P6 Mathematics SA2 2018 — Henry Park

Q: Express 3.025 as a mixed number in the simplest form.

D. 3 1/40. 3.025 = 3 + 25/1000 = 3 + 1/40, so the mixed number is 3 1/40.

Q: Simplify 12 + 10y − 5 − 9y + 2

C. 9 + y. Combine constants: 12 − 5 + 2 = 9. Combine y terms: 10y − 9y = y. Result: 9 + y.

Q: In the figure below, ABCD is made up of four identical squares. What fraction of the figure is shaded?

D. 1/4. The large square ABCD is split into four identical small squares (a 2×2 grid). Two shaded triangles each have base = half a side and height = one side, together forming 1/4 of the whole figure.

Q: Which of the following is the same as 2030 cm?

C. 20 m 30 cm. 2030 cm = 2000 cm + 30 cm = 20 m 30 cm.

Q: What is the area of triangle ABC shown below?

A. 15 cm². Base CB = 6 cm + 4 cm = 10 cm; perpendicular height from A = 3 cm. Area = ½ × 10 × 3 = 15 cm².

Q: In the square grid below, which two lines are perpendicular to each other?

B. BE and ED. Reading the gradients of the segments off the square grid, BE and ED meet at right angles (their slopes are negative reciprocals), so they are perpendicular.

Q: Use the information below to answer questions 7 and 8. The pie chart shows the different games a number of students played during recess. Half of the students played soccer. What fraction of the students played basketball?

B. 1/6. Soccer = 1/2 and Frisbee = 1/12. The Basketball and Badminton sectors meet at a right angle at the centre, so Badminton = 1/4. Remaining for Basketball = 1 − 1/2 − 1/12 − 1/4 = 12/12 − 6/12 − 1/12 − 3/12 = 2/12 = 1/6.

Q: There were 75 more students who played soccer than frisbee. How many students played badminton?

C. 45. Soccer − Frisbee = 1/2 − 1/12 = 5/12 of total = 75 students, so total = 75 ÷ 5/12 = 180. Badminton = 1/4 of 180 = 45.

Q: Joan baked a pie. She ate 1/6 of it and her sister ate 1/4 of the remainder. What fraction of the pie was left?

B. 5/8. After Joan eats 1/6, remainder = 5/6. Sister eats 1/4 of 5/6 = 5/24. Left = 5/6 − 5/24 = 20/24 − 5/24 = 15/24 = 5/8.

Q: The bottom half of a symmetric figure is shown below. AB is the line of symmetry. Which one of the following completes the symmetric figure?

D. (option 4). The completed figure must be the mirror image of the given bottom strip reflected across line AB. Option (4) shows the top strip that is the correct reflection of the given pattern of shaded and half-shaded squares.

P6 Mathematics 2018 SA2 47 questions 100 marks

Source: Henry Park, 2018

This P6 Mathematics SA2 paper from Henry Park (2018) covers measurement, geometry and angles, money, area and perimeter, fractions and graphs and data 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.

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Q1 MCQ 1 mark

Express 3.025 as a mixed number in the simplest form.

Q2 MCQ 1 mark

Simplify 12 + 10y − 5 − 9y + 2

Q3 MCQ 1 mark 🖼 Visual

In the figure below, ABCD is made up of four identical squares. What fraction of the figure is shaded?

Q4 MCQ 1 mark

Which of the following is the same as 2030 cm?

Q5 MCQ 1 mark 🖼 Visual

What is the area of triangle ABC shown below?

Q6 MCQ 1 mark 🖼 Visual

In the square grid below, which two lines are perpendicular to each other?

Q7 MCQ 1 mark 🖼 Visual

Use the information below to answer questions 7 and 8. The pie chart shows the different games a number of students played during recess. Half of the students played soccer. What fraction of the students played basketball?

Q8 MCQ 1 mark 🖼 Visual

There were 75 more students who played soccer than frisbee. How many students played badminton?

Q9 MCQ 1 mark

Joan baked a pie. She ate 1/6 of it and her sister ate 1/4 of the remainder. What fraction of the pie was left?

Q10 MCQ 1 mark 🖼 Visual

The bottom half of a symmetric figure is shown below. AB is the line of symmetry. Which one of the following completes the symmetric figure?

Q11 MCQ 2 marks 🖼 Visual

Use the information below to answer questions 11 and 12. Tom received $30 each week for his pocket money. The line graph below shows the amount of pocket money he had left at the end of each day. On which day did Tom spend the most amount of money?

Q12 MCQ 2 marks 🖼 Visual

What was the average amount of pocket money that Tom spent each day from Monday to Friday?

