When it comes to P5 and PSLE Math questions, some of the hardest challenges your child will face involve complex problem sums that test their ability to apply multiple math concepts. These PSLE math questions often combine topics like fractions, decimals, and percentages, pushing your child to solve the questions by integrating their understanding across areas.

It’s not enough to simply know the formulas; your child must be able to integrate all these concepts and work through multi-step problems to find the solution. That’s what makes these questions difficult, but mastering them is crucial to succeeding in the Primary 5 Maths exams. To succeed, students must master these connections by practising primary 5 maths regularly with test papers and practice questions.

In essence, it’s not just about knowing the math concepts—it’s about understanding how all the pieces fit together. And that’s where many students struggle, as they must think critically, problem-solve, and manage multiple steps—all under the pressure of exams.

## How to Answer Hard P5 Math Questions?

Answering hard P5 Math questions in Singapore requires a strong understanding of problem-solving strategies and techniques.

At BlueTree, we’ve developed a proven and structured method called the** S.O.L.VE. technique**, which teaches students how to approach even the toughest math problems with confidence.

This step-by-step approach equips students with the exact strategies they need to break down complex questions and arrive at the right answer. With the **S.O.L.VE. method**, your child will not only improve their understanding of core concepts but also learn how to tackle higher-order questions that frequently appear in PSLE and primary 5 math exams.

Here’s a structured approach you can teach students to tackle these challenging questions effectively:

### 1. Understand the Question Thoroughly

- Read carefully: Remind students to read the problem multiple times to ensure they get all the crucial details. The
**S.O.L.V.E. Technique**that Bluetree emphasizes can be beneficial to help students answer hard P5 Math questions. - Search for Clues: Identify and highlight important information, such as numbers, operations, and relationships.

### 2. Break the Problem into Smaller Parts

- Multi-step problems can feel overwhelming. Encourage students to dissect the question and deal with one part at a time.
- If the problem involves multiple sentences, get them to write down each piece of information in a step-by-step manner.

### 3. Use Models or Drawings

- Visual representations will help students to break down the question and solve it easier.
- Students can either draw a model/table to represent their answers.

### 4. Apply the CPA Approach

Concrete to Pictorial to Abstract (CPA):

- If manipulatives are available, use them to explore concepts.
- Then move to bar models or other visual representations (pictorial) before transitioning to equations or algebra (abstract).

### 5. Use the Unitary Method for Ratio/Fraction Problems

- In complex word problems, the
**unitary method**(finding the value of one unit) often provides clarity. - This aligns with Step 3 of the S.O.L.V.E. Technique,
**Find the Key**, where identifying one unit can simplify the rest of the problem.

### 6. Re-read & Solve

- After solving, students should re-read the question to ensure they’ve answered what is asked.
- This final step corresponds to Step 4 of the S.O.L.V.E. Technique,
**Solve the Mystery**.

### 7. Time Management & Strategy

- For hard problems, if students get stuck, they should move on to other questions first and return later.
- It’s important to
**not get bogged down**on one question for too long in exams.

### 8. Practice & Familiarity

- The more students practice complex questions, the more familiar they’ll become with patterns and strategies to tackle them.
- This approach, along with constant practice, will help students handle difficult P5 Math questions effectively.

## Hardest P5 Math Questions & Solutions

### Concept 1: One Item Stays Unchanged

#### Q1: There were 300 more apple muffins than banana muffins in a bakery. After 150 banana muffins were sold, the ratio of the number of banana muffins to the number of apple muffins was 3 : 8. How many apple muffins were there?

Only banana muffins were sold, hence apple muffins stay unchanged.

8u → 3u + 150 + 300

8u – 3u = 150 + 300

5u → 450

1u → 450 5 = 90

8u → 90 x 8 = **720 (Ans) **

**There were 720 apple muffins.**

## Concept 2: Difference Stays The Same

#### Q2: Wilma is 7 years old now and her father is 37 years old. In how many years’ time will she be 13 as old as her father?

2u → 30

1u → 30 2 = 15

15 – 7 = **8 (Ans)**

**Wilma will be \(\frac{1}{3}\) as old as her father in 8 years’ time.**

### Concept 3: Total Stays The Same

#### Q3. The ratio of the amount of money Alice had to the amount of money Ben had was 4 : 5. When Alice gave $34 to Ben, the ratio of the amount of money Alice had to the amount of money Ben had became 3 : 8. How much money did Ben have at first?

Alice gave $34 to Ben, Internal Transfer = Total stays the same.

