Primary 5 Mathematics Semestral Assessment 2 (End of Year) Paper 4

TuitionGoWhere Practice Paper - Mathematics Primary 5 (SA2 Version 4) - Answer Key

Total Marks: 80

---

SECTION A: Multiple-Choice Questions (20 marks)

1. Answer: (2) 800 000 [2]

Working: The digit 8 is in the hundred thousands place.
Value = 8 × 100 000 = 800 000.

2. Answer: (2) 7 490 000 [2]

Working: Look at the ten thousands digit (8) and the thousands digit (9). Since 9 ≥ 5, round up the ten thousands digit from 8 to 9.
7 489 321 → 7 490 000.

3. Answer: (2) 3 045 001 [2]

Working: For a number to round to 3 050 000 to the nearest ten thousand, it must be from 3 045 000 to 3 054 999.
Option (2) 3 045 001 falls in this range.

4. Answer: (1) 21 000 [2]

Working: $84 \times 250 = 84 \times 25 \times 10 = 2100 \times 10 = 21 000$.
Alternatively: $84 \times 250 = 84 \times \frac{1000}{4} = \frac{84 000}{4} = 21 000$.

5. Answer: (1) 20 000 [2]

Working: $6 000 000 \div 300 = 6 000 000 \div (3 \times 100) = (6 000 000 \div 100) \div 3 = 60 000 \div 3 = 20 000$.

6. Answer: (1) 72 [2]

Working: Order of operations (BODMAS):
$48 + 12 \times (15 - 9) \div 3$
$= 48 + 12 \times 6 \div 3$
$= 48 + 72 \div 3$
$= 48 + 24$
$= 72$.

7. Answer: (2) $7 \times 500 + 7 \times 30$ [2]

Working: This uses the distributive property: $a \times (b + c) = a \times b + a \times c$.
$7 \times (500 + 30) = 7 \times 500 + 7 \times 30$.

8. Answer: (1) 7 350 [2]

Working: February production = 3 × January production = 3 × 2 450 = 7 350.

9. Answer: (2) $3 825 [2]

Working:
Money spent on TV = $\frac{2}{5} \times 8 500 = 3 400$
Remainder = $8 500 - 3 400 = 5 100$
Money spent on sound system = $\frac{1}{4} \times 5 100 = 1 275$
Money left = $5 100 - 1 275 = 3 825$.

10. Answer: (2) 1 200 [2]

Working:
Number of boys = $\frac{3}{8} \times 4 800 = 1 800$
Number of girls = $4 800 - 1 800 = 3 000$
Difference = $3 000 - 1 800 = 1 200$.

---

SECTION B: Short-Answer Questions (25 marks)

11. Six million seventy thousand and fifty [1]

Explanation: Group digits in threes from right: 6 070 050 → 6 million, 070 thousand, 050.
Write as: Six million seventy thousand and fifty.

12. 224 000 [1]

Working: $5 600 \times 40 = 5 600 \times 4 \times 10 = 22 400 \times 10 = 224 000$.

13. 90 [1]

Working: $72 000 \div 800 = 720 \div 8 = 90$. (Cancel two zeros from both numbers)

14. 200 [2]

Working: Order of operations:
$360 - 45 \times 4 + 120 \div 6$
$= 360 - 180 + 20$
$= 180 + 20$
$= 200$.

15. 4 549 [2]

Explanation: When rounding to the nearest hundred, numbers from 4 450 to 4 549 round to 4 500. The greatest possible value is 4 549.

16. 105 [2]

Working:
$24 \times (18 + 12) \div 6 - 15$
$= 24 \times 30 \div 6 - 15$
$= 720 \div 6 - 15$
$= 120 - 15$
$= 105$.

17. 60 [2]

Working:
Total apples = $15 \times 24 = 360$
Number of bags = $360 \div 6 = 60$.

