P6 Mathematics SA2 2021 — Methodist Girls | Singapore Past Year Paper

Q: 2 021 021 = 2 000 000 + 2 × ____ + 1021. What is the missing number in the box?

D. 10 000. 2,021,021 − 2,000,000 − 1,021 = 20,000. So 2 × ? = 20,000, giving ? = 10,000.

Q: Which of the following is the same as 7030 mℓ?

B. 7 ℓ 30 mℓ. 1 ℓ = 1000 mℓ, so 7030 mℓ = 7000 mℓ + 30 mℓ = 7 ℓ 30 mℓ.

Q: Which digit in 31.507 is in the tenths place?

D. 5. The tenths place is the first digit to the right of the decimal point, which is 5.

Q: Which one of the following is the closest estimate of 14.6 × 38.4?

A. 15 × 38. 14.6 × 38.4 ≈ 560.6. 15 × 38 = 570 is closest (other products: 15×39=585, 14×38=532, 14×39=546).

Q: XYZ is an equilateral triangle. WZY is a straight line and WV is parallel to ZX. Find ∠a.

D. 300°. ∠XZY = 60° (equilateral triangle). With WV ∥ ZX and transversal WY, corresponding angle ∠VWY = 60°. The reflex angle ∠a = 360° − 60° = 300°.

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

C. 5/6. Distance from 1: |3/4 − 1| = 0.250, |4/3 − 1| ≈ 0.333, |5/6 − 1| ≈ 0.167, |6/5 − 1| = 0.200. 5/6 is closest.

Q: ABCD is a rectangle. E is the mid-point of AB and ∠DEC = 78°. Find ∠ADE.

A. 39°. Triangles ADE and BCE are congruent (AE = EB, AD = BC, both right angles at A and B), so ∠AED = ∠BEC. Since ∠AED + 78° + ∠BEC = 180°, ∠AED = 51°. ∠ADE = 90° − 51° = 39°.

Q: Chee Seng packed 216 pens into 3 boxes. The ratio of the number of pens in box A to the number of pens in box B to the number of pens in box C is 1 : 3 : 4. How many more pens were there in box B than in box A?

B. 54. Total units = 1 + 3 + 4 = 8. 1 unit = 216 ÷ 8 = 27 pens. B − A = 3 − 1 = 2 units = 54 pens.

Q: In the programme guide shown below, one programme leads to another without any break in between. How much longer is the Art and Craft programme than the Music Appreciation programme?

A. 25 min. Art and Craft runs 2.45 p.m. to 4.00 p.m. = 1 h 15 min. Music Appreciation runs 4.00 p.m. to 4.50 p.m. = 50 min. Difference = 75 − 50 = 25 min.

Q: The average mass of 3 bags of rice is 10 kg. A fourth bag of rice weighing 6 kg is added to the total mass. What is the average mass of the 4 bags of rice now?

A. 9 kg. Total of 3 bags = 3 × 10 = 30 kg. New total = 30 + 6 = 36 kg. New average = 36 ÷ 4 = 9 kg.

Q1 MCQ 1 mark

2 021 021 = 2 000 000 + 2 × ____ + 1021. What is the missing number in the box?

Q2 MCQ 1 mark

Which of the following is the same as 7030 mℓ?

Q3 MCQ 1 mark

Which digit in 31.507 is in the tenths place?

Q4 MCQ 1 mark

Which one of the following is the closest estimate of 14.6 × 38.4?

Q5 MCQ 1 mark

3/5 of Ali's marbles are blue and the rest are yellow. What percentage of Ali's marbles are blue?

Q6 MCQ 1 mark 🖼 Visual

XYZ is an equilateral triangle. WZY is a straight line and WV is parallel to ZX. Find ∠a.

Q7 MCQ 1 mark

Which of the following fractions is closest to 1?

Q8 MCQ 1 mark 🖼 Visual

ABCD is a rectangle. E is the mid-point of AB and ∠DEC = 78°. Find ∠ADE.

Q9 MCQ 1 mark

Chee Seng packed 216 pens into 3 boxes. The ratio of the number of pens in box A to the number of pens in box B to the number of pens in box C is 1 : 3 : 4. How many more pens were there in box B than in box A?