LCM of 11 and 9 = 99

44u – 27u = 17u

17u → 34

1u → 34 17 = 2

55u → 2 x 55 = **110 (Ans)**

**Ben has $110 at first.**

### Concept 4: Assumption Type 1

#### Q4: In an open parking lot, there are a total of 36 vehicles consisting of bicycles (2 wheels) and trucks (6 wheels). There are a total of 128 wheels altogether. How many bicycles are there?

Step 1: Always assume the opposite. (All are trucks)

Step 2: Remember this “catchy phrase” **(TBSO)**

**T**o: Total: 36 x 6 = 216 wheels

**B**: Big gap: 216 – 128 = 88

**S**o: Small gap: 6 – 2 = 4

**O**pposite: Number of bicycles → Big gap Small gap → 88 4 = **22 (Ans)**

There are 22 trucks.

### Concept 4: Assumption Type 2

#### Q5: Elliot was employed to deliver 80 potted plants. For each potted plant that was safely delivered, he was paid $18. For each broken pot of plant, he had to pay $10. If he was paid $320, how many potted plants were broken?

There was a penalty involved of $10 for each broken pot of plant, hence this is a Double Penalty Assumption Type 2 question.

Step 1: Always assume the POSITIVE. (All are safely delivered)

Step 2: Remember this “catchy phrase” **(TBSO)**

**T**o: Total: 80 x $20 = $1440

**B**: Big gap: $1440 – $320 = $1120

**S**o: Small gap: $18 + $10 = $28 (For each pot of broken plant, $28 were “lost”)

**O**pposite: Number of broken pots → Big gap Small gap → 1120 28 = **40 (Ans)**

There are 40 broken pots.

### Concept 5: Equal Concept (Equal Beginning)

#### Q6: Alex and Jamie had the same number of game cards. After Jamie lost 20% of his game cards to Alex, Jamie had 30 cards fewer than Alex. How many game cards did Alex and Jamie have altogether?

Since Alex and Jamie had the same number of game cards at first = Equal Beginning Concept.

Always convert Percentage to Fractions. 20% = \(\frac{1}{5}\)

Difference → 6u – 4u = 2u

2u → 30

1u → 30 2 = 15

Total → 5u + 5u = 10u

10u → 15 x 10 = **150 (Ans)**

Alex and Jamie have 150 game cards altogether.

### Concept 6: Equal Concept (Equal Ending)

#### Q7: There were 216 red and green marbles in a box. After 30% of the red marbles and 50% of the green marbles were given away, there was an equal number of green marbles and red marbles left. How many red marbles were in the box at first?

Always convert Percentage to Fractions.

Red marbles given away → 30% = \(\frac{3}{10}\)

Green marbles given away → 50% = \(\frac{1}{2}\)

Since there was an equal number of green and red marbles left = Equal Ending Concept.

10u + 14u = 216

24u → 216

1u → 216 24 = 9

10u → 9 x 10 = **90 (Ans)**

There were 90 red marbles at first.

### Concept 7: Set Approach, Qty x Value

#### Q8: At a grocery store, apples were sold in packets of 3 for $6, while bananas were sold in packets of 6 for $5. Jordan bought twice as many bananas as apples. He paid $220 for the fruits.

#### (a) How many fruits did he buy altogether?

#### (b) How much more did he spend on apples than bananas?

This question has both quantity and value.

Quantity = number of packets of fruits

Value = cost of each packet of fruits

The total of $215 collected is a hint that this is also a set approach.

Add 2 Pictures

A bag of 3 apples for $6

A bag of 6 bananas for $5

1 set (total) → $5 + $5 = $11

220 11 = 20 sets

(a) 1 set → 3 + 6 = 9 fruits

20 sets → 20 x 9 = **180 (Ans)**

Jordan bought 180 fruits altogether.

(b) 1 set (diff) → $6 – $5 = $1

20 sets x $1 = **$20 (Ans)**

Jordan spent $20 more on apples than bananas.

## Want to know how your child can tackle the hardest P5

Ready to boost your child’s math skills and tackle even the toughest P5 Math questions? 💪 Claim your **free trial class** today and experience BlueTree’s proven **S.O.L.V.E. technique**, designed to help students break down complex problems with ease. Our structured approach builds a strong foundation in Primary Math, equipping your child with the skills and confidence to excel in exams.

Don’t miss this opportunity! Learn more about our primary math tuition programme, P5 Exam Preparatory Course, and headstart/holiday programmes today.

You can also sign up now and give your child the BlueTree advantage on their journey to academic success. 📈