Primary 6 PSLE Mathematics Weighted Assessment 3 (Term 3) Paper 2

Answer Key & Marking Scheme - Mathematics Primary 6 PSLE

Paper: WA3 Practice Paper (Version 2 of 5)
Topic: Whole Numbers

Section A (1 mark each)

1. 4,060,005
Teaching Note: Break down the place values. Millions: 4. Thousands: 060 (sixty thousand). Ones: 005 (five). Ensure zeros are placed correctly in the hundred-thousands, ten-thousands, hundreds, and tens columns.

2. 8,460,000
Teaching Note: Identify the ten-thousands digit (5). Look at the digit to its right (thousands digit is 6). Since $6 \ge 5$, round up the ten-thousands digit. $5 \rightarrow 6$. Replace digits to the right with zeros.

3. 700,000 (or 7 hundred thousands)
Teaching Note: The digit 7 is in the hundred-thousands place. Its value is $7 \times 100,000$.

4. 9,310
Teaching Note: Standard multiplication algorithm.
$245 \times 8 = 1960$
$245 \times 30 = 7350$
$1960 + 7350 = 9310$.

5. 378
Teaching Note: Long division.
$45 \div 12 = 3$ rem $9$. Bring down 3 $\rightarrow 93$.
$93 \div 12 = 7$ rem $9$. Bring down 6 $\rightarrow 96$.
$96 \div 12 = 8$.
Result: 378.

6. 11
Teaching Note: $5000 \div 13$.
$50 \div 13 = 3$ rem $11$.
$110 \div 13 = 8$ rem $6$ ($13 \times 8 = 104$).
$60 \div 13 = 4$ rem $8$ ($13 \times 4 = 52$).
Wait, let's re-calculate carefully.
$13 \times 300 = 3900$. Remainder $1100$.
$13 \times 80 = 1040$. Remainder $60$.
$13 \times 4 = 52$. Remainder $8$.
Correction: $5000 = 13 \times 384 + 8$.
Let's check $13 \times 384$: $13 \times 300 = 3900$, $13 \times 80 = 1040$, $13 \times 4 = 52$. Sum $= 4992$.
$5000 - 4992 = 8$.
Answer is 8.
(Self-Correction during generation: Previous mental check was flawed. Final answer is 8.)

7. 105
Teaching Note: Order of operations (BODMAS). Multiplication first: $25 \times 4 = 100$.
Then addition/subtraction from left to right: $15 + 100 - 10 = 115 - 10 = 105$.

8. 6
Teaching Note: Factors of 18: 1, 2, 3, 6, 9, 18.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Common factors: 1, 2, 3, 6. Highest is 6.

9. 24
Teaching Note: Multiples of 6: 6, 12, 18, 24, 30...
Multiples of 8: 8, 16, 24, 32...
Lowest common multiple is 24.

10. 36
Teaching Note: A number divisible by 4 and 9 must be divisible by their LCM. Since 4 and 9 are coprime (HCF is 1), $\text{LCM}(4, 9) = 4 \times 9 = 36$. The smallest positive whole number is 36.

Section B (2 marks each)

11. 45 packets
Working:
Total pencils $= 15 \times 24 = 360$.
Number of packets $= 360 \div 8$.
$360 \div 8 = 45$.
Alternative Method:
$\frac{15 \times 24}{8} = 15 \times 3 = 45$.
Marking: 1 mark for total pencils (360), 1 mark for correct division (45).

12. 300
Working:
Let the smaller number be $1$ unit.
Larger number $= 2$ units.
Total $= 3$ units $= 450$.
$1$ unit $= 450 \div 3 = 150$.
Larger number $= 2 \times 150 = 300$.
Marking: 1 mark for finding 1 unit (150), 1 mark for larger number (300).

13. 2,880 toys
Working:
Rate per day $= 1200 \div 5 = 240$ toys/day.
Toys in 12 days $= 240 \times 12$.
$240 \times 10 = 2400$.
$240 \times 2 = 480$.
$2400 + 480 = 2880$.
Marking: 1 mark for daily rate (240), 1 mark for final answer (2880).

14. 27
Working:
$3 \times (A - 12) = 45$
Divide both sides by 3:
$A - 12 = 45 \div 3$
$A - 12 = 15$
$A = 15 + 12$
$A = 27$
Marking: 1 mark for intermediate step ($A-12=15$), 1 mark for final answer (27).

15. 7 friends
Working:
Let number of friends be $u$.
Case 1: Total stickers $= 5u + 3$.
Case 2: Total stickers $= 6u - 4$.
Equating the totals:
$5u + 3 = 6u - 4$
$3 + 4 = 6u - 5u$
$7 = u$
Check:
If 7 friends, Case 1: $5(7)+3 = 38$.
Case 2: $6(7)-4 = 42-4 = 38$. Matches.
Marking: 1 mark for setting up equation or logical difference method, 1 mark for answer (7).
Note on Difference Method: Difference in stickers per friend is $6-5=1$. Difference in total surplus/deficit is $3 - (-4) = 7$. Number of friends $= 7 \div 1 = 7$.

Section C (2 marks each)

16. 18
Working:
Find three consecutive numbers whose product is 210.
Estimate cube root of 210. $5^3 = 125$, $6^3 = 216$. So numbers are around 5, 6, 7.
Check: $5 \times 6 \times 7 = 30 \times 7 = 210$.
The numbers are 5, 6, and 7.
Sum $= 5 + 6 + 7 = 18$.
Marking: 1 mark for identifying numbers (5, 6, 7), 1 mark for sum (18).

17. 1,003
Working:
Formula: $\text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}$.
Number $= (8 \times 125) + 3$.
$8 \times 125 = 1000$.
$1000 + 3 = 1003$.
Marking: 1 mark for multiplication ($1000$), 1 mark for adding remainder ($1003$).

18. 100 dots
Working:
Pattern analysis:
Figure 1: $1^2 = 1$
Figure 2: $2^2 = 4$
Figure 3: $3^2 = 9$
Figure 4: $4^2 = 16$
Rule: Number of dots $= n^2$ where $n$ is the figure number.
For Figure 10: $10^2 = 100$.
Marking: 1 mark for identifying square number pattern, 1 mark for correct calculation (100).

19. 60 marbles
Working:
Let Box B have $1$ unit. Box A has $3$ units.
Transfer 20 from A to B:
Box A becomes $3u - 20$.
Box B becomes $1u + 20$.
They are equal:
$3u - 20 = 1u + 20$
$2u = 40$
$1u = 20$.
Box A initially $= 3u = 3 \times 20 = 60$.
Check: A=60, B=20. Transfer 20: A=40, B=40. Equal.
Marking: 1 mark for finding 1 unit (20), 1 mark for Box A initial (60).

20. **\2$** *Working:* Let$p$be cost of pen,$n$be cost of notebook. (1)$3p + 2n = 14$(2)$2p + 3n = 16$Multiply (1) by 3:$9p + 6n = 42$Multiply (2) by 2:$4p + 6n = 32$Subtract the second new equation from the first:$(9p + 6n) - (4p + 6n) = 42 - 32$$5p = 10$$p = 2$*Marking:* 1 mark for correct elimination/substitution method setup, 1 mark for answer ($2).
Alternative: Add both equations: $5p + 5n = 30 \rightarrow p+n=6$.
Subtract original equations: $(2p+3n)-(3p+2n) = 16-14 \rightarrow n-p=2$.
Solve system: $p+n=6$ and $n-p=2$. Adding them: $2n=8, n=4$. Then $p=2$.