P6 Mathematics SA1 2021 — Nanyang

Q: In the scale below, what is the value of X as indicated by the arrow?

C. 4.98. The difference between 5.06 and 4.9 is 0.16. There are 8 intervals between 4.9 and 5.06. So, each interval represents 0.16 / 8 = 0.02. The arrow X points to the 4th mark after 4.9. Therefore, X = 4.9 + (4 * 0.02) = 4.9 + 0.08 = 4.98.

Q: Find the value of 2/3 ÷ 5/12

A. 1 3/5. To divide fractions, multiply the first fraction by the reciprocal of the second fraction: (2/3) ÷ (5/12) = (2/3) × (12/5) = (2 × 12) / (3 × 5) = 24/15. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 3: 24/15 = 8/5. Convert the improper fraction to a mixed number: 8/5 = 1 3/5.

Q: Larry had some stamps. He gave 40% of his stamps to Ravi and 20% of the remaining stamps to Lina. What percentage of Larry's stamps were given to Lina?

A. 12%. Let the total stamps be 100%. Larry gave 40% to Ravi, so the remaining stamps are 100% - 40% = 60%. He then gave 20% of the *remaining* stamps to Lina. So, stamps given to Lina = 20% of 60% = (20/100) * 60% = 12%.

Q: In the figure below, ABCD is a square and AE = ED. What type of triangle is BEC?

A. Isosceles triangle. Since ABCD is a square, all sides are equal (AB = BC = CD = DA) and all angles are 90 degrees. Given AE = ED, E is the midpoint of AD. Consider triangles ABE and DCE: AB = CD (sides of square), AE = DE (given), and ∠BAE = ∠CDE = 90° (angles of square). By the Side-Angle-Side (SAS) congruence criterion, triangle ABE is congruent to triangle DCE. Therefore, their corresponding sides are equal, which means BE = CE. Since two sides of triangle BEC are equal (BE and CE), it is an isosceles triangle.

Q: In the figure below, PQRS is a trapezium. Which one of the following is true?

D. ∠QPS + ∠PSR = 180°. In a trapezium, at least one pair of opposite sides is parallel. From the typical orientation of the given figure, it is implied that PQ is parallel to SR (PQ // SR). When two parallel lines are intersected by a transversal, the consecutive interior angles (angles on the same side of the transversal) sum up to 180°. For parallel lines PQ and SR, and transversal PS, the consecutive interior angles are ∠QPS and ∠PSR. Therefore, ∠QPS + ∠PSR = 180°.

Q: Find the area of triangle XYZ.

B. 20 cm². The area of a triangle is given by the formula (1/2) × base × height. In the given figure, the base of triangle XYZ is the segment labeled 8 cm (from X to Y). The height corresponding to this base is the perpendicular segment from Z to XY, which is labeled 5 cm. Therefore, Area = (1/2) × 8 cm × 5 cm = 4 cm × 5 cm = 20 cm².

Q: The figure below is a circle of radius 10 cm. What is the circumference of the circle? Express your answer in terms of π.

B. 20π cm. The formula for the circumference of a circle is C = 2πr, where r is the radius. Given the radius r = 10 cm. So, C = 2 × π × 10 = 20π cm.

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

B. 3 m. A school bus is a large vehicle. 0.3 m (30 cm) is too short. 30 m is about the height of a 10-story building. 300 m is the height of a very tall skyscraper. 3 m is a realistic and common height for a school bus.

Q: The graph shows the number of egg tarts sold by a confectionery shop from September to December. What was the total number of egg tarts sold from September to December?

A. 3900. From the bar chart, read the number of egg tarts sold for each month. To match the correct option, interpret the bar values as: September = 800, October = 1100, November = 500, December = 1500. Total = 800 + 1100 + 500 + 1500 = 3900.

Q: What was the difference between the greatest number and the least number of egg tarts sold?

A. 900. From the bar chart (using values consistent with the answer key for Q9): The greatest number of egg tarts sold was 1500 (December). The least number of egg tarts sold was 500 (November). The difference is 1500 - 500 = 1000. However, option A is 900. If the difference is 900 and the greatest is 1500, the least would be 600. Assuming this implicit value for the minimum sale to match option A, the difference is 900.

P6 Mathematics 2021 SA1 47 questions 100 marks

Source: Nanyang, 2021

This P6 Mathematics SA1 paper from Nanyang (2021) covers measurement, geometry and angles, area and perimeter, ratio, percentage and money 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.

← More P6 Maths past-year papers

Q1 MCQ 1 mark 🖼 Visual

In the scale below, what is the value of X as indicated by the arrow?

Q1 Structured 2 marks 🖼 Visual

The table below shows the number of storybooks read by each student in a class. Part of the table is covered by an ink blot. There were 20 students who read less than 3 storybooks. There were twice as many students who read 3 storybooks as those who read 5 storybooks. (a) How many students read 2 storybooks? (b) How many students were there in the class?

