{
"paper": {
"school": "Nan Hua",
"year": 2024,
"level": "P6",
"label": "Non-Weighted Assessment 1",
"source_prefix": "Nan Hua 2024 P6 Non-Weighted Assessment 1",
"has_answer_key": false
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "Arrange the following fractions from the greatest to the smallest.
\\(\\dfrac{3}{4}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{5}{6}\\)",
"answer0": "\\(\\dfrac{4}{5}\\), \\(\\dfrac{3}{4}\\), \\(\\dfrac{5}{6}\\)",
"answer1": "\\(\\dfrac{5}{6}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{3}{4}\\)",
"answer2": "\\(\\dfrac{3}{4}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{4}{5}\\)",
"answer3": "\\(\\dfrac{4}{5}\\), \\(\\dfrac{5}{6}\\), \\(\\dfrac{3}{4}\\)",
"correct_answer": 1,
"skill_id": 206,
"difficulty_id": 1,
"explanation": "Use a common denominator of 60: \\(\\dfrac{3}{4}=\\dfrac{45}{60}\\), \\(\\dfrac{4}{5}=\\dfrac{48}{60}\\), \\(\\dfrac{5}{6}=\\dfrac{50}{60}\\). Greatest to smallest: \\(\\dfrac{5}{6}\\), \\(\\dfrac{4}{5}\\), \\(\\dfrac{3}{4}\\). Answer: option 2.",
"hints": ["Convert all to a common denominator (60).", "Larger numerator over the same denominator means a larger fraction."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved"
},
{
"n": 2,
"type_id": 1,
"question": "Express \\(2\\dfrac{6}{25}\\) as a decimal.",
"answer0": "2.06",
"answer1": "2.24",
"answer2": "2.25",
"answer3": "2.60",
"correct_answer": 1,
"skill_id": 206,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{6}{25}=\\dfrac{24}{100}=0.24\\). So \\(2\\dfrac{6}{25}=2+0.24=2.24\\). Answer: option 2.",
"hints": ["Convert the fraction to hundredths: multiply numerator and denominator by 4.", "Add the whole number 2 to the decimal part."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved"
},
{
"n": 3,
"type_id": 1,
"question": "What is \\(\\dfrac{5}{12}\\times\\dfrac{3}{2}\\)?",
"answer0": "\\(\\dfrac{1}{3}\\)",
"answer1": "\\(\\dfrac{4}{7}\\)",
"answer2": "\\(\\dfrac{5}{8}\\)",
"answer3": "\\(1\\dfrac{1}{4}\\)",
"correct_answer": 2,
"skill_id": 206,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{5}{12}\\times\\dfrac{3}{2}=\\dfrac{15}{24}=\\dfrac{5}{8}\\). Answer: option 3.",
"hints": ["Multiply numerators together and denominators together.", "Simplify the resulting fraction by dividing by the common factor 3."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved"
},
{
"n": 4,
"type_id": 1,
"question": "\\(\\dfrac{2}{3}-\\dfrac{?}{12}=\\dfrac{1}{4}\\)
What is the missing number?",
"answer0": "1",
"answer1": "5",
"answer2": "3",
"answer3": "11",
"correct_answer": 1,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Convert to twelfths: \\(\\dfrac{2}{3}=\\dfrac{8}{12}\\) and \\(\\dfrac{1}{4}=\\dfrac{3}{12}\\). So \\(\\dfrac{8}{12}-\\dfrac{?}{12}=\\dfrac{3}{12}\\), giving \\(?=8-3=5\\). Answer: option 2.",
"hints": ["Rewrite every fraction with denominator 12.", "The missing numerator equals 8 minus 3."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q4",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved"
},
{
"n": 5,
"type_id": 1,
"question": "A handbag cost $250. Kelly bought the bag and was given a 20% discount. She had to pay 8% GST on the discounted price. How much did she pay for the handbag inclusive of the GST?",
"answer0": "$180",
"answer1": "$184",
"answer2": "$216",
"answer3": "$220",
"correct_answer": 2,
"skill_id": 209,
"difficulty_id": 2,
"explanation": "Discounted price = 80% of $250 = $200. GST = 8% of $200 = $16. Total paid = $200 + $16 = $216. Answer: option 3.",
"hints": ["A 20% discount means paying 80% of the price.", "Add 8% GST onto the discounted price."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q5",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved"
},
{
"n": 6,
"type_id": 1,
"question": "Find the value of \\(\\dfrac{5}{6}\\times 2\\). Express your answer as a mixed number in the simplest form.",
"answer0": "\\(1\\dfrac{2}{3}\\)",
"answer1": "\\(1\\dfrac{4}{6}\\)",
"answer2": "\\(\\dfrac{5}{3}\\)",
"answer3": "\\(1\\dfrac{1}{3}\\)",
"correct_answer": 0,
"skill_id": 206,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{5}{6}\\times 2=\\dfrac{10}{6}=\\dfrac{5}{3}=1\\dfrac{2}{3}\\). Answer: \\(1\\dfrac{2}{3}\\) (option 1).",
