Q1
MCQ
1 mark
Simplify the following algebraic expression:
5x − 8 − 2x + 10
P6 Mathematics SA1 2012 — Nanyang
Source: Nanyang, 2012
This P6 Mathematics SA1 paper from Nanyang (2012) covers measurement, patterns and algebra, area and perimeter, percentage, money and average, rate and speed across 48 questions worth 100 marks. Practise Mathematics the way it's tested at P6 level in Singapore, with step-by-step answers on LearnBuddy.
Q2
MCQ
1 mark
Arrange the following fractions in ascending order.
5/3 , 8/5 , 5/6
Q3
MCQ
1 mark
Find the value of 364 ÷ 5.
Q4
MCQ
1 mark
Ben took 1 3/4 h to bake a cake. Josh took 2/3 of the time taken by Ben to bake a similar cake. How long did Josh take to bake the similar cake?
Q5
MCQ
1 mark
There were 50 pens in a box. May Ling put 14 more pens into the box. What was the percentage increase in the number of pens?
Q6
MCQ
1 mark
🖼 Visual
The graph below shows the pattern of Judy's monthly savings. What would her savings be in September?
Q7
MCQ
1 mark
🖼 Visual
Which of the following nets can be folded to form a cube?
Q8
MCQ
1 mark
🖼 Visual
Find the area of triangle ABC.
Q9
MCQ
1 mark
🖼 Visual
The figure below is made up of 3 identical rectangles each measuring 4 cm by 2 cm. Find its perimeter.
Q10
MCQ
1 mark
A car uses 0.09 ℓ of petrol for every 1 kilometre travelled. How many litres of petrol are needed if the car travels 50 kilometres?
Q11
MCQ
2 marks
At a restaurant, 50% of the customers were women. There were 45 men and the rest were children. If there were 150 customers, what percentage of the customers were children?
Q12
MCQ
2 marks
🖼 Visual
Study the Venn Diagram below. What is the maximum number of factors of 90 that can be placed in the shaded part of the diagram?
Q13
MCQ
2 marks
A coach travelled at a uniform speed of 60 km/h for 3 1/2 h. For the rest of the journey, it travelled 22 km for 1/2 h. What was the average speed for the whole journey?
Q14
MCQ
2 marks
🖼 Visual
In the figure below, the ratio of the area of the unshaded part to that of the shaded part is 9 : 14. The ratio of the area of the shaded square to that of the shaded triangle is 4 : 3. The area of the shaded square is 160 cm². Find the area of the unshaded part.
Q15
MCQ
2 marks
🖼 Visual
The figure below shows a running track made up of a rectangle, a semicircle and a square. What is the perimeter of the track? (Take π = 22/7)
Q16
Open-ended
1 mark
If r = 4, find the value of 12r + 14 + 17 − 6r.
Q17
Open-ended
1 mark
In a bookshop, there were 850 Chinese books and 2500 English books. There were 500 more Japanese books than English books. How many books were there?
Q18
Open-ended
1 mark
Find the value of 45 − 5 × 7 + ( 6 + 24 ÷ 6 × 3 ).
Q19
Open-ended
1 mark
Express 18.24 as a mixed number. Give your answer in the simplest form.
Q20
Open-ended
1 mark
A total of $34 845.63 was collected from a fund-raising event. Express this amount to the nearest ten dollar.
Q21
Open-ended
1 mark
Express 12 kg 23 g as kg.
Q22
Open-ended
1 mark
What is the missing number in the box?
54 : 36 = 90 : ____
Q23
Open-ended
1 mark
🖼 Visual
The pattern in the box shows part of a tessellation. Extend the tessellation by drawing two more unit shapes in the space provided.
Q24
Open-ended
1 mark
Jun Kai paid $60 for a book. If he applied to be a member of the bookshop, he would only need to pay $45 for the book. Find the percentage discount given to Jun Kai if he applied to be a member.
Q25
Open-ended
1 mark
Mdm Azizah bought some chocolates. She kept 1/3 of them for her husband. Her children shared the remaining chocolates. Each child ate 1/6 of the chocolates. How many children did she have?
Q26
Open-ended
2 marks
The average of 3 consecutive numbers is 33. Find the smallest number.
Q27
Open-ended
2 marks
Ahmad and Bobby started walking from the school to the library at the same time. Bobby walked at a faster speed of 30 m/min than Ahmad and reached the library in 20 min. Ahmad took 25 min to reach the library. What was the distance between the school and the library?
Q28
Open-ended
2 marks
One plastic block and one wooden block weigh 500 g. Each plastic block weighs 100 g less than each wooden block. Find the mass of each plastic block. Leave your answer in kg.
Q29
Open-ended
2 marks
🖼 Visual
Two semicircles of diameters 10 cm and 20 cm are removed from a square of sides 60 cm each. Find the perimeter of the remaining figure. Express your answer in terms of π.
Q30
Open-ended
2 marks
🖼 Visual
A disc of diameter 14 cm is rolled from point X to point Y. The disc makes 15 revolutions to reach point Y. What is the distance travelled by the disc? (Take π = 22/7)
Q31
Open-ended
2 marks
Paper 2 — The masses of Parcel A, Parcel B and Parcel C are 600 g, 2 kg 400 g and 3 2/5 kg respectively. Find the ratio of the mass of Parcel A to the mass of Parcel B to the mass of Parcel C.
