser $10, Pencil Case $14. The correct bar chart should show Magazine and (Story Book = Eraser) of equal middle height, with Pencil Case the tallest. Option 3 shows two short bars (one for the Story Book/Eraser pair) and the tallest bar for Pencil Case, matching the data.

Q: Which of the following is likely to be the volume of a can of soft drink?

C. 330 ml. A standard can of soft drink contains about 330 ml.

Q1 MCQ 1 mark

Which of the following numbers is 12 000 when rounded to the nearest hundred?

Q1 Open-ended 2 marks

Carel had (5k + 13) shells at first. She added k more shells and the total number of shells she had became 151. How many shells did Carel add?

Q2 MCQ 1 mark

4 tens and 28 hundredths is ____.

Q2 Open-ended 2 marks

Every minute, Machine A prints 3 pages. Every hour, Machine A and Machine B print a total of 450 pages. How many pages does Machine B print per hour?

Q3 Open-ended 2 marks

The average of four different 2-digit odd numbers is 27. Two of the numbers are 15 and 29. What could the other two numbers be?

Q3 MCQ 1 mark 🖼 Visual

In the scale below, what is the value of A?

Q4 MCQ 1 mark 🖼 Visual

Which pair of lines is parallel?

Q4 Open-ended 2 marks 🖼 Visual

Diana was given $30 to buy some cupcakes from a bakery. Cupcake price: $2 each, 30% discount for every 10 cupcakes. What was the greatest number of cupcakes Diana could buy with all her money?

Q5 MCQ 1 mark 🖼 Visual

In the figure below, ∠BCD = 183°, ∠ECD = 117° and ∠ACE = 45°. Find ∠BCA.

Q5 Open-ended 2 marks 🖼 Visual

ACDF and BCDE are parallelograms. ∠AFE = 70° and ∠CDB = 42°. Find ∠BDE.

Q6 MCQ 1 mark 🖼 Visual

In the figure below, PQRS is a rhombus. Which of the following statements is false?

Q6 Structured 3 marks 🖼 Visual

In the square grid below, JK and KL are straight lines. (a) Measure and write down the size of ∠JKL. (b) JK and KL form two sides of a trapezium JKLM. JM is parallel to KL. KL is twice the length of JM. Complete the drawing of trapezium JKLM. (c) KL forms one side of a parallelogram KLNP. The length of JP is twice the length of KP and JKP forms a straight line. Complete the drawing of parallelogram KLNP such that it does not overlap with the trapezium.

Q7 MCQ 1 mark 🖼 Visual

A wheel of radius 14 cm made 10 complete turns. Find the distance covered. Take π = 22/7.

Q7 Open-ended 3 marks

Heidi bought 4 staplers and 6 files. Each stapler cost $1.20 more than each file. The total cost of the files was $6.40 more than the total cost of the staplers. Find the cost of one stapler.

Q8 Open-ended 3 marks

Maggie baked some pies and muffins. The number of pies was 7/11 of the number of muffins. Maggie gave away 6 pies and 14 muffins. In the end, the number of pies left was equal to the number of muffins left. How many pies and muffins did Maggie bake altogether?

Q8 MCQ 1 mark

Mrs Field sold (6n + 1) coconuts on Monday. She sold n more coconuts on Tuesday than on Monday. How many coconuts did she sell altogether?

Q9 MCQ 1 mark 🖼 Visual

The table below shows how Megan spent her money. Which of the following bar graph best represents Megan's spending?

Q9 Open-ended 3 marks 🖼 Visual

Three children received their scores for a Mathematics test. The average scores of any two of the three children are listed below as 83, 86 and 94. What was the highest score among the three children?

Q10 Open-ended 3 marks 🖼 Visual

Susie had a rectangular piece of paper. She folded the piece of paper along the line EF. Find ∠y.

Q10 MCQ 1 mark 🖼 Visual

Which of the following is likely to be the volume of a can of soft drink?

Q11 Structured 4 marks 🖼 Visual

A rectangular tank measuring 60 cm long and 20 cm wide was 4/5-filled with water at first. After Matthias poured some water from the tank into some identical jugs, the height of the water level decreased by 18 cm. Each jug can hold at most 2.25 ℓ of water. (a) What was the least number of such jugs used? (b) 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. Statement 1: 20% of the tank was not filled with water at first. Statement 2: The height of the tank is 22 cm.

Q11 MCQ 2 marks

Which of the following fractions is nearest to 2/3?

Q12 Structured 4 marks

Edwina and Georgia had the same number of bottles. Edwina and Georgia each had a mix of big bottles and small bottles. Edwina had 5 small bottles while Georgia had 16 big bottles. Each small bottle had a capacity of 400 ml. Each big bottle had a capacity of 0.6 ℓ. The total capacity of Edwina's bottles was 0.8 ℓ more than the total capacity of Georgia's bottles. (a) How many big bottles did Edwina have? (b) What was the total capacity of Edwina's bottles?

Q12 MCQ 2 marks 🖼 Visual

Seven landmarks on a map of a school are shown in the square grid below. The library is north of the pond. Samad is standing at a location south-east of the library and south of the canteen. Which landmark is Samad standing at?

Q13 MCQ 2 marks 🖼 Visual

Two of Object B are placed into a beaker on a weighing scale as shown in Figure 1. Object A is placed into an identical beaker as shown in Figure 2. Object A and Object B are placed into an identical beaker as shown in Figure 3. Find the mass of the empty beaker.