"hints": ["Multiply the numerator by 2.", "Convert the improper fraction to a mixed number and simplify."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved; answer is a mixed number so rendered as MCQ"
},
{
"n": 7,
"type_id": 1,
"question": "The product of two fractions is \\(\\dfrac{3}{8}\\). One of the fractions is \\(\\dfrac{1}{2}\\). What is the other fraction?",
"answer0": "\\(\\dfrac{3}{16}\\)",
"answer1": "\\(\\dfrac{3}{4}\\)",
"answer2": "\\(\\dfrac{3}{10}\\)",
"answer3": "\\(\\dfrac{7}{8}\\)",
"correct_answer": 1,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Other fraction = \\(\\dfrac{3}{8}\\div\\dfrac{1}{2}=\\dfrac{3}{8}\\times 2=\\dfrac{6}{8}=\\dfrac{3}{4}\\). Answer: \\(\\dfrac{3}{4}\\) (option 2).",
"hints": ["To find a missing factor, divide the product by the known fraction.", "Dividing by \\(\\dfrac{1}{2}\\) is the same as multiplying by 2."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved; answer is a fraction so rendered as MCQ"
},
{
"n": 8,
"type_id": 1,
"question": "\\(\\dfrac{2}{3}\\) of a pie was distributed equally among 5 boys. What fraction of the whole pie did each boy receive?",
"answer0": "\\(\\dfrac{2}{15}\\)",
"answer1": "\\(\\dfrac{2}{5}\\)",
"answer2": "\\(\\dfrac{1}{15}\\)",
"answer3": "\\(\\dfrac{10}{3}\\)",
"correct_answer": 0,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Each boy gets \\(\\dfrac{2}{3}\\div 5=\\dfrac{2}{3}\\times\\dfrac{1}{5}=\\dfrac{2}{15}\\) of the whole pie. Answer: \\(\\dfrac{2}{15}\\) (option 1).",
"hints": ["Dividing by 5 is multiplying by \\(\\dfrac{1}{5}\\).", "Multiply \\(\\dfrac{2}{3}\\) by \\(\\dfrac{1}{5}\\)."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved; answer is a fraction so rendered as MCQ"
},
{
"n": 9,
"type_id": 2,
"question": "Mrs Tan has 4 kg of flour. She needs \\(\\dfrac{1}{5}\\) kg of flour to bake a cake. How many of such cakes can she bake? [?]",
"answer0": "20",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 206,
"difficulty_id": 1,
"explanation": "Number of cakes = \\(4\\div\\dfrac{1}{5}=4\\times 5=20\\). She can bake 20 cakes.",
"hints": ["Dividing by \\(\\dfrac{1}{5}\\) is the same as multiplying by 5.", "4 multiplied by 5 gives the number of cakes."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved"
},
{
"n": 10,
"type_id": 2,
"question": "Some students attended a concert at a school auditorium. 40% of the students who attended the concert were girls. There were 168 boys who attended the concert. How many students attended the concert altogether? [?]",
"answer0": "280",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 207,
"difficulty_id": 2,
"explanation": "If 40% were girls, then 60% were boys. 60% = 168 students, so 1% = 2.8 students and 100% = 280 students. Altogether 280 students attended.",
"hints": ["Boys make up 100% - 40% = 60%.", "Find 100% from 60% = 168."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q10",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved"
},
{
"n": 11,
"type_id": 2,
"question": "After an increase of $80, Daniel's monthly allowance became $400. What is the percentage increase in his allowance? [?]",
"answer0": "25",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 208,
"difficulty_id": 2,
"explanation": "Original allowance = $400 - $80 = $320. Percentage increase = \\(\\dfrac{80}{320}\\times 100\\% = 25\\%\\). Answer: 25 (%).",
"hints": ["Find the original amount before the increase.", "Percentage increase = increase divided by original amount, times 100%."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved; answer in % (units stated on paper)"
},
{
"n": 12,
"type_id": 1,
"question": "Jenny made some milkshake. She drank \\(\\dfrac{3}{5}\\) of it and her three siblings shared the remainder equally. What fraction of the original amount of milkshake did each of her siblings get?",
"answer0": "\\(\\dfrac{2}{15}\\)",
"answer1": "\\(\\dfrac{2}{5}\\)",
"answer2": "\\(\\dfrac{1}{5}\\)",
"answer3": "\\(\\dfrac{3}{15}\\)",
"correct_answer": 0,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Remainder = \\(1-\\dfrac{3}{5}=\\dfrac{2}{5}\\). Shared among 3 siblings: \\(\\dfrac{2}{5}\\div 3=\\dfrac{2}{15}\\). Each sibling gets \\(\\dfrac{2}{15}\\) of the original. Answer: \\(\\dfrac{2}{15}\\) (option 1).",
"hints": ["Find the fraction left after Jenny drinks \\(\\dfrac{3}{5}\\).", "Divide the remainder by 3."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved; answer is a fraction so rendered as MCQ"
