Secondary 1 Other Practice Paper 5

TuitionGoWhere Practice Paper - Other Secondary 1 (Answer Key)

Subject: Other
Level: Secondary 1
Paper: Practice Paper Version 5
Total Marks: 60

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Section A: Ratio and Proportion [15 marks]

Question 1 [2 marks]

Answer: $18 : 5$ or $3.6 : 1$

Working:

1. Convert decimal to fraction: $3.6 = \frac{36}{10} = \frac{18}{5}$
2. Write ratio: $\frac{18}{5} : \frac{4}{5}$
3. Multiply both sides by 5 (LCM of denominators): $18 : 4$
4. Simplify by dividing by 2: $9 : 2$

Alternative method: $3.6 : \frac{4}{5} = 3.6 \div 0.8 = 4.5 = \frac{9}{2}$, so ratio is $9 : 2$

Marking notes:

• 1 mark for correct conversion of decimal to fraction or correct method
• 1 mark for final simplified ratio $9 : 2$
• Accept $18 : 5$ if student multiplies by 5 but forgets to simplify (1 mark only)
• Common error: Not simplifying fully (e.g., leaving as $18 : 4$)

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Question 2 [2 marks]

Answer: 200 students

Working:

• Ratio Bus : Walk = $5 : 3$
• 3 units = 120 students
• 1 unit = $120 \div 3 = 40$ students
• 5 units = $5 \times 40 = 200$ students

Marking notes:

• 1 mark for finding value of 1 unit (40)
• 1 mark for correct final answer (200)
• Common error: Multiplying 120 by 5/3 directly without unit method

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Question 3 [3 marks]

Answer:
Orange juice: 1000 mL
Apple juice: 1500 mL
Water: 2500 mL

Working:

• Total ratio parts = $2 + 3 + 5 = 10$ parts
• Total volume = 5 litres = 5000 mL
• 1 part = $5000 \div 10 = 500$ mL
• Orange juice = $2 \times 500 = 1000$ mL
• Apple juice = $3 \times 500 = 1500$ mL
• Water = $5 \times 500 = 2500$ mL

Check: $1000 + 1500 + 2500 = 5000$ mL ✓

Marking notes:

• 1 mark for correct total parts (10) and conversion to mL (5000)
• 1 mark for correct value of 1 part (500 mL)
• 1 mark for all three correct amounts
• Common error: Forgetting to convert litres to millilitres

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Question 4 [3 marks]

Answer: 1008 cm²

Working:

• Let length = $7x$ cm, breadth = $4x$ cm
• Perimeter = $2(7x + 4x) = 22x = 132$
• $x = 132 \div 22 = 6$
• Length = $7 \times 6 = 42$ cm
• Breadth = $4 \times 6 = 24$ cm
• Area = $42 \times 24 = 1008$ cm²

Marking notes:

• 1 mark for setting up $22x = 132$ or equivalent
• 1 mark for finding $x = 6$ and correct dimensions
• 1 mark for correct area calculation
• Common error: Finding dimensions but forgetting to calculate area

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Question 5 [3 marks]

Answer: $1350

Working:

• Ratio Ahmad : Bala : Cindy = $4 : 5 : 6$
• Difference between Cindy and Ahmad = $6 - 4 = 2$ units
• 2 units = $180
• 1 unit = $90
• Total units = $4 + 5 + 6 = 15$ units
• Total sum = $15 \times 90 =$1350

Check: Ahmad = $360, Bala =$450, Cindy = $540. Difference =$540 - $360 =$180 ✓

Marking notes:

• 1 mark for identifying 2 units = $180
• 1 mark for finding 1 unit = $90
• 1 mark for correct total sum
• Common error: Using wrong difference (e.g., 6 - 5 = 1 unit)

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Question 6 [2 marks]

Answer: 2.1 km

Working:

• Scale $1 : 25\,000$ means 1 cm on map = 25,000 cm in reality
• Map distance = 8.4 cm
• Actual distance = $8.4 \times 25\,000 = 210\,000$ cm
• Convert to km: $210\,000 \div 100\,000 = 2.1$ km

Marking notes:

• 1 mark for correct multiplication ($8.4 \times 25\,000$)
• 1 mark for correct conversion to km (÷ 100,000)
• Common error: Wrong conversion factor (e.g., ÷ 1000 or ÷ 10,000)

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Section B: Percentage and Discount [15 marks]

Question 7 [2 marks]

Answer: $23.80

Working:

• Discount = $15\% \times 28 = 0.15 \times 28 =$4.20
• Sale price = $28 -$4.20 = $23.80

Alternative: Sale price = $85\% \times 28 = 0.85 \times 28 =$23.80

Marking notes:

• 1 mark for correct discount calculation or correct method
• 1 mark for correct final answer
• Common error: Calculating 15% of 28 incorrectly

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Question 8 [3 marks]

Answer: $61.20

Working:

