🧠 WHY BOX — Why learn this?

Understanding this topic helps you solve real-life math problems and prepares you for the SSPA exam.

學好這個課題能幫助你解決生活數學問題,為 SSPA 考試做好準備。

📖 Story Context / 故事情境

Imagine you are shopping and need to calculate totals, discounts, or split bills. Math is everywhere in daily life!

想像你在購物時需要計算總額、折扣或分攤帳單。數學無處不在!

📋 Parent Corner / 家長專區
This topic covers key SSPA exam concepts. Encourage your child to practice the worked examples and common trap questions.
本課題涵蓋 SSPA 考試重點。請鼓勵孩子練習例題和陷阱題。
Primary 5 · Lesson 39 · Student Handout
SSPA ultimate cross-topic killer questions
T1-T10 Full Trap Mix · Most difficult lectures throughout the school year · 65 minutes · 1-to-3 Online Lesson
Positioning:The most difficulthandout for this school year |||SEP|||. Simulate the real SSPA sub-test finale question style - each question contains 3+ trap typesCore traps:
🪤 T1-T10 full series - each question contains traps, training students' "trap detection radar"SSPA correlation:
🔴 Extremely high frequencyThe last 5-8 questions in the actual sub-test are all cross-topic comprehensive questions, which are highly consistent with the question types of this handoutPrerequisite knowledge:
All topics in the whole school year (multiple digits·decimals·fractions·area·volume·equations·data·word questions)Class objectives:
❶ Cultivate trap detection ability ❷ Parallel processing of multiple traps ❸ Maintain calculation accuracy under high pressureDifficulty setting:
No basic questions in the whole volume - all 🌳 Advanced or 🏔️ Challenge level. This is preparation for SSPA actual combat.There are no basic questions in the whole volume - all 🌳 advanced or 🏔️ challenge levels. This is preparation for SSPA actual combat.
Student Name: Class: Date: Time Spent:
I. Warm-up start - trap radar test (total 3 questions, 5 minutes)
🏆 SSPA衝刺·限時挑戰
模擬真實SSPA考試!限時作答,每題計分。答對率達80%解鎖「SSPA戰士」勳章!
⚡ 開始模擬考 →
#QuestionDifficultyWorking Space
1Calculation:23× 0.75 + 1.25 = ? (First find out how many traps are hidden in this question! Hint: decimal point + fraction + order of operations)🌳
2A triangle has a base of 0.25 m and a height of 40 cm. What is the area in square centimeters? (Unit trap + formula trap)🌳
3A rectangular water tank: 50cm×30cm×40cm. Contains34water. What is the volume of water in liters? (Three hits of volume + fraction + unit conversion)🏔️
🧠 Our core philosophy: "When you see a question, don't worry about it. Scan where the traps are. Mark the traps before writing and defeat them one by one."
II.Core Knowledge
Knowledge point 1: Calculation killer questions 🔴 - Each question contains at least two T1 (advance and retreat) + T2 (decimal point) + T9 (fraction)
Features |||SEP|||: The questions involve multi-digit operations on integers, decimal point positioning, fraction generalization/reductionStrategy |||SEP|||: First unify the format (fraction first), then calculate in sections, and check each step
SSPA Live |||SEP|||: The last three questions of paper 1 calculation questions are usually such mixed questions, and the score loss rate in Hong Kong > 60%The deadliest combination |||SEP|||: large number advance and retreat (T1) + decimal division shift (T2) + fractional reduction (T9) = three consecutive traps
SSPA Live: The last three calculation questions in Paper 1 are usually mixed questions of this type, and the score loss rate in Hong Kong is > 60%
The deadliest combination: Large number advance and retreat (T1) + decimal division shift (T2) + fractional reduction (T9) = triple trap
🪤 Killer example (T1+T2+T9 three consecutive hits)
Calculation: (125.5 + 874.5) ×23 ÷ 0.5 = ?
❌ Common ways to die
125.5+874.5=990 (carry leakage), 990×2/3=1980/3=660 (regarded as ×3), 660÷0.5=330
Two traps in a row: wrong carry + fraction multiplication, one wrong step and the next wrong step
✅ Correct solution
1000 × 23 ÷ 0.5 = 20003 × 2 = 40003 = 133313
Addition check: 125.5+874.5=1000 ✓; ÷0.5 = ×2; Fraction multiplication: 1000×2/3×2=4000/3
Knowledge Point - Killer Questionspractice (trap included in perquestion annotation, total 12 questions - all 🌳/🏔️ level)
#QuestionDifficultyWorking Space