Q13 Structured 4 marks 🖼 Visual

The table below shows the number of pupils who wear glasses in Primary 3A and the number of girls who wear glasses in Primary 3B. The number of boys who wear glasses in Primary 3B is not shown. The total number of pupils in each class is fewer than 40. Class 3A: Boys 12, Girls 11; Class 3B: Boys ?, Girls 10. (a) The total number of pupils in Primary 3A can be divided equally into 4 groups with no pupils leftover. The total number of pupils in Primary 3A can also be divided equally into 6 groups with no pupils leftover. There are 2 girls in Primary 3A who do not wear glasses. How many boys in Primary 3A do not wear glasses? (b) The total number of boys in Primary 3B is 5/8 of the total number of pupils in Primary 3B. How many girls in Primary 3B do not wear glasses?

Q14 MCQ 2 marks

At a fruit stall, the price of 3 mangoes is the same as the price of 5 grapefruits. The price of 3 mangoes is also the same as the price of 10 pears. What is the ratio of the price of a mango to the price of a grapefruit to the price of a pear?

Q14 Structured 4 marks

There were three types of fruit in a box. The ratio of the number of mangoes to the total number of apples and oranges was 2 : 5. The ratio of the number of apples to the number of oranges was 9 : 1. There were 30 more apples than mangoes. After some mangoes were added into the box, 70% of the fruits in the box were mangoes. (a) How many mangoes were there in the end? (b) How many mangoes were added in the box?

Q15 MCQ 2 marks 🖼 Visual

A repeated pattern is formed using the numbers 0, 1 and 2. The first 18 numbers are shown below: 2 0 2 1 2 0 2 0 2 1 2 0 2 0 2 1 2 0. What is the sum of the first 100 numbers?

Q15 Structured 4 marks 🖼 Visual

QRUV and RSTU are trapeziums. QRS, VUT and QWT are straight lines. QS is parallel to VT. ∠QST = 58°, ∠STQ = 86° and ∠RUT = 108°. (a) Find ∠RWQ. (b) In the following statement, circle the words that describe QRW correctly and fill in the blanks accordingly: QRW (is / is not) an isosceles triangle because ∠RQW (is / is not) equal to ∠RWQ. Show your working clearly to explain your answer.

Q16 Open-ended 1 mark

Find the value of 5/8 × 24.

Q16 Structured 5 marks 🖼 Visual

The bar graph below shows the types of coin that Max had in his piggy bank. The number of 50¢ coins he had was not shown in the graph. He had $44 altogether. The total amount of $1 coins that he had was $16 more than the total amount of 20¢ coins that he had. (a) How many 20¢ coins did he have? (b) Draw the bar for the number of 50¢ coins that Max had in the graph above.

Q17 Structured 5 marks 🖼 Visual

The figure is made up of 5 identical circles. AEBGF are centres of the circles. The area of rectangle ABCD is 400 cm². (a) Find the radius of the circle. (b) Find the area of the shaded parts. Take π = 3.14.

Q17 Open-ended 1 mark

Express 735 ml in litres.

Q18 Open-ended 1 mark 🖼 Visual

There is 1 line of symmetry for the figure below. Draw in the line of symmetry.

Q19 Open-ended 1 mark 🖼 Visual

Yong Yi stacked 7 unit cubes and glued them together to form the solid below. Draw the side view of the solid on the grid below.

Q20 Open-ended 1 mark 🖼 Visual

The solid below is made up of 1-cm cubes. What is the volume of the solid?

Q21 Open-ended 2 marks

Write down all the common factors of 12 and 18.

Q22 Open-ended 2 marks

Mdm Hafiz bought a table for $151.25 and a chair for $24.15. (a) How much did she spend altogether? (b) Find the cost of 20 such tables.

Q23 Open-ended 2 marks

Michelle started reading her book at 8.56 a.m. She stopped reading her book at 10.05 a.m. on the same day. How long did Michelle spend reading her book?

Q24 Open-ended 2 marks

Mrs Tay baked 120 cookies on Monday and 150 cookies on Tuesday. What was the percentage increase in the number of cookies baked on Tuesday compared to Monday?

Q25 Open-ended 2 marks

Nayla divided some beads equally into 2 groups. She packed the first group of beads equally into 4 boxes and the second group of beads equally into 6 packets. 2 such boxes and 5 such packets contained a total of 6016 beads. How many beads were there in one such packet?

Q26 Open-ended 2 marks

Calissa had a piece of cloth. She used 1/5 m of it to sew a handkerchief and 3/5 m of it to sew a pouch. She then had 1/4 m of the cloth left. What was the length of the piece of cloth Calissa had at first?

Q27 Open-ended 2 marks

Kyan had 5 kg of salt. He packed the salt into bags. Each bag contained 3/8 kg of salt. What was the greatest number of such bags of salt Kyan could have packed?

Q28 Open-ended 2 marks 🖼 Visual

In the figure, ABC is an equilateral triangle. AB = CD and ∠ACD = 38°. BED and AEC are straight lines. Find ∠AEB.

Q29 Open-ended 2 marks 🖼 Visual

In the figure, PQRS and STUQ are two squares. STVR is a parallelogram. Find ∠SRV.

Q30 Open-ended 2 marks 🖼 Visual

The table shows the number of toys produced by a factory from Monday to Sunday. Day: Monday to Friday – 2y per day; Saturday – 4y − 3; Sunday – 6y + 8. Find the total number of toys produced in a week given that y = 5.

P6 Mathematics SA2 2020 — Nanyang

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