P6 Mathematics SA1 2019 — Methodist Girls

Q: Express 37 + 12n - 2n + 7n in the simplest form.

(2) 37 + 17n. Combine the terms with 'n': 12n - 2n + 7n = (12 - 2 + 7)n = 17n. So the expression simplifies to 37 + 17n.

Q: 0.15 x ____ + 4 = 154 What is the missing number in the box?

(4) 1000. Let the missing number be x. The equation is 0.15x + 4 = 154. Subtract 4 from both sides: 0.15x = 150. Divide by 0.15: x = 150 / 0.15 = 150 / (15/100) = 150 * (100/15) = 10 * 100 = 1000.

Q: The ratio of Hassan's age to Meng Li's age is 3: 8. What fraction of their total age is Meng Li's age?

(3) 8/11. Hassan's age is 3 units, Meng Li's age is 8 units. The total age is 3 + 8 = 11 units. The fraction of their total age that is Meng Li's age is 8/11.

Q: Express 2/7 as a decimal corrected to 2 decimal places.

(3) 0.29. 2 ÷ 7 ≈ 0.2857. Rounded to 2 decimal places, this is 0.29.

Q: There are 70 fruits in a box, 56 are apples and the rest are pears. What is the ratio of the number of pears to the number of apples?

(1) 1:4. Number of pears = Total fruits - Apples = 70 - 56 = 14. The ratio of pears to apples is 14 : 56. Dividing both sides by 14 gives 1 : 4.

Q: A box contains 200 blue, red and yellow marbles. There are 65 blue marbles, 45 red marbles and the rest are yellow. What percentage of the total number of marbles is yellow?

(1) 45%. Number of yellow marbles = Total marbles - Blue marbles - Red marbles = 200 - 65 - 45 = 90. Percentage of yellow marbles = (Number of yellow marbles / Total marbles) × 100% = (90 / 200) × 100% = 0.45 × 100% = 45%.

Q: Gayle has p stickers. Zahra has three times as many stickers as Gayle and Lee Qin has 4 stickers fewer than Gayle. How many stickers do they have altogether?

(3) (5p-4). Gayle has p stickers. Zahra has 3p stickers. Lee Qin has (p - 4) stickers. Total stickers = p + 3p + (p - 4) = 5p - 4.

Q: Which one of the following shapes does not have both of the properties below? (a) Diagonally opposite angles are equal. (b) Angles between parallel lines are equal.

(3) Trapezium. A rhombus, rectangle, and parallelogram all have diagonally opposite angles equal and two pairs of parallel lines, meaning angles between parallel lines (e.g., alternate interior angles, corresponding angles) can be equal depending on the transversal. A trapezium has only one pair of parallel lines, and its diagonally opposite angles are generally not equal, nor are angles between parallel lines (like consecutive interior angles) necessarily equal.

Q: In the figure, AB, CD and OE are straight lines. ∠a = ∠b. Find ∠a.

(3) 75°. Since AB is a straight line, the sum of angles on the line is 180°. So, ∠a + 30° + ∠b = 180°. Given that ∠a = ∠b, substitute ∠a for ∠b: ∠a + 30° + ∠a = 180°. This simplifies to 2∠a + 30° = 180°. Subtract 30° from both sides: 2∠a = 150°. Divide by 2: ∠a = 75°.

Q: In the figure below, CD, EF and GH are straight lines. EF and GH are parallel to each other. Which one of the following statements is true?

(2) ∠c = ∠g. Given that EF is parallel to GH, and CD is a transversal line: (1) ∠d and ∠e are vertically opposite angles, so ∠d = ∠e is always true. (2) ∠c and ∠g are corresponding angles, so ∠c = ∠g is true because EF || GH. (3) ∠a and ∠f are alternate interior angles, so ∠a = ∠f is true because EF || GH. (4) ∠b and ∠e are vertically opposite angles, so ∠b = ∠e is always true. In typical geometry questions about parallel lines, the expected answer points to a property directly resulting from the parallel lines. Both (2) and (3) fit this criteria. Given the solution points to (2), ∠c = ∠g is the intended correct statement based on corresponding angles.

P6 Mathematics 2019 SA1 47 questions 100 marks

Source: Methodist Girls, 2019

This P6 Mathematics SA1 paper from Methodist Girls (2019) covers measurement, geometry and angles, fractions, percentage, ratio and area and perimeter 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 37 + 12n - 2n + 7n in the simplest form.