18. 1 080 [2]

Working:
Rate = $450 \div 5 = 90$ pages per minute
Pages in 12 minutes = $90 \times 12 = 1 080$.

19. 112 [3]

Working (Model/Algebra method):
Let total marbles = 28 units (LCM of 7 and 4).
Gave to John = $\frac{3}{7} \times 28 = 12$ units.
Remainder = $28 - 12 = 16$ units.
Gave to Mary = $\frac{1}{4} \times 16 = 4$ units.
Left = $16 - 4 = 12$ units.
12 units = 48 marbles
1 unit = 4 marbles
Total at first = 28 units = $28 \times 4 = 112$ marbles.

Alternative (Fraction method):
Fraction left = $1 - \frac{3}{7} - \frac{1}{4}(1 - \frac{3}{7}) = \frac{4}{7} - \frac{1}{4} \times \frac{4}{7} = \frac{4}{7} - \frac{1}{7} = \frac{3}{7}$.
$\frac{3}{7}$ of total = 48
Total = $48 \div \frac{3}{7} = 48 \times \frac{7}{3} = 112$.

20. 5 040 [3]

Working:
Let smaller number = 1 unit.
Larger number = 4 units.
Total = 5 units = 12 600
1 unit = $12 600 \div 5 = 2 520$
Difference = 3 units = $3 \times 2 520 = 7 560$.

Wait, recheck:
Sum = 12 600, larger = 4 × smaller.
Smaller + 4 × Smaller = 12 600
5 × Smaller = 12 600
Smaller = 2 520
Larger = 10 080
Difference = 10 080 - 2 520 = 7 560.

Correction: The answer is 7 560, not 5 040. Let me recalculate.
Difference = Larger - Smaller = 4 units - 1 unit = 3 units.
3 units = $3 \times 2 520 = 7 560$.
Correct Answer: 7 560 [3]

---

SECTION C: Long-Answer / Structured Questions (35 marks)

21. [4]

(a) 3 380 English books [1]
Working: $\frac{2}{5} \times 8 450 = 3 380$.

(b) 1 014 Chinese books [1]
Working:
Remaining after English = $8 450 - 3 380 = 5 070$
Chinese books = $\frac{1}{3} \times 5 070 = 1 690$.

Wait, recheck: $\frac{1}{3}$ of 5 070 = 1 690. Yes.

(c) 1 352 Tamil books [2]
Working:
Remaining after Chinese = $5 070 - 1 690 = 3 380$
Malay : Tamil = 3 : 2 (Total 5 units)
5 units = 3 380
1 unit = 676
Tamil books = 2 units = $2 \times 676 = 1 352$.

Mark breakdown:
(a) 1 mark for correct calculation
(b) 1 mark for correct calculation
(c) 2 marks (1 mark for finding remainder 3 380, 1 mark for correct ratio division and answer)

---

22. [5]

**(a) $4 500** [1] **Working:**$\frac{3}{8} \times 12 000 = 4 500$.

**(b) $1 000** [2] **Working:** Remainder after laptop =$12 000 - 4 500 = 7 500$Printer cost =$\frac{2}{5} \times 7 500 = 3 000$Remainder after printer =$7 500 - 3 000 = 4 500$Donation =$\frac{1}{3} \times 4 500 = 1 500$.

Wait, recheck: $\frac{1}{3}$ of 4 500 = 1 500. Yes.

**(c) $3 000** [2] **Working:** Money left =$4 500 - 1 500 = 3 000$.

Mark breakdown:
(a) 1 mark
(b) 2 marks (1 mark for finding remainder after printer $4 500, 1 mark for correct donation)
(c) 2 marks (1 mark for correct subtraction, 1 mark for final answer)
Alternatively: (b) 1 mark for printer, 1 mark for donation; (c) 1 mark for final left

---

23. [4]

(a) 1 500 men [1]
Working: $\frac{5}{12} \times 3 600 = 1 500$.