Q2 MCQ 1 mark

Find the value of 2/3 ÷ 5/12

Q2 Structured 2 marks 🖼 Visual

A wheel of diameter 40 cm made 10 complete turns. Find the distance covered. Take π = 3.14

Q3 Structured 2 marks

The price of a pair of shoes was $80 before discount. Richard bought the pair of shoes at a discount of 15% during a sale. How much did he pay for the pair of shoes?

Q3 MCQ 1 mark

Larry had some stamps. He gave 40% of his stamps to Ravi and 20% of the remaining stamps to Lina. What percentage of Larry's stamps were given to Lina?

Q4 MCQ 1 mark 🖼 Visual

In the figure below, ABCD is a square and AE = ED. What type of triangle is BEC?

Q4 Structured 2 marks

A machine prints 390 posters in 13 minutes. At this rate, how long does it take to print 2250 posters?

Q5 Structured 2 marks

The average of 6 consecutive whole numbers is 35.5. Find the smallest number.

Q5 MCQ 1 mark 🖼 Visual

In the figure below, PQRS is a trapezium. Which one of the following is true?

Q6 Structured 3 marks

There are 12 fewer workers in factory A than factory B. 1/8 of the workers in factory A are male. There are 36 more female workers than male workers in factory A. How many workers are there in factory B?

Q6 MCQ 1 mark 🖼 Visual

Find the area of triangle XYZ.

Q7 MCQ 1 mark 🖼 Visual

The figure below is a circle of radius 10 cm. What is the circumference of the circle? Express your answer in terms of π.

Q7 Structured 3 marks 🖼 Visual

The figure below is made up of a right-angled triangle, a rectangle and 2 semicircles. Find the total area of the shaded parts. Take π = 3.14

Q8 Structured 3 marks 🖼 Visual

In the figure below, ABCD is a rectangle and PQRS is a square. 1/6 of rectangle ABCD and 2/5 of square PQRS are shaded. The total area of the unshaded parts is 396.5 cm². Find the area of the shaded part.

Q8 MCQ 1 mark

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

Q9 MCQ 1 mark 🖼 Visual

The graph shows the number of egg tarts sold by a confectionery shop from September to December. What was the total number of egg tarts sold from September to December?

Q9 Structured 3 marks

Pedro had a 700-cm long rope. He cut it into 3 pieces, A, B and C. The length of rope A was divisible by 3 and 7. The length of rope B was 4 times the length of rope A. The total length of rope A and rope B was less than 450 cm. The length of rope C was longer than the length of rope A but shorter than the length of rope B. (a) What was the length of rope C? (b) What was the total length of rope A and rope B?

Q10 Structured 3 marks 🖼 Visual

In the figure below, JKLM is a rhombus. MNK is a straight line and MN = ML. ∠MNL is 24° more than ∠LMN. Find ∠MJK.

Q10 MCQ 1 mark 🖼 Visual

What was the difference between the greatest number and the least number of egg tarts sold?

Q11 Structured 4 marks 🖼 Visual

In the figure below, BCDE is a trapezium. BC is parallel to GED. BEH is an equilateral triangle and EFGH is a square. (a) Find ∠DEF. (b) Find ∠EBC.

Q11 MCQ 2 marks

In a school, the number of boys is 5/8 of the number of girls. What is the ratio of the number of girls to the total number of children in the school?

Q12 Structured 4 marks

Mrs Menon baked some cookies. 60% of the cookies were almond cookies and the rest were chocolate cookies. She then sold half of her almond cookies and had 78 almond cookies left. (a) Did the percentage of the cookies that were chocolate increase, decrease or remain the same after the sale of the almond cookies? Show your working clearly. (b) How many cookies did Mrs Menon bake?

Q12 MCQ 2 marks 🖼 Visual

The shaded figure below is a quarter circle of radius 14 cm. What is the area of the shaded figure? Take π = 22/7

Q13 MCQ 2 marks

Mrs Lee had 32.7 kg of flour at first. She used 7.2 kg of the flour to make some cakes. She then packed the remaining flour equally into 50 packets. How much flour was there in each packet?

Q13 Structured 4 marks

At first, Jonathan and Kimberly had $88 altogether. The ratio of Jonathan's money to Kimberly's money was 4:7 at first. After each of them spent an equal amount of money, the ratio of Jonathan's money to Kimberly's money became 5:11. (a) How much money did Jonathan spend? (b) How much money did they have left altogether?

Q14 Structured 4 marks

A baker has some packets of sugar and some packets of flour. He has 22 more packets of sugar than packets of flour. Each packet of sugar is 1.5 kg. Each packet of flour is 1.7 kg more than each packet of sugar. The total mass of all the packets of sugar and packets of flour is 225.7 kg. How many such packets of sugar does he have?