K1-1T1+T9 (45678 + 12345) × 13=? (Large number addition after carry × fraction)🌳
K1-2T2+T9 3.14 × 56+ 0.86 = ? (Decimal × fraction, decimal places of product + fraction reduction)🌳
K1-3T1+T2128.5 × 64 − 256.8 ÷ 0.4 = ? (Carry for large number multiplication + decimal division)🌳
K1-4T2+T9+T1 (0.125 × 8000) + (58× 0.64) = ? (Three traps are launched in unison)🏔️
#QuestionDifficultyWorking Space
K1-5T1+T9 (9999 + 5678) × 37=? (Carry to tens of thousands + fractional result reduction)🌳
K1-6T2+T9 0.075 ÷ 38+ 0.04 = ? (Decimal ÷ Fraction → × Reciprocal → Number of decimal places)🏔️
K1-7T1+T2725.6 × 1.5 − 488.4 = ? (Carry for multiplication + number of decimal places + carry for subtraction)🌳
K1-8T9+T2+T1 23× (456 ÷ 0.25) = ? (Carry for decimal division within parentheses + multiplication of outer fractions)🏔️
K1-9T2+T9 0.375 + 58− 0.125 × 4 = ? (First multiply and divide, then add and subtract + mixed fractions and decimals)🏔️
K1-10T1+T9+T2 (15000 − 8765) × 25÷ 0.2 = ? (Five-step calculation: subtraction abdication → × fraction → ÷ decimal → all traps)🏔️
K1-11T2+T9 1.25 × (34 + 16) ÷ 0.25 = ? (Common fraction of fractions in brackets → × decimal → ÷ decimal)🏔️
K1-12T1+T2+T9 (888 × 999) × 0.125 + 18=? (SSPA level ultimate difficulty: multiplication of very large numbers + decimals + fractions)🏔️
═══════════════ PAGE 4: KP2 — Application killer question ═══════════════
Knowledge point 2: Application killer questions 🔴 - Each question contains T3 (word comprehension) + T7 (unit conversion) + at least one other trap
Features |||SEP|||: Long text questions + multiple units + interfering information + multi-step reasoningStrategy |||SEP|||: Circle keywords → draw line graphs → mark units → column formulas → step by step calculation → check units
40%Fatal combination |||SEP|||: Understanding reversal (T3) + Unit disunity (T7) + Careless calculation (T1/T2/T9)
SSPA Live: The last 2 questions of paper 2, usually 6-8 points, the average score rate in Hong Kong is < 40%
deadly combination: Understanding reversal (T3) + Unit inconsistency (T7) + Careless calculation (T1/T2/T9)
Killer example (T3+T7+T9)
A rope is52meters long. I used14on the first day, the remaining23on the second day, and 75 cm on the third day. How many centimeters are left at the end?
Knowledge Point 2 Killer Questionspractice (total 12 questions - all 🌳/🏔️ levels, including complete answer sentences need to find)
#QuestionDifficultyWorking Space (column → calculate → answer sentence, both are indispensable)
K2-1T3+T7A rectangular field: 0.15 km long and 80 m wide. How many hectares is the area? (1 hectare = 10000m², 1km = 1000m, first convert everything into meters)🌳
K2-2T3+T9+T7One bottle of juice 2.5 liters. I drank15for breakfast, 350 ml for lunch, and the rest of12for dinner. How many milliliters are left at the end?🏔️
K2-3T3+T2+T7A water tank can hold 12.5 liters of water. If 8750 ml is injected now, how many liters can be injected? (Note that "okay" = capacity - existing, the units must be unified)🌳
K2-4T3+T7+T9Xiao Ming has $360. I used13to buy books, then used the remaining 0.25 to buy stationery, and finally used $45.50 to buy snacks. How many dollars are left?🏔️
#QuestionDifficultyWorking Space
K2-5T3+T7+T1A packet of sugar weighs34kg. After using 280g, divide the remainder into 95g bags. How many bags can be divided into at most? How many grams are left? (Multiple steps + unit conversion + packaging issues)🏔️
K2-6T3+T9+T2The engineering team completed the project in three days. Complete25on the first day, 0.05 more on the second day, and the rest on the third day. What fraction of the project was completed on the third day?🏔️
K2-7T3+T2+T7Original price for a coat is $680. First increase the price by 15% (i.e. ×1.15), and then discount it by 20%. Is the final selling price more expensive or cheaper than the original price? How much difference?🏔️
K2-8T3+T7+T9+T2A rectangular swimming pool: 25 meters long, 12 meters wide and 1.5 meters deep. Contains35water. How many liters of water are there in the pool? (1m³=1000L, four traps in a row)🏔️