(b) 700 women [1]
Working:
Remaining after men = $3 600 - 1 500 = 2 100$
Women = $\frac{1}{3} \times 2 100 = 700$.

(c) $\frac{7}{18}$ [2]
Working:
Children = $2 100 - 700 = 1 400$
Fraction = $\frac{1 400}{3 600} = \frac{14}{36} = \frac{7}{18}$.

Mark breakdown:
(a) 1 mark
(b) 1 mark
(c) 2 marks (1 mark for finding children = 1 400, 1 mark for correct fraction in simplest form)

---

24. [4]

(a) 12 000 toys [1]
Working: $\frac{4}{5} \times 15 000 = 12 000$.

(b) 9 000 toys [1]
Working: $\frac{3}{4} \times 12 000 = 9 000$.

(c) 36 000 toys [2]
Working: Total = $15 000 + 12 000 + 9 000 = 36 000$.

Mark breakdown:
(a) 1 mark
(b) 1 mark
(c) 2 marks (1 mark for correct addition of three months, 1 mark for final answer)

---

25. [5]

(a) 7.2 kg [3]
Working (Algebra method):
Let mass of Box B = $x$ kg.
Box A = $x + 1.2$
Box C = $x - 0.8$
Box D = $x$
Total = $(x + 1.2) + x + (x - 0.8) + x = 4x + 0.4 = 28.8$
$4x = 28.4$
$x = 7.1$

Wait, recheck: $28.8 - 0.4 = 28.4$, $28.4 \div 4 = 7.1$.
Box B = 7.1 kg.

Alternative check:
A = 8.3, B = 7.1, C = 6.3, D = 7.1
Sum = 8.3 + 7.1 + 6.3 + 7.1 = 28.8 ✓

(b) 13.4 kg [2]
Working:
Box A + Box C = $(x + 1.2) + (x - 0.8) = 2x + 0.4$
$= 2(7.1) + 0.4 = 14.2 + 0.4 = 14.6$ kg.

Wait, recheck: $2 \times 7.1 = 14.2$, $+ 0.4 = 14.6$.
But A = 8.3, C = 6.3, sum = 14.6. Yes.

Mark breakdown:
(a) 3 marks (1 mark for setting up equation/let statement, 1 mark for correct equation, 1 mark for correct answer)
(b) 2 marks (1 mark for correct expression $2x + 0.4$ or correct individual masses, 1 mark for final answer)

---

Common Mistakes to Watch For:

1. Place value errors: Confusing hundred thousands with millions (Q1)
2. Rounding rules: Forgetting to look at the digit to the right when rounding (Q2, Q3, Q15)
3. Order of operations: Doing addition before multiplication/division (Q6, Q14, Q16)
4. Distributive property: Not multiplying the outside number by both terms inside brackets (Q7)
5. Fraction of remainder: Using original denominator instead of remainder denominator (Q9, Q19, Q21, Q22, Q23)
6. Ratio problems: Not finding the value of one unit correctly (Q21c)
7. Multi-step word problems: Missing intermediate steps (Q19, Q22, Q25)
8. Simplest form: Not reducing fractions fully (Q23c)
9. Decimal mass problems: Calculation errors with decimals (Q25)

Teaching Notes:

• Whole Numbers up to 10 million: Students must be comfortable reading, writing, and identifying place values up to 7 digits.
• Rounding: Emphasize the "look at the next digit" rule. For "greatest possible value" questions, the answer is always one less than the halfway point to the next rounded value.
• Four Operations: BODMAS is critical. Practice mixed operations regularly. Multiplying/dividing by multiples of 10, 100, 1000 uses zero cancellation.
• Fractions with Whole Numbers: "Fraction of a quantity" → multiply. "Fraction of remainder" → find remainder first, then multiply. Model drawing helps visualize.
• Problem Solving: Read carefully for keywords: "remainder", "difference", "total", "each". Break multi-step problems into clear steps with statements.