Q10 MCQ 1 mark 🖼 Visual

In the programme guide shown below, one programme leads to another without any break in between. How much longer is the Art and Craft programme than the Music Appreciation programme?

Q11 MCQ 2 marks

The average mass of 3 bags of rice is 10 kg. A fourth bag of rice weighing 6 kg is added to the total mass. What is the average mass of the 4 bags of rice now?

Q12 MCQ 2 marks 🖼 Visual

The table shows the charges for bicycle rental. Dinesh rented 2 bicycles from 4 p.m. to 7 p.m. How much did he pay?

Q13 MCQ 2 marks 🖼 Visual

ABCD is a rectangle. AE is twice of ED and AE = AB. What fraction of the figure is shaded?

Q14 MCQ 2 marks

A pair of sandals costs $w in a shop. The cost of a pair of boots is $25 more than the cost of 3 pairs of sandals. Find the cost of 3 pairs of boots.

Q15 MCQ 2 marks

A printer started to print a set of documents at 10.00 a.m. At 10.24 a.m., half of the set of documents was printed. At what time would 7/8 of the set of documents be printed?

Q16 Open-ended 1 mark

Find the value of 0.78 × 80.

Q17 Open-ended 1 mark

A number has 7 factors. Five of its factors are 1, 2, 4, 16 and 64. What are the other two factors?

Q18 Open-ended 1 mark 🖼 Visual

In the number line below, AB = BC. What is the fraction at point B? Give your answer in the simplest form.

Q19 Open-ended 1 mark

Find the value of 2y − y/5 when y = 7.

Q20 Open-ended 1 mark 🖼 Visual

In the grid below, Siti is standing at Point P, facing North. She makes a 225° turn anticlockwise, and then a 90° turn clockwise. Which point is she facing now?

Q21 Structured 2 marks 🖼 Visual

JKLM is a rectangle. Find the shaded area.

Q22 Structured 2 marks 🖼 Visual

The figure below is made up of a square and an equilateral triangle. The area of the square is 81 cm². Find the perimeter of the figure.

Q23 Structured 2 marks 🖼 Visual

Three classes of pupils sold second-hand books for charity. They collected $7 for each fiction book and $5 for each picture book. The table shows the number of books sold by the three classes. Which class collected the most money and how much was it?

Q24 Structured 2 marks 🖼 Visual

The solid figures below are made up of 1-cm cubes. How many 1-cm cubes must be removed from Figure X to form Figure Y?

Q25 Structured 2 marks 🖼 Visual

In the grid below, the line AB has been drawn for you. (a) Draw an isosceles triangle, such that AB = AC. Label point C clearly. (b) Measure BC.

Q26 Structured 2 marks 🖼 Visual

The figure shows a semicircle and 2 quarter circles drawn inside a square. Find the area of the shaded region. Express your answer in terms of π.

Q27 Structured 2 marks 🖼 Visual

Mrs Lim bought some apples. She gave the fruit seller $50 and received $14 change. How many apples did she buy?

Q28 Structured 2 marks 🖼 Visual

ABCD is a parallelogram and AD = AE. Find ∠DAE.

Q29 Structured 2 marks 🖼 Visual

Mrs Chan paid $600 for a vacuum cleaner after a discount of 25%. What was the price of the vacuum cleaner before discount?

Q30 Structured 2 marks

The pupils in a school are divided equally into Group X and Group Y. The ratio of the number of boys to the number of girls in Group X is 3 : 1 and in Group Y, it is 1 : 2. What is the ratio of the total number of girls to the total number of pupils?

Q31 Open-ended 2 marks

A cup is 2/5-filled with water. It is then poured into an empty jug which has a volume that is three times that of the cup. What fraction of the jug is filled with water?

Q32 Open-ended 2 marks 🖼 Visual

DEFG is a rhombus. HJ is parallel to DE and GF. ∠GDE = 86°. Find ∠HKE.

