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# Solving the 5 Hardest PSLE Math Questions: A Walk-Through of 2023 PSLE Questions with Sample Solutions

The Primary School Leaving Examination (PSLE) is a significant milestone for students, with mathematics being one of the key subjects assessed. Year after year, students face challenges tackling some of the hardest PSLE math questions. Let's delve into solving the 5 trickiest math questions from the 2023 PSLE math paper and explore step-by-step methods to tackle them effectively.

## Question 1: Dividing Teams Equally

(Adapted from PSLE 2023, Paper 1, Question 14)

Mrs Wong wanted to divide 72 girls and 60 boys equally into as many teams as possible. Each team had the same number of children. The number of boys in each team was the same. How many boys were there in each team?

1. 12

2. 2

3. 5

4. 6

### Common misconception:

• Taking option 4 as the answer, as 6 is a common factor of 72 and 60.

• However, this is incorrect because options do not represent the number of teams but the number of boys in each team.

• With 6 boys in each team, it gives us 60 ÷ 6 = 10 teams.

• We cannot divide 72 girls by 10 teams so the option is incorrect.

### Solution:

Since the question mentioned that each team had the same number of children, we need to find out how many teams there are in the first place.

We need the least number of boys to get the most teams.

• We start with option 2: With 2 boys in each team, it gives us 60 ÷ 2 = 30 teams. We cannot divide 72 girls by 30 teams so the option is incorrect.

• We move on to option 3: With 5 boys in each team, it gives us 60 ÷ 5 = 12 teams. We can divide 72 girls by 12 teams to give us 6 girls in each team so the option is correct.

## Question 2: Calculating Liquid Volumes

(Adapted from PSLE 2023, Paper 1, Question 29)

Gopal had 3 identical tins of paint that were filled. He poured 760 ml out of each tin. The total amount of paint left in the 3 tins after pouring was equal to the amount of paint in 1 tin at first. What was the amount of paint in each tin at first?

### Common misconception:

Taking 760 ml × 3 as the answer.

However, this is incorrect because 760 ml × 3 is the amount of paint poured out. What was equal to the amount of paint in 1 tin is the amount of paint left in the 3 tins, not being poured out.

### Solution:

First, students are always encouraged to draw models for better visualization.

If the amount of paint left in the 3 tins is equal to 1 tin, it means that the amount of paint poured out is equal to 2 tins.

2 tins → 760 ml × 3 = 2280 ml

1 tin → 2280 ml ÷ 2 = 1140 ml

## Question 3: Fraction Calculation

(Adapted from PSLE 2023, Paper 2, Question 5)

### Common misconception:

If bag A contained twice as many pens, we take the fraction x 2.

However, this is incorrect because, in a fraction, the denominator represents the total unit, not the numerator. We need to make the ratio of A twice of B and also a multiple of 3 and 5 (= 15). To achieve that, we have to multiply the ratio by 15.

## Question 4: Grid Formation Analysis

(Adapted from PSLE 2023, Paper 2, Question 11)

Jean used a total of 17 rods and straws to form a rectangular grid that was 2 rods long and 3 straws wide as shown.

1. Jean added more rods and straws to form a larger rectangular grid. The grid was 3 rods long and 4 straws wide. How many rods and straws were there in this grid?

1. Leong also used some rods and straws to form another rectangular grid. Part of his grid is as shown. What was the total number of rods and straws used?

### Solution:

(a) Identify the pattern first.

Number of straws → Wide x (Long + 1)

Number of rods → Long x (Wide  + 1)

For 3 long and 4 wide,

Number of straws → 4 x (3 + 1) = 16

Number of rods → 3 x (4 + 1) = 15

(b) For 4 long and 52 wide,

Number of straws → 52 x (4 + 1) = 260

Number of rods → 4 x (52 + 1) = 212

260 + 212 = 472

## Question 5: Perimeter and Area Calculation

(Adapted from PSLE 2023, Paper 2, Question 17)

Figure 1 shows a trapezium which has a perimeter of 96 cm. Jiayu joins three such trapeziums to form Figure 2 which has a perimeter of 204 cm.

### Solution:

(a) First, we need to understand that the figure has some overlapped PQs.

### Common misconception:

The total number of overlapped PQs is 2. This is incorrect because when they overlapped, we need to take into account both sides that are overlapped which means the total number of overlapped PQs is 4.

We are given the perimeter of the figure and we can find the total perimeter of 3 separate trapeziums by multiplying by 3. The difference will give us the total length of the overlapped PQs.

Total perimeter of 3 trapeziums → 3 x 96 = 288 cm

Lengths of 4 PQs → 288 - 204 = 84 cm

1 PQ → 84 ÷ 4 = 21 cm

Understanding the method to solve PSLE maths difficult questions is crucial for success. By addressing common misconceptions and employing step-by-step approaches, students can navigate even the most problematic questions with confidence.

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