},
{
"n": 13,
"type_id": 2,
"question": "The mass of a container that was \\(\\dfrac{2}{3}\\)-filled with sand was 1200 g. When 220 g of sand was poured out of the container, it became \\(\\dfrac{1}{2}\\)-filled. Find the mass of the empty container. [?]",
"answer0": "320",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 206,
"difficulty_id": 3,
"explanation": "The 220 g of sand removed corresponds to \\(\\dfrac{2}{3}-\\dfrac{1}{2}=\\dfrac{1}{6}\\) of a full container of sand. So a full container of sand = \\(220\\times 6=1320\\) g. Sand in the \\(\\dfrac{2}{3}\\)-filled container = \\(\\dfrac{2}{3}\\times 1320=880\\) g. Empty container = \\(1200-880=320\\) g.",
"hints": ["The poured-out sand represents the difference \\(\\dfrac{2}{3}-\\dfrac{1}{2}=\\dfrac{1}{6}\\) of full.", "Work out the sand in the \\(\\dfrac{2}{3}\\)-filled container, then subtract from 1200 g."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved; answer in g (units stated on paper)"
},
{
"n": 14,
"type_id": 2,
"question": "There were 520 principals at a conference. \\(\\dfrac{2}{5}\\) of them were primary school principals. \\(\\dfrac{1}{4}\\) of the remainder were junior college principals. The rest were secondary school principals. Find the number of secondary school principals at the conference. [?]",
"answer0": "234",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 206,
"difficulty_id": 2,
"explanation": "Primary = \\(\\dfrac{2}{5}\\times 520=208\\). Remainder = \\(520-208=312\\). Junior college = \\(\\dfrac{1}{4}\\times 312=78\\). Secondary = \\(312-78=234\\) principals.",
"hints": ["Find the number of primary principals, then the remainder.", "Take \\(\\dfrac{1}{4}\\) of the remainder for JC; the rest are secondary."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Paper 2 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved; Paper 2 Q1, calculator allowed"
},
{
"n": 15,
"type_id": 2,
"question": "At a concert, 45% of the audience were female adults, 30% were male adults and the rest were children. There were 450 children at the concert.
(a) How many female adults were there at the concert? [?]
(b) 150 female adults left the concert before it ended. What percentage of the audience was made up of female adults at the end of the concert? [?]",
"answer0": "810",
"answer1": "40",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 207,
"difficulty_id": 3,
"explanation": "(a) Children = 100% - 45% - 30% = 25% = 450, so 100% = 1800 audience. Female adults = 45% of 1800 = 810. (b) After 150 female adults leave: female adults = 810 - 150 = 660; total audience = 1800 - 150 = 1650. Percentage = \\(\\dfrac{660}{1650}\\times 100\\% = 40\\%\\). Answers: (a) 810, (b) 40 (%).",
"hints": ["Children are 25% of the audience; use 25% = 450 to find the whole.", "For (b) subtract 150 from both the female-adult count and the total, then recompute the percentage."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Paper 2 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved; Paper 2 Q2 (a)/(b); part (b) answer in %"
},
{
"n": 16,
"type_id": 2,
"question": "Mr Chan bought a laptop and a printer from a shop. He paid a total of $1824 for these two items after discount. The total discount given for the laptop and printer was $246. The laptop's usual price is $1290 with a discount of 10% given. Find the percentage discount given for the printer. [?]",
"answer0": "15",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 208,
"difficulty_id": 3,
"explanation": "Laptop discount = 10% of $1290 = $129; laptop paid = $1290 - $129 = $1161. Printer paid = $1824 - $1161 = $663. Printer discount = total discount - laptop discount = $246 - $129 = $117. Printer usual price = paid + discount = $663 + $117 = $780. Percentage discount = \\(\\dfrac{117}{780}\\times 100\\% = 15\\%\\). Answer: 15 (%).",
"hints": ["Find the laptop's discount and price paid first.", "Printer usual price = printer paid + printer discount; then percentage = discount over usual price."],
"source": "Nan Hua 2024 P6 Non-Weighted Assessment 1 Paper 2 Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "no answer key — solved; Paper 2 Q3; laptop/printer figures are decorative product images with price boxes (transcribed into stem), answer in %"
}
]
}