Primary 6 PSLE Mathematics Problem Solving Heuristics Quiz Set 1

P6 Maths Quiz: Problem Solving Heuristics

Questions: 15 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. Sarah has some stickers. After giving away 12 stickers, she has twice as many stickers left as she gave away. How many stickers did she have originally? a) 24 b) 30 c) 36 d) 48

2. A pattern starts: 2, 6, 18, 54, ... What is the next number? a) 108 b) 126 c) 162 d) 180

3. Tom thinks of a number. He multiplies it by 4, then subtracts 7, and gets 29. What was his original number? a) 8 b) 9 c) 10 d) 11

4. A rectangle has the same perimeter as a square with side 12 cm. If the rectangle's length is 16 cm, what is its width? a) 6 cm b) 8 cm c) 10 cm d) 12 cm

5. In a class of 30 students, 18 like basketball and 20 like football. If 5 students like neither sport, how many students like both sports? a) 8 b) 10 c) 13 d) 15

Section B: Short Answer Questions (10 marks)

Answer all questions. Show your working clearly.

6. Working Backwards Strategy: Amy bought some books. She gave 1/3 of them to her sister, then gave 4 books to her friend. She was left with 8 books. How many books did she buy originally? (4 marks)

7. Make a Table Strategy: A car rental charges $30 per day plus$0.25 per kilometre. Complete the table and find the total cost for driving 200 km in one day. (3 marks)

Distance (km)	Cost ($)
0
50
100
200

8. Draw a Diagram Strategy: A rectangular garden is 8 m by 6 m. A path 1 m wide runs around the inside edge of the garden. What is the area of the path? (3 marks)

Section C: Problem Solving Questions (10 marks)

Answer all questions. Show your working clearly.

9. Guess and Check Strategy: The sum of three consecutive even numbers is 126. Find the three numbers. (5 marks)

10. Use a Pattern Strategy: Study the pattern:

    • 1st figure: 4 dots
    • 2nd figure: 7 dots
    • 3rd figure: 10 dots
    • 4th figure: 13 dots

    a) What is the pattern rule? (2 marks) b) How many dots will be in the 10th figure? (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