Q1 Structured 2 marks 🖼 Visual

Buns were sold at $1.60 each or 2 for $3. What was the greatest number of buns that Siti could buy with $20?

Q2 Structured 2 marks

Ben had enough money to buy either 4 notebooks or 20 exercise books. He bought 5 exercise books and some note books. How many notebooks did he buy?

Q2 MCQ 1 mark

0.15 x ____ + 4 = 154 What is the missing number in the box?

Q3 Structured 2 marks

Find the value of 6 + 3n/5 when n = 7. Give your answer as a mixed number in the simplest form.

Q3 MCQ 1 mark

The ratio of Hassan's age to Meng Li's age is 3: 8. What fraction of their total age is Meng Li's age?

Q4 MCQ 1 mark

Express 2/7 as a decimal corrected to 2 decimal places.

Q4 Structured 2 marks 🖼 Visual

The figure below is a rectangle. The ratio of the area P to the area of Q is 3: 7. What is the ratio of the area of Q to the area of R?

Q5 MCQ 1 mark

There are 70 fruits in a box, 56 are apples and the rest are pears. What is the ratio of the number of pears to the number of apples?

Q5 Structured 2 marks

May bought 160 red and blue buttons. 25% of the buttons bought were red. May used 75% of the blue buttons for art work. How many blue buttons did May use?

Q6 Structured 3 marks 🖼 Visual

The figure shows a square of side 10 cm, a semicircle and a quadrant of radius 5 cm. Find the perimeter of the shaded part. Take π = 3.14.

Q6 MCQ 1 mark

A box contains 200 blue, red and yellow marbles. There are 65 blue marbles, 45 red marbles and the rest are yellow. What percentage of the total number of marbles is yellow?

Q7 Open-ended 3 marks 🖼 Visual

The grid below shows a straight line, CD. Draw 3 more lines to form a square CDEF. Label your diagram clearly.

Q7 MCQ 1 mark

Gayle has p stickers. Zahra has three times as many stickers as Gayle and Lee Qin has 4 stickers fewer than Gayle. How many stickers do they have altogether?

Q8 Structured 3 marks

Gavin had some chicken pies and vegetable pies in the ratio of 5: 2. He sold 18 chicken pies and made 15 more vegetable pies. In the end, he has equal number of chicken pies and vegetable pies. How many vegetables pies did he have at first?

Q8 MCQ 1 mark

Which one of the following shapes does not have both of the properties below? (a) Diagonally opposite angles are equal. (b) Angles between parallel lines are equal.

Q9 MCQ 1 mark 🖼 Visual

In the figure, AB, CD and OE are straight lines. ∠a = ∠b. Find ∠a.

Q9 Structured 3 marks

Su Mei is k years older than her sister. The sum of their ages is 38 years. (a) How old is Su Mei now? Express Su Mei's age is terms of k. (b) If k = 6, how old will Su Mei be in 7 years' time?

Q10 MCQ 1 mark 🖼 Visual

In the figure below, CD, EF and GH are straight lines. EF and GH are parallel to each other. Which one of the following statements is true?

Q10 Structured 3 marks

The books in a library are packed equally into Box A and Box B. The ratio of the number of fiction books to the number of non-fiction books in Box A is 2: 1. The ratio of the number of fiction books to the number of non-fiction books in Box B is 4:11. What is the ratio of the total number of fiction books to the total number of non-fiction books in the library?

Q11 Structured 4 marks

Diana has 1625 ml of orange juice in a jug. She poured the juice into similar glasses, filling each glass with 250 ml of orange juice. (a) What was the maximum number of such glasses Diana could fill? (b) How much of the orange juice was left in the jug? Give your answer in litres.

Q11 MCQ 2 marks

Find the value of 3/10 + 2/5.

Q12 Structured 4 marks

There were 350 goldfish and guppies in a shop. 20% of them were goldfish. After some goldfish were added, the percentage of goldfish increased to 30%. How many goldfish were added?

Q12 MCQ 2 marks

Mother had 5/9 m of ribbon. She used 3/5 of it to tie a present. How much ribbon had she left?