Q33 Open-ended 2 marks 🖼 Visual

The length of each side of a cube is 12 m. The volume of the cube is twice the volume of a cuboid. Find the volume of the cuboid.

Q34 Open-ended 2 marks

The ratio of the number of ten-cent coins to the number of twenty-cent coins in a purse was 3 : 5. When 60 twenty-cent coins were removed, there were an equal number of ten-cent coins and twenty-cent coins. How many ten-cent coins were there in the purse at first?

Q35 Open-ended 2 marks 🖼 Visual

The figure is made up of a 3 quarter circles and a rectangle. O is the centre of the circle and the diameter of the circle is 14 cm. Find the perimeter of the figure. (Take π = 22/7)

Q36 Open-ended 3 marks 🖼 Visual

PQ is parallel to SR. TR is perpendicular to SR and PR is perpendicular to RQ. Find ∠TVR.

Q37 Structured 3 marks

Mei Ling bought 7/8 m of ribbon to make some bows. She needed 3/20 m of ribbon to make one bow. (a) How many bows can she make? (b) What was the length of ribbon left? Give your answer in the simplest form.

Q38 Structured 4 marks

Three teachers accompanied a group of 38 pupils to an amusement park. The ticket for a child cost $y. An adult ticket cost $2 more than a child's ticket. (a) Find the total amount paid for all. Express your answer in terms of y. (b) The total amount paid was $211. What was the cost of a child's ticket?

Q39 Structured 3 marks 🖼 Visual

The line graph below shows the number of tracksuits sold in a shop from January to June. (a) In which 2 months were the sale of tracksuits sold from January to June above the average number of tracksuits sold during that same period? (b) What was the percentage increase in the sale of tracksuits from May to June?

Q40 Structured 4 marks 🖼 Visual

The table and the bar graph below show the distribution of all Primary 5 pupils in the different CCA groups. The percentage of pupils who joined Clubs was covered by a blot of ink. (a) What was the total number of pupils in Primary 5? (b) Draw the bar in the graph above for the number of pupils in Clubs.

Q41 Open-ended 3 marks

During a sale, Ban Meng bought 10 identical plates. His aunt bought 6 such plates. She also bought 4 mugs at $3.20 each. Altogether, she spent $2.40 less than Ban Meng. How much did Ban Meng and his aunt spend altogether?

Q42 Open-ended 3 marks

In a test, the average class score was 77 marks. Mr Lim discovered that he had recorded 14 students' marks wrongly. After adding 3 marks to each of these students, the average class score became 79. How many students were there in the class?

Q43 Structured 4 marks 🖼 Visual

The solid below is made up of 13 1-cm cubes. (a) Draw the Front view and Top view of the solid in the grid provided. (b) The whole solid is completely dipped into a pot of red paint. Find the total area of the solid that has red paint.

Q44 Open-ended 4 marks 🖼 Visual

The square QRST is made up of two rectangles and a square. The ratio of the area of Rectangle A to the area of Rectangle B is 5 : 3. The ratio of the area of Rectangle B to the area of Square C is 2 : 3. The area of square QRST is 625 cm². Find the breadth of Rectangle B.

Q45 Structured 5 marks 🖼 Visual

ABCD is a square and BCE is an equilateral triangle. AEFG is a trapezium and AG is parallel to EF. (a) Find ∠EAC. (b) Find ∠CEF. (c) The figure above is not drawn to scale. Each of the statements below is either true, false or not possible to tell from the information given. For each of the statements, put a tick (✓) to indicate your answer. Statements: (i) ABEC is a trapezium. (ii) ∠CEF is greater than ∠EFG. (iii) ∠ECG + ∠FGC = 180°.

Q46 Structured 4 marks 🖼 Visual

The figure is made up of shaded and unshaded squares. (a) Complete the table for Figure 5. (b) There are a total of 81 squares. How many shaded and unshaded squares are there?

Q47 Open-ended 5 marks 🖼 Visual

The figure below shows a circle enclosed in a square, WXYZ, of side 40 cm. WP = PX and ZQ = QY. Find the area of the shaded parts. (Take π = 3.14)

P6 Mathematics SA2 2021 — Methodist Girls

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