Q13 MCQ 2 marks 🖼 Visual

In the figure, ABEF is a rectangle, BCD is an equilateral triangle and ∠ABC = 242°. Find ∠DBE.

Q14 MCQ 2 marks

Adam and Bella had the same number of stamps. After Adam gave Bella 1/6 of his stamps, Bella had 84 stamps. How many stamps did Adam have at first?

Q15 MCQ 2 marks 🖼 Visual

A family of 8 adults and 5 children went for the high tea buffet at Royal Café. What is the least amount of money the family had to pay? Royal Café High Tea Buffet — Adult price: $22.50, Child price: $11.10. Promotion! For 3 paying adults, 2 children dine free!

Q16 Open-ended 1 mark

Find the value of (85 − 7a)/4 when a = 5. Express your answer as a decimal.

Q17 Open-ended 1 mark

Find the value of 4/5 ÷ 3/7.

Q18 Open-ended 1 mark

A number with 3 decimal places is 7.9 when rounded to 1 decimal place. What is the greatest possible value of this number?

Q19 Open-ended 1 mark

The ratio of the length to the breadth of a cuboid is 3 : 1. The ratio of the height to breadth of the cuboid is 4 : 3. Find the ratio of the length to the height of the cuboid.

Q20 Open-ended 1 mark 🖼 Visual

The graph shows the amount of money collected by 3 classes for a charity. What was the total amount of money collected by the 3 classes?

Q21 Structured 2 marks 🖼 Visual

The figure shows a rectangular box partly filled with 1-cm cubes. What is the capacity of the rectangular box?

Q22 Structured 2 marks 🖼 Visual

The airmail rates to Country X and Country Y are shown below. (First 20 g or part thereof: Country X $1.25, Country Y $0.75. Every additional 10 g or part thereof: Country X $0.30, Country Y $0.45.) Jayen sent a letter weighing 18 g to Country X and a letter weighing 41 g to Country Y. How much did he pay altogether?

Q23 Structured 2 marks 🖼 Visual

The receipt below shows the cost of 3 dresses Mrs Koh bought. The cost of Dress C was 20% of the total cost of the 3 dresses. Find the total cost of the 3 dresses. (Dress A $136, Dress B $104, Dress C $____)

Q24 Structured 2 marks 🖼 Visual

In the figure, ABC, CDE, EFC and CGA are identical isosceles triangles. ∠ABC = 38° and ∠BCD = 43°. Find ∠GCF.

Q25 Structured 2 marks 🖼 Visual

Three rhombuses, A, B and C are shown in the square grid below. Each statement below is either true, false or not possible to tell from the information given. For each statement, put a tick (✓) in the correct column. (a) Rhombus A has the same perimeter as Rhombus C. (b) Rhombus A has the same area as Rhombus B.

Q26 Structured 2 marks 🖼 Visual

Figure 1 is a parallelogram. Figure 2 is made up of 7 such parallelograms. The perimeter of Figure 2 is 180 cm. What is the length of the side AB of the parallelogram?

Q27 Structured 2 marks

The average of three different 2-digit numbers is 30. Find the largest possible sum of two of the numbers.

Q28 Structured 2 marks 🖼 Visual

The figure shows 2 identical three-quarter circles on a rectangle. Given that the length of the rectangle is 30 cm, find the area of the unshaded parts of the figure. (Take π = 3.14)

Q29 Structured 2 marks 🖼 Visual

Figure 1 shows a cuboid measuring 5 cm by 7 cm by 10 cm. The base of the cuboid is shaded. Figure 2 shows the net of the cuboid. (a) Find the length of side AB of the net in Figure 2. (b) Shade two more faces in Figure 2 so that the total shaded area of the net is 120 cm².

Q30 Structured 2 marks

Mr Tan is between 30 and 70 years old. This year, his age is a multiple of 6. Next year, his age will be a multiple of 7. How old is Mr Tan this year?

Q31 Structured 2 marks 🖼 Visual

(Paper 2, ____) 3/5 of the length of Bar X is glued to 2/5 of the length of Bar Y as shown. Find the ratio of the length of Bar X to the length of Bar Y. Express your answer in the simplest form.

Q32 Structured 2 marks 🖼 Visual

(Paper 2, ____) Seven places of interest, A, B, C, D, E, F and G, of a town are shown in the square grid below. (a) In which direction is D from E? (b) Mr Lee is at one of the places of interest. He is facing C. When he turns 270° anti-clockwise, he faces F. Which place of interest is Mr Lee at?