Q13 Structured 4 marks

In May, Mr Ahmad saved 1/3 of his salary and used 1/5 of his monthly salary to buy a mobile phone. He spent 3/8 of the remainder on transport and the rest of the $1750 was spent on food. (a) What fraction of his monthly salary in May was spent on food? (b) What was Mr Ahmad's monthly salary in May?

Q13 MCQ 2 marks

Mr Tan spent 10% of his money on food and 15% on transport. He then had $300 left. How much money did he have at first?

Q14 MCQ 2 marks 🖼 Visual

The figure is formed by an equilateral triangle and 2 semicircles of diameter 6 cm. Find the perimeter of the figure. Leave your answer in terms of π.

Q14 Structured 4 marks 🖼 Visual

The figures below are formed using similar matchsticks and dots. (a) Complete the following table. (b) Ans: (b) ____ Table: Figure Number | Number of dots | Number of matchsticks 1 | 1 | 4 2 | 3 | 10 3 | 6 | 18 4 | (i) | (ii)

Q15 MCQ 2 marks 🖼 Visual

The figure is a semicircle of diameter 14 cm. What is the area of the figure? Take π = 22/7.

Q15 Structured 4 marks 🖼 Visual

In the diagram below, EDB is a straight line and AB is parallel to DC. ∠ABD = 42° and BD = CD. (a) Find ∠DCB. (b) Find ∠FAB.

Q16 Structured 5 marks

Mary has 4/7 as many stickers as Sandy and 2/5 as many stickers as Cindy. Cindy has 15 more stickers than Sandy. (a) What fraction of Cindy's stickers is Sandy's stickers? (b) How many stickers do the 3 girls have altogether?

Q16 Open-ended 1 mark

Write in two million, ten thousand and nine in numerals.

Q17 Open-ended 1 mark

A number when rounded to the nearest hundred is 1 600. What is the greatest possible whole number?

Q17 Structured 5 marks 🖼 Visual

ABC Bubble Tea $4.50 per cup. For every 5 cups of bubble tea purchased, a 20% discount will be given to the 5th cup. Each cup of bubble tea cost $4.50 before discount. (a) How much did Mrs Yeo pay for 5 cups of bubble tea? (b) Mrs Yeo paid $151.20 for some cups of bubble tea. How many cups of bubble tea did she buy?

Q18 Open-ended 1 mark

Find the value of 1/10 + 9/1000. Give your answer as a decimal.

Q19 Open-ended 1 mark

Express 0.9% as a fraction.

Q20 Open-ended 1 mark

Mr Wong has a 10-m long string. He cuts the string into shorter lengths of 5/6 m each. How many such shorter pieces of string will he get?

Q21 Open-ended 2 marks 🖼 Visual

Shade the least number of squares or triangles, such that AB is the line of symmetry.

Q22 Structured 2 marks 🖼 Visual

Figure A is made up of 2 identical quadrants. Both Figure A and Figure B have the same diameter of 20 cm. 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. Statement: Both Figure A and Figure B have the same perimeter. Statement: Both Figure A and Figure B have the same area.

Q23 Open-ended 2 marks 🖼 Visual

In the figure below, ABCD is a square. Find ∠ADE.

Q24 Open-ended 2 marks

James bought 1 1/8 kg of beef. He used 3/4 kg of it to make some beef patties. How much beef had he left?

Q25 Open-ended 2 marks 🖼 Visual

What fraction of the figure is shaded?

Q26 Open-ended 2 marks

There were 50 children at a party. Each child received a packet of sweets which had a mass of 0.15 kg. What was the total mass of the sweets that was given out?

Q27 Open-ended 2 marks

Mr Tan bought 7d pencils. He gave 3 pencils to each of his pupils and had 2d pencils left. Express the number of pupils Mr Tan had in terms of d.

Q28 Open-ended 2 marks 🖼 Visual

In the diagram below, ABE is an equilateral triangle. BC is parallel to AD and DC is perpendicular to BC. Find ∠FBC.

Q29 Open-ended 2 marks 🖼 Visual

The figure is made up of 4 identical rectangles. What is the ratio of the shaded area to the total area of 4 identical rectangles?

Q30 Structured 2 marks 🖼 Visual

The graph below shows the total number of books borrowed from January to April. (a) In which month was there a decrease in the number of books borrowed? (b) What was the percentage increase in the number of books borrowed in February compared to January?

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