Discussions over tough PSLE maths questions are undoubtedly an annual affair.

Apart from leaving some, if not many students deflated for not being able to tackle the questions, it has also led to parents taking issue with the difficulty as they take to online platforms to voice their concerns.

As a matter of fact, maths questions in recent years are more than just tackling standard problem sums. More creative questions have emerged that tests students’ ability to approach them with greater thinking and visualisation.

With this year’s PSLE maths examinations soon to take place on 2 October 2020, we have compiled a list of challenging PSLE Maths Questions from previous years that can better prepare your child in tackling the examinations.

*Note: It is still important to note that the level of difficulty of these maths questions may be subjective, which depends on the student’s ability as well.*

## PSLE Maths Prep: Challenging PSLE Maths Questions Over the Years

**1. Year 2009**

*Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim’s sweets to chocolates becomes 1:7 and the ratio of Ken’s sweets to chocolates becomes 1:4. How many sweets did Ken buy? ***Answer:** 68 sweets.

**Why it was difficult:** This question requires more advanced methods to solve, in particular, the simultaneous equations method which is a secondary school maths topic. While pupils can solve it using the ‘Singapore Model Method’ or ‘Guess and Check’, the most effective way would be using the ‘Units and Parts’ method.

**2. Year 2012**

*A bakery and a library are 120m apart. They are located between Hong’s house and Jeya’s house, as shown below. The bakery is exactly half-way between the two houses.*

*One day, Hong and Jeya started cycling from their houses at the same time and they arrived at the library together. Jeya cycled at 70m per min while Hong cycled at a speed 15m per min faster than Jeya.*

a) How much further did Hong cycle than Jeya? **Answer: 240m**

b) How far is Jeya’s house from the library? **Answer: 1,120m **

**Why it was difficult: **While the question appeared straightforward, there is more than meets the eye. In the event of using the straightforward approach, students might derive that Hong cycled 120m further than Jeya.

However, upon closer look will students notice that apart from Hong who went 120 metres extra, Jeya went 120 metres less than half the distance between two houses. Therefore, the conclusion is Hong cycled 240 m more than Jeya.

**3. Year 2013**

*One machine took 70 minutes while another took 100 minutes to print the same number of copies of a newsletter. The faster machine printed six more copies of the newsletter per minute that the slower one.*

a) The slower machine completed the job at 1pm. At what time was the printing started? **Answer: 11.20am**

b) What was the total number of copies printed by the two machines? **Answer: 2,800**

**Why it was difficult: **Like the maths question that perplexed students in 2012, this is another concept—rate—that isn’t taught until secondary school. The question requires students to apply the concept of speed in which they have learnt, to the concept of rate in their own terms.

**4. Noteworthy: Year 2015**

While not exactly meant for PSLE-level maths examinations, one of the most puzzling questions for students and parents alike is this question that has even made its rounds on U.S. site BuzzFeed.

*Question: Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates. *

May 15, May 16, May 19

June 17, June 18

July 14, July 16

August 14, August 15, August 17

*Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.*

*Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.*

*Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.*

*Albert: Then I also know when Cheryl’s birthday is.*

*So when is Cheryl’s birthday? ***Answer: July 16**

**Why it was difficult: **There is no direct logic to follow in this question that also involves a tricky word play. Tackling the question would require creative thinking and using the process of elimination.

**5. ****Year 2017**

*Jess needs 200 pieces of ribbon, each of length 110cm, to decorate a room for a party. Ribbon is sold in rolls of 25m each. What is the least number of rolls of ribbon that Jess needs to buy? ***Answer: 10 rolls**

**Why it was difficult:** This question requires some creative problem solving on students’ part. The key is to first recognise that the unused portion of each roll is discarded. Following that, students can use division to solve the problem.

**6. Year 2019**

The year in which many found the maths questions to be particularly difficult, such as this pattern question:

PSLE Maths Prep for the upcoming exams. | Image source: StudyRoom

a) Fill in the graph above. **Answer: Total number of triangles in Figure 1: 1, Figure 2: 4, Figure 3: 9, Figure 4: 16, Figure 5: 25; white triangles in Figure 5: 15; grey triangles in Figure 5: 10.**

b) Find the total number of grey and white triangles for Figure 250. **Answer: 62,500 triangles**

c) Find the percentage of grey triangles in Figure 250. **Answer: **50.2 per cent

**Why it was difficult: **This is unlike what students have been exposed to in previous years’ PSLE Maths papers and papers from other primary schools. For such pattern questions, if a particular row’s value is higher than the other, it should be consistent when moving from one figure to another, in ascending order. However, in this question, their values alternate for the white and grey triangles.

Another complex question from the 2019 PSLE maths paper came into spotlight as well, involving five identical semi-circles.

Image source: StudyRoom from Facebook/Serene Eng-Yeo

**Why it was difficult: **The question requires a level of analytical and creative thinking, not expected of a Primary 6 student. Students can ultilise a variety of ways to solve this question, from using multiple equations, drawing a model and labelling overlapping lengths—or even redrawing the figure to complete the circles.

One Singaporean mother was so upset at the difficulty of the 2019 PSLE math paper that she took to Facebook to write an open letter to Education Minister Ong Ye Kung.

“Make it challenging. Make it doable, I agree. But what I don’t understand is the cruel decision to make it so unreasonably tough that children came out crying, deflated, demoralised and crushed.”

While it’s understandable that parents would be concerned over their children’s well-being, PSLE is just one of the many checkpoints in a child’s education journey. Besides, there are varying difficulty of questions in these papers to test different students’ abilities—which is essentially the point of these examinations.

Perhaps it would offer a sense of relief for parents to know that having the young ones face such challenges now will give them the opportunity to build resilience and rise through tougher times in the future.

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