Q32
Open-ended
2 marks
Paper 2 — A car departed from City X at 11.25 a.m. and reached City Y at 2.45 p.m. It travelled at a constant speed of 105 km/h. Find the distance between the two cities.
Q33
Open-ended
2 marks
Paper 2 — The ratio of the capacity of Tank A to the capacity of Tank B is 2 : 5. The ratio of the capacity of Tank B to the capacity of Tank C is 3 : 4. How many times is Tank C as large as Tank A? Leave your answer as a mixed number.
Q34
Open-ended
2 marks
🖼 Visual
Paper 2 — The figure below is made up of 25 identical squares. The area of the figure is 625 cm². What is the perimeter of the figure?
Q35
Open-ended
2 marks
Paper 2 — David is 9m years older than his brother. In 5 years' time, his brother will be 4/7 as old as he. What is their total age now?
Q36
Structured
3 marks
Paper 2 — Jason worked 25 days in a month. He saved 0.28 of his salary and gave 0.5 of the remainder to his mother and spent the rest. He spent $540. How much was he paid per month?
Q37
Structured
3 marks
Paper 2 — A bus and a car left Town A and travelled towards Town B. The bus left Town A at 11.00 a.m. while the car left Town A one hour later. The car overtook the bus at 2.00 p.m. The bus arrived at Town B at 8 p.m. At what time did the car reach Town B?
Q38
Structured
3 marks
🖼 Visual
Paper 2 — The line graph below shows the amount of rainfall recorded in Singapore from January to June. Study the graph carefully and answer the following questions.
(a) What was the percentage decrease in the amount of rainfall between the wettest and the driest months? Express your answer in 2 decimal places.
(b) What was the average amount of rainfall for the first five months?
Q39
Structured
3 marks
Paper 2 — George and Hamid drove at constant speeds from City A to City B. They started their journey at the same time. When George completed 3/4 of the journey, Hamid was 18 km behind George. George reached City B 20 min before Hamid. Find Hamid's speed in km/h.
Q40
Structured
3 marks
🖼 Visual
Paper 2 — (a) Name the solid that can be formed by the net shown below.
(b) The figure below shows a common dice with one to six dots on the different faces. Find the sum of the number of dots shown on the other faces which are not shown.
Q41
Structured
4 marks
🖼 Visual
Paper 2 — Sunhub Telco has a few mobile phone service plans as shown below.
Plan A: 300 SMS, 80 minutes talk time, $27.
Plan B: 400 SMS, 90 minutes talk time, $33.50.
Plan C: 200 SMS, 120 minutes talk time, price ?
Sunhub Telco is going to launch Plan C which offers 200 sms and 120 minutes of talk time. If the cost per sms and the cost per minute of talk time stay the same for the three plans, how much should Sunhub Telco charge for Plan C?
Q42
Structured
4 marks
Paper 2 — Daisy had 3/4 as much money as Vijay after spending $25 on a bag. Then Daisy received $220 from her mother and Vijay spent $50. In the end, Daisy had twice as much money as Vijay. How much money did Daisy have before buying the bag?
Q43
Structured
4 marks
Paper 2 — In a stadium, there were 840 more men than women. 1/7 of the men and 20% of the women left the stadium. In the end, there were 960 more men than women. How many people were at the stadium in the end?
Q44
Structured
4 marks
Paper 2 — Kexin has 25% as many postcards as Si Ming. Si Ming has 140% as many postcards as Lina. If Si Ming gives 28 postcards to Lina, Si Ming and Lina will have equal number of postcards. How many postcards do they have altogether?
Q45
Structured
4 marks
Paper 2 — At first, the total number of beads in Bag A and Bag B was 1760. After 1/4 of the beads in Bag A and 260 beads in Bag B were removed, the ratio of the number of beads in Bag A to the number of beads in Bag B became 6 : 7. Find the ratio of the number of beads in Bag A to that of Bag B at first. Leave your answer in its simplest form.
Q46
Structured
5 marks
🖼 Visual
Paper 2 — In the figure below, ABFG is a rectangle, BCDE is a square, ADF is a triangle and AHI is a quadrant. H is the mid-point of AG. CD is 10 cm, AG is 40 cm and GF is 50 cm. Find the area of the shaded part. (Take π = 3.14)
Q47
Structured
5 marks
Paper 2 — In a bag, the ratio of the number of $2 notes to the number of $10 notes was 3 : 4. Ten $10 notes were removed from the bag to exchange for $2 notes which were then put back into the bag. The total value of money in the bag was unchanged after the exchange. The ratio of the number of $2 notes to the number of $10 notes then became 8 : 3. Find the ratio of the value of the $2 notes to the value of the $10 notes in the bag after the exchange. Leave your answer in its simplest form.
Q48
Structured
5 marks
🖼 Visual
Paper 2 — The figures below are made up of identical circles.
(a) How many shaded circles are there in Pattern 141?
(b) How many unshaded circles are there in Pattern 25?
(c) 1682 circles are needed to form a certain pattern. Which pattern is it?