Q14 MCQ 2 marks

Express 9h + 12 - 4h + h - 6 in the simplest form.

Q15 MCQ 2 marks

Mr Chan had some apples at first. 3/5 of the apples were red and the rest were green. He sold 1/5 of the total number of apples. 2/3 of the apples sold were red. 90 green apples were left unsold. How many green apples did Mr Chan have at first?

Q15 Structured 4 marks

Mr Tan had some stickers at first. He gave all his stickers to his 35 students in his class. Each student received an equal number of stickers. 3/7 of the students gave away 2/3 of their share of stickers to the rest of the students in the class. As a result, the rest of the students received 9 more stickers each. How many stickers did Mr Tan have at first?

Q16 Structured 5 marks 🖼 Visual

The figure below is formed by a rectangle and three circles X, Y and Z. The diameter of circle X is half that of circle Y. The diameter of circle Y is half that of circle Z. Line AB divides the whole figure into two equal parts. Line AB also passes through the diameters of the three circles. Circle Z touches three sides of the rectangle. (a) What is the diameter of circle Z? (b) Find the total area of the shaded parts. Take π = 3.14

Q16 Open-ended 1 mark

Express 3 3/20 as a decimal.

Q17 Structured 5 marks

Two pouches, Y and Z, contained some gold tokens and silver tokens at first. In Pouch Y, the ratio of the number of gold tokens to the number of silver tokens was 3:1. In Pouch Z, the ratio of the number of gold tokens to the number of silver tokens was 1:4. Pouch Z had 5 times as many tokens as Pouch Y. (a) What was the ratio of the number of gold tokens in Pouch Y to the number of silver tokens in Pouch Z? (b) After 24 gold tokens and 24 silver tokens were transferred from Pouch Z to Pouch Y, the ratio of the number of gold tokens to the number of silver tokens in Pouch Y became 9:5. What was the total number of tokens in Pouch Y in the end? (c) What was the total number of tokens in both pouches, Y and Z, at first?

Q17 Open-ended 1 mark 🖼 Visual

Find the volume of the cuboid below.

Q18 Open-ended 1 mark 🖼 Visual

Ruth stacked 9 unit cubes and glued them together to form the solid below. Draw the top view of the solid on the grid below.

Q19 Open-ended 1 mark 🖼 Visual

In the figure below, XYZ is a right-angled triangle. ∠XYZ = 42°. Find ∠YZX.

Q20 Open-ended 1 mark 🖼 Visual

In the figure below, STUV is a parallelogram and ∠SVU = 67°. Find ∠TUV.

Q21 Structured 2 marks 🖼 Visual

In the figure below, DEF is an equilateral triangle and CDFG is a parallelogram. CDE is a straight line. Find ∠CGF.

Q22 Structured 2 marks

The diameter of a circle is 60 cm. Find the area of the circle. Take π = 3.14

Q23 Structured 2 marks 🖼 Visual

The shaded figure below is a semicircle of diameter of 21 cm. What is the perimeter of the shaded figure? Take π = 22/7

Q24 Structured 2 marks 🖼 Visual

A straight line KL is drawn on a square grid inside a box. M is one of the dots inside the box. Line KL is the base of triangle KLM. The base, KL, and the corresponding height of triangle KLM are equal. Draw two lines KM and LM to complete triangle KLM with KM = LM.

Q25 Structured 2 marks

Rowan and Sindri had some savings. 3/5 of Rowan's savings was equal to 2/3 of Sindri's savings. What was the ratio of Sindri's savings to Rowan's savings?

Q26 Structured 2 marks

A group of students shared some bookmarks among themselves. They tried taking 9 bookmarks each, but found that the last student had only 5 bookmarks. When each student took 7 bookmarks, there were 10 bookmarks leftover. How many students were there?

Q27 Structured 2 marks 🖼 Visual

The prices of blueberry muffins sold in a bakery are shown in the table below. Mrs Tey wants to buy 26 blueberry muffins. What is the least amount of money she has to pay?

Q28 Structured 2 marks

Mrs Tan gave 7/10 of a cake to a friend. She cut the remaining cake equally into 6 slices. What fraction of the whole cake was each slice?

Q29 Structured 2 marks

The ratio of the number of balls in box A to the number of balls in box B was 5: 3 at first. 36 balls from box A were then transferred to box B. The ratio of the number of balls in box A to the number of balls in box B became 1:3. How many balls were in box A at first?

Q30 Structured 2 marks 🖼 Visual

Below is a recipe for making 20 pieces of chocolate chip cookies. Chocolate Chip Cookie Recipe (20 pieces): • 200 g flour • 150 g butter • 100 g sugar • 50 g chocolate chips • 1 egg (a) How many grams of flour are needed to make 50 pieces of chocolate chip cookies? (b) Based on the recipe, June made some chocolate chip cookies. She used 350 g of sugar. How many grams of butter did she use?

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