Primary 6 PSLE Mathematics Problem Solving Heuristics Quiz Set 2

P6 Maths Quiz: Problem Solving Heuristics

Questions: 16 Time: 40 minutes Total Marks: 30

Section A: Multiple Choice Questions (10 marks)

Choose the best answer for each question. Each question carries 2 marks.

1. Before and After Strategy: Lisa saves $8 every week. After 5 weeks, she has$65. How much money did she have initially? a) $15 b)$20 c) $25 d)$30

2. Pattern Recognition: The sequence is 1, 4, 9, 16, 25, ... What is the 8th term? a) 36 b) 49 c) 64 d) 81

3. Logical Reasoning: In a box, there are only red and blue balls. There are 5 more red balls than blue balls. If there are 23 balls in total, how many blue balls are there? a) 9 b) 10 c) 12 d) 14

4. Systematic Listing: How many 2-digit numbers can be formed using the digits 2, 5, and 8 (with repetition allowed)? a) 6 b) 9 c) 12 d) 15

5. Make Suppositions: A farmer has chickens and cows. There are 15 heads and 42 legs in total. How many chickens are there? a) 6 b) 7 c) 8 d) 9

Section B: Short Answer Questions (10 marks)

Answer all questions. Show your working clearly.

6. Simplify the Problem: A school ordered pizza for a party. Each pizza was cut into 8 slices. If 45 students each ate 3 slices, how many whole pizzas were needed? (3 marks)

7. Use a Model/Draw a Diagram: Three friends - Alex, Ben, and Charlie - are standing in a line. Alex is not first, Ben is not last, and Charlie is between Alex and Ben. In what order are they standing? (3 marks)

8. Look for Patterns: Complete the table showing the number of handshakes when people meet: (4 marks)

Number of people	Number of handshakes
2	1
3	3
4	6
5	?
6	?

Section C: Problem Solving Questions (10 marks)

Answer all questions. Show your working clearly.

9. Guess and Check + Working Backwards: Mrs. Tan bought some apples. She used half of them to make pies, gave 6 apples to her neighbor, and had 9 apples left. How many apples did she buy originally? (5 marks)

10. Multi-step Problem Solving: A rectangular swimming pool is 20 m long and 12 m wide. A concrete walkway 2 m wide surrounds the entire pool.

    a) What are the outer dimensions of the area including the walkway? (2 marks) b) What is the total area covered by the pool and walkway? (3 marks)

P6 Maths Quiz: Problem Solving Heuristics - Answer Key

Section A: Multiple Choice Questions (10 marks)

1. c) 36 Working backwards:

   • Let original stickers = x
   • After giving away 12: x - 12 stickers left
   • She has twice as many left as she gave away: x - 12 = 2 × 12 = 24
   • So x = 24 + 12 = 36 stickers

2. c) 162 Pattern recognition:

   • 2 × 3 = 6
   • 6 × 3 = 18
   • 18 × 3 = 54
   • 54 × 3 = 162
   • Pattern: multiply by 3 each time

3. b) 9 Working backwards:

   • Let the number = x
   • 4x - 7 = 29
   • 4x = 36
   • x = 9

4. b) 8 cm Use known information:

   • Square perimeter = 4 × 12 = 48 cm
   • Rectangle perimeter = 2(length + width) = 48
   • 2(16 + width) = 48
   • 16 + width = 24
   • width = 8 cm

5. c) 13 Venn diagram strategy:

   • Students liking neither = 5
   • Students liking at least one sport = 30 - 5 = 25
   • Using: Basketball + Football - Both = Total liking at least one
   • 18 + 20 - Both = 25
   • Both = 38 - 25 = 13 students

Section B: Short Answer Questions (10 marks)

6. 24 books (4 marks) Working backwards:

   • Final books: 8
   • Before giving to friend: 8 + 4 = 12 books
   • This represents 2/3 of original (since 1/3 was given to sister)
   • Original books = 12 ÷ (2/3) = 12 × 3/2 = 18 books

   Wait, let me recalculate:

   • Let original = x books
   • After giving 1/3 to sister: (2/3)x books left
   • After giving 4 to friend: (2/3)x - 4 = 8
   • (2/3)x = 12
   • x = 18 books

   Actually, let me check: 18 → give 6 to sister → 12 left → give 4 to friend → 8 left ✓ Answer: 18 books

7. Table completion (3 marks)

Distance (km)	Cost ($)
0	30.00
50	42.50
100	55.00
200	80.00

Working:

• Fixed cost = $30 per day
• Variable cost = $0.25 × distance
• For 200 km: $30 +$0.25 × 200 = $30 +$50 = $80

8. Area of path = 20 m² (3 marks) Draw a diagram strategy:

   • Garden: 8 m × 6 m = 48 m²
   • Inner area (after 1 m path): (8-2) × (6-2) = 6 × 4 = 24 m²
   • Path area = 48 - 24 = 24 m²

   Wait, let me reconsider the problem. If the path runs around the inside edge:

   • Original garden: 8 m × 6 m = 48 m²
   • Remaining garden area: (8-2) × (6-2) = 6 × 4 = 24 m²
   • Path area = 48 - 24 = 24 m²

Section C: Problem Solving Questions (10 marks)

9. The three numbers are 40, 42, 44 (5 marks) Guess and check strategy:

   • Let the three consecutive even numbers be: x, x+2, x+4
   • Sum: x + (x+2) + (x+4) = 126
   • 3x + 6 = 126
   • 3x = 120
   • x = 40
   • The numbers are: 40, 42, 44
   • Check: 40 + 42 + 44 = 126 ✓

10. Pattern analysis (5 marks)

    a) Pattern rule: Start with 4, add 3 each time (2 marks)

    • 1st: 4 dots
    • 2nd: 4 + 3 = 7 dots
    • 3rd: 7 + 3 = 10 dots
    • 4th: 10 + 3 = 13 dots
    • Rule: Add 3 dots for each new figure

    b) 31 dots in the 10th figure (3 marks)

    • Pattern formula: 4 + 3(n-1) where n is the figure number
    • For 10th figure: 4 + 3(10-1) = 4 + 3(9) = 4 + 27 = 31 dots
    • Or counting: 4, 7, 10, 13, 16, 19, 22, 25, 28, 31