• First discount (20%): Price = $80\% \times 85 = 0.8 \times 85 =$68
• Second discount (10% for members): Price = $90\% \times 68 = 0.9 \times 68 =$61.20

Alternative (single step): $85 \times 0.8 \times 0.9 =$61.20

Marking notes:

• 1 mark for correct first discounted price ($68)
• 1 mark for applying second discount correctly
• 1 mark for correct final answer
• Common error: Adding discounts (20% + 10% = 30%) and calculating $70\% \times 85 =$59.50 (incorrect)

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Question 9 [2 marks]

Answer: $1600

Working:

• Let original price = $x$
• After 25% discount: $75\% \times x = 1200$
• $0.75x = 1200$
• $x = 1200 \div 0.75 = 1600$

Check: 25% of 1600 = 400, 1600 - 400 = 1200 ✓

Marking notes:

• 1 mark for correct equation ($0.75x = 1200$ or equivalent)
• 1 mark for correct answer
• Common error: Calculating $1200 \times 1.25 = 1500$ (incorrect - this adds 25% of discounted price, not original)

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Question 10 [2 marks]

Answer: 40%

Working:

• Cost price = $45
• Selling price = $63
• Profit = $63 -$45 = $18
• Profit % = $\frac{18}{45} \times 100\% = 40\%$

Marking notes:

• 1 mark for correct profit calculation ($18)
• 1 mark for correct percentage calculation
• Common error: Using selling price as denominator ($\frac{18}{63} \times 100\% \approx 28.6\%$)

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Question 11 [2 marks]

Answer: 20%

Working:

• Increase = $54\,000 - 45\,000 = 9\,000$
• Percentage increase = $\frac{9\,000}{45\,000} \times 100\% = 20\%$

Marking notes:

• 1 mark for correct increase (9000)
• 1 mark for correct percentage calculation
• Common error: Using new population as denominator ($\frac{9000}{54000} \times 100\% \approx 16.7\%$)

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Question 12 [4 marks]

Answer: $300

Working:

• Let cost price = $C$
• Selling price after 15% discount = $306
• Marked price $\times 0.85 = 306$
• Marked price = $306 \div 0.85 = 360$
• Profit = 20% on cost price, so Selling price = $120\% \times C = 1.2C$
• $1.2C = 306$
• $C = 306 \div 1.2 = 255$

Wait, let me re-read: "sold for $306 after a discount of 15%. If the shopkeeper made a profit of 20% on the cost price"

So $306 is the selling price (after discount). This selling price gives 20$306 = 1.2 \times \text{Cost price}$Cost price =$306 \div 1.2 = 255$

Marking notes:

• 1 mark for recognising $306 is the selling price (after discount)
• 1 mark for setting up $306 = 1.2 \times \text{Cost price}$
• 1 mark for correct calculation of cost price
• 1 mark for correct final answer ($255)
• Common error: Finding marked price first ($360) then calculating 20% profit on that

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Section C: Rate and Speed [15 marks]

Question 13 [2 marks]

Answer: 30 km

Working:

• Speed = 72 km/h
• Time = 25 minutes = $\frac{25}{60}$ hours = $\frac{5}{12}$ hours
• Distance = Speed $\times$ Time = $72 \times \frac{5}{12} = 6 \times 5 = 30$ km

Marking notes:

• 1 mark for correct time conversion (25/60 hours)
• 1 mark for correct distance calculation
• Common error: Using 25 directly without converting to hours ($72 \times 25 = 1800$)

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Question 14 [2 marks]

Answer: 1350 pages

Working:

• Rate = $36 \text{ pages} \div 2 \text{ min} = 18 \text{ pages/min}$
• Time = 1 hour 15 minutes = 75 minutes
• Pages = $18 \times 75 = 1350$ pages

Marking notes:

• 1 mark for correct rate (18 pages/min)
• 1 mark for correct time conversion (75 min) and final calculation
• Common error: Not converting 1 hour 15 min to minutes

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Question 15 [2 marks]

Answer: 1 hour 0 minutes (or 1 hour)

Working:

• Rate = 4 L/min
• Capacity = 240 L
• Time = $240 \div 4 = 60$ minutes = 1 hour

Marking notes:

• 1 mark for correct division (240 ÷ 4 = 60)
• 1 mark for correct conversion to hours and minutes
• Common error: Leaving answer as 60 minutes without converting

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Question 16 [3 marks]

Answer: 18 km

Working:

• Let distance = $d$ km
• Time from A to B = $\frac{d}{18}$ hours
• Time from B to A = $\frac{d}{12}$ hours
• Total time = $2.5$ hours
• $\frac{d}{18} + \frac{d}{12} = 2.5$
• Multiply by 36: $2d + 3d = 90$
• $5d = 90$
• $d = 18$ km

Check: Time A→B = 1 hour, Time B→A = 1.5 hours, Total = 2.5 hours ✓

Marking notes:

• 1 mark for correct equation setup
• 1 mark for solving equation correctly
• 1 mark for correct answer with units
• Common error: Using average of speeds $(18+12)/2 = 15$ km/h

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Question 17 [3 marks]

Answer: 680 widgets

Working:

• Machine 1 rate = $480 \div 3 = 160$ widgets/hour
• Machine 2 rate = $720 \div 4 = 180$ widgets/hour
• Combined rate = $160 + 180 = 340$ widgets/hour
• In 2 hours: $340 \times 2 = 680$ widgets

Marking notes:

• 1 mark for correct individual rates
• 1 mark for correct combined rate
• 1 mark for correct final answer
• Common error: Averaging the rates instead of adding

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Question 18 [3 marks]

Answer: 3 hours 26 minutes (or 3 hours 25.7 minutes ≈ 3 h 26 min)

Working:

• Pump 1 rate = $\frac{1}{6}$ pool/hour
• Pump 2 rate = $\frac{1}{8}$ pool/hour
• Combined rate = $\frac{1}{6} + \frac{1}{8} = \frac{4}{24} + \frac{3}{24} = \frac{7}{24}$ pool/hour
• Time = $1 \div \frac{7}{24} = \frac{24}{7}$ hours = $3\frac{3}{7}$ hours
• $\frac{3}{7} \times 60 \approx 25.7$ minutes ≈ 26 minutes
• Time = 3 hours 26 minutes

Marking notes:

• 1 mark for correct individual rates
• 1 mark for correct combined rate ($\frac{7}{24}$)
• 1 mark for correct time calculation and conversion
• Accept 3 hours 25 minutes or 3 hours 26 minutes
• Common error: Adding times (6 + 8 = 14 hours) or averaging

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Section D: Data Handling and Interpretation [15 marks]

Question 19 [6 marks]

(a) [1 mark]
Answer: 30 students
Working: $3 + 8 + 10 + 5 + 4 = 30$

(b) [1 mark]
Answer: 2 books
Reasoning: The highest frequency is 10 students (for 2 books).

(c) [2 marks]
Answer: 1.8 books
Working:

• Total books = $(0 \times 3) + (1 \times 8) + (2 \times 10) + (3 \times 5) + (4 \times 4)$
• $= 0 + 8 + 20 + 15 + 16 = 54$ books
• Mean = $54 \div 30 = 1.8$ books

(d) [2 marks]
Answer: $\frac{19}{30}$
Working:

• Students with at least 2 books = $10 + 5 + 4 = 19$
• Total students = 30
• Probability = $\frac{19}{30}$

Marking notes for Q19:

• (a) 1 mark for correct total
• (b) 1 mark for correct mode
• (c) 1 mark for correct total books (54), 1 mark for correct mean (1.8)
• (d) 1 mark for correct numerator (19), 1 mark for correct fraction $\frac{19}{30}$
• Common error in (c): Dividing by 5 (number of categories) instead of 30 (number of students)

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Question 20 [8 marks]

(a) [1 mark]
Answer: January
Reasoning: January has the highest bar at 230 mm.

(b) [1 mark]
Answer: 70 mm
Working: Highest = 230 mm (Jan), Lowest = 160 mm (Jun). Difference = $230 - 160 = 70$ mm.

(c) [2 marks]
Answer: 190 mm
Working:

• Total rainfall = $230 + 180 + 210 + 190 + 170 + 160 = 1140$ mm
• Average = $1140 \div 6 = 190$ mm

(d) [2 marks]
Answer: 192 mm
Working:

• June rainfall = 160 mm
• July = $160 \times 1.2 = 192$ mm
• Or: 20% of 160 = 32, so $160 + 32 = 192$ mm

(e) [2 marks]
Answer: No, the claim is incorrect. The rainfall increased from February (180 mm) to March (210 mm), so it did not decrease every month.
Required elements for full marks:

• State "No" or "Incorrect"
• Identify the specific increase (Feb to Mar: 180 → 210 mm)
• Use data from chart to support

Marking notes for Q20:

• (a) 1 mark for correct month
• (b) 1 mark for correct difference with units
• (c) 1 mark for correct total (1140), 1 mark for correct average (190)
• (d) 1 mark for correct method (×1.2 or +20%), 1 mark for correct answer (192)
• (e) 1 mark for "No/Incorrect", 1 mark for correct evidence (Feb→Mar increase)
• Common error in (e): Saying "Yes" or not providing specific counter-example

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Total Marks: 60

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General Marking Guidance

• Method marks (M): Awarded for correct method/approach even if arithmetic error occurs
• Accuracy marks (A): Awarded for correct final answer (dependent on correct method)
• Units: Deduct 1 mark per question for missing or incorrect units where applicable
• Fractions: Must be in simplest form unless otherwise stated
• Rounding: Follow standard conventions (3 significant figures unless exact)
• Alternative methods: Accept any mathematically valid method that leads to correct answer