Q33 Structured 2 marks 🖼 Visual

(Paper 2, ____) The figure below shows a parallelogram PQRS drawn on the square grid. (a) Draw an isosceles triangle PXY in the square grid such that PX is twice of PS, PX = XY and ∠PXY is 90°. Triangle PXY does not overlap with parallelogram PQRS. (b) What is the ratio of the area of triangle PXY to the area of parallelogram PQRS? Express your answer in the simplest form.

Q34 Structured 2 marks 🖼 Visual

(Paper 2, ____) The pie chart below shows the different types of muffins in a bakery. 1/4 of the muffins were either vanilla or plain. There were twice as many vanilla muffins as plain muffins. The different types of muffins are also represented by the bar graph below. Draw the bars for the number of chocolate muffins and plain muffins.

Q35 Structured 2 marks 🖼 Visual

(Paper 2, ____) In the figure, ABCD is a trapezium, ABC is an isosceles triangle, ∠ADC = 84° and ∠ABC = 104°. Find ∠CAD.

Q36 Structured 3 marks

(Paper 2, ____) Ali, Ben and Chen have an average of 42 stamps. Ali has y stamps, Ben has 4 times as many stamps as Ali and Chen has 27 stamps less than Ben. (a) Find the number of stamps Chen has in terms of y. (b) How many stamps does Ali have?

Q37 Structured 3 marks

(Paper 2, ____) The ratio of the volume of water in Jug A to the volume of water in Jug B is 8 : 3. After 50 ml of water was poured from Jug A to Jug B, Jug A had twice amount of water as Jug B. How much water was there in Jug B in the end?

Q38 Structured 3 marks

(Paper 2, ____) 25% of the coins in a coin box are 50-cent coins, 35% are 20-cent coins and the rest are 10-cent coins. The total amount of money in the box is $28.20. How many 10-cent coins are there in the box?

Q39 Structured 3 marks 🖼 Visual

(Paper 2, ____) At a minimart, rice is sold in bags of different masses as shown below. (1-kg $4.40, 2-kg $8.05, 5-kg $19.90.) What is the least amount of money that a customer has to pay to buy 16 kg of rice?

Q40 Structured 3 marks 🖼 Visual

(Paper 2, ____) Figure 1 is made up of 5 identical rectangles. The area of Figure 1 is 375 cm². The rectangles are rearranged into Figure 2. Find the perimeter of Figure 2.

Q41 Structured 3 marks

(Paper 2, ____) Aisyah and Jenny competed in a 200-m race. Both did not change their speeds from start to finish. Aisyah ran at 8 m/s and Jenny ran at a speed 3 m/s slower than Aisyah. How far was Jenny from Aisyah when Aisyah reached the finishing line?

Q42 Structured 4 marks 🖼 Visual

(Paper 2, ____) The graph below shows the number of magazines sold each month by a new publishing company from January to June. (a) What was the percentage increase in the number of magazines sold in March compared to January? (b) What was the average increase in the number of magazines sold per month from January to June?

Q43 Structured 4 marks 🖼 Visual

(Paper 2, ____) Two rectangular tanks, A and B, are shown below. The height of Tank A is 54 cm. After Annie poured 41 472 cm³ of water into an empty Tank A, it was 4/9 filled as shown below. (a) Find the base area of Tank A. (b) After Annie poured some water from Tank A into an empty Tank B, the height of the water level in Tank A decreased to 21.5 cm. Given that the base area of Tank B is 270 cm², find the height of the water level in Tank B.

Q44 Structured 4 marks 🖼 Visual

(Paper 2, ____) Shiva has a piece of paper, ABCD, in the shape of a parallelogram. He folded it along the line EF as shown below. Given that ∠BCD = 167°, ∠BEF = 138°, AE and BFC are straight lines, find: (a) ∠x, (b) ∠y.

Q45 Structured 5 marks 🖼 Visual

(Paper 2, ____) In the figure below, ABCD is a rectangle and BCX is a quarter circle. The length of BC is 28 cm. The total area of the shaded parts of the figure is 514 cm². Find the area of the unshaded part CXY of the figure. (Take π = 22/7)

Q46 Structured 5 marks

(Paper 2, ____) 3/8 of Abby's savings was $100 more than 1/3 of Betty's savings. After Abby spent 5/8 of her savings and Betty spent 1/2 of her savings, Betty had $30 more than Abby. Find Betty's savings at first.

Q47 Structured 5 marks 🖼 Visual

(Paper 2, ____) Farah uses black and white buttons to form figures that follow a pattern. The first four figures are shown below. (a) The table shows the number of black and white buttons used for each figure. Complete the table for Figure 5. (b) A figure in the pattern has a total of 176 black and white buttons. What is the Figure Number? (c) A figure in the pattern has 784 white buttons. How many black buttons are there in that figure?

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