K2-9T3+T9+T2A book has 480 pages. I read14on the first day, the remaining 0.6 on the second day, and 85 pages on the third day. How many pages are left to read?🏔️
K2-10T3+T7+T1The rectangular garden is 0.08 km long and 45 m wide. The gardener walked 5 times around the garden, how many kilometers did he cover in total? (Perimeter × number of circles, please note the unit: km↔m)🌳
K2-11T3+T7+T9+T2Inside of a water tank: 60cm×40cm×50cm. The original water height was 30cm. An irregular stone (volume 7200cm³) was placed and completely sunk. How high will the new water level be? Answer with rice.🏔️
K2-12T3+T2+T9+T7Xiao Ming saves $500. The first interest class used |||SEP|||, the second used the remaining 0.375, and the third used $85. How much is left? If you use the remaining25to buy books, how much did you spend on the books? (Four traps + double layer remaining)34How much did it cost to buy the book? (Four traps + double layer remaining)🏔️
═══════════════ PAGE 6: KP3 — Geometry killer question ═══════════════
Knowledge point 3: Geometry killer questions 🔴 - Each question contains T4 (confusion of geometric formulas) + T5 (solid geometry) + at least one other trap
Features |||SEP|||: Composite graphics + three-dimensional + unit trap + calculation trapStrategy |||SEP|||: Label all known quantities first → write the required formulas → unify the units → algebraic calculation → check the rationality of the units
SSPA Live |||SEP|||: The highest score loss rate for geometry questions in the sub-test, because there are many formulas and hidden unit trapsFatal combination |||SEP|||: Triangle ÷2 forget (T4) + volume representative surface area formula (T5) + cm/m mixed (T7)
SSPA Live: The geometry questions in the sub-test have the highest score loss rate because there are many formulas and hidden unit traps
deadly combination: Triangle ÷ 2 Forget (T4) + Volume representative surface area formula (T5) + cm/m Mix (T7)
Killer Example (T4+T5+T7)
The interior of a rectangular water tank: 0.5 m long, 30 cm wide, and 40 cm high. After filling the water the water level reaches 25 cm. Another triangular prism with a base area of ​​200cm² is placed (completely sunk) and the water level rises to 32cm. What is the height of the triangular prism in centimeters?
Knowledge Point 3 Killer Questionspractice (total 12 questions - all 🌳/🏔️ levels)
#QuestionDifficultyWorking Space
K3-1T4+T7A triangle has a base of 0.4 meters and a height of 25 centimeters. What is the area in square centimeters? (Bottom×height÷2, note: 0.4m=40cm)🌳
K3-2T4+T5+T7A trapezoidal garden bed: upper base 8 meters, lower base 12 meters, height 5 meters. A layer of soil 15 cm thick should be spread on top. How many cubic meters of soil are needed? (Trapezoidal area × thickness = volume, thickness is converted to meters first)🏔️
K3-3T4+T5+T2A cube has a side length of 0.5 meters. What is the surface area in square meters? How many cubic meters is the volume? How many liters is the volume?🌳
K3-4T4+T1+T7Composite graphic: a rectangle (12m×8m) with a triangle (base 12m and height 5m) stacked on top. Total area=? (Rectangle + triangle, please note that the units are consistent)🌳
#QuestionDifficultyWorking Space
K3-5T5+T7+T9A rectangular water tank: 50cm×40cm×60cm. Original Water13Box. Put in a rectangular iron block (20cm×15cm×10cm) and sink it completely. How many centimeters will the water level rise?🏔️
K3-6T4+T5+T7+T2A parallelogram has a base 0.25 m and a height 18 cm. A cuboid is formed with its base and height (base × height is the base, thickness is 5 cm). Calculation: area of ​​parallelogram + volume of cuboid. (Four traps!)🏔️
K3-7T4+T5+T9A cuboid: length 24 cm, width equal to the length |||SEP|||, height equal to the width |||SEP|||. Volume=? Surface area=? (First find the width and height, fraction operation + geometric double kill)13, high is wide12. Volume=? Surface area=? (First find the width and height, fraction operation + geometric double kill)🏔️
K3-8T4+T7+T1A trapezoid: the upper base is 3.5 meters, the lower base is 6.5 meters, and the height is 400 centimeters. How many square meters is the area? Use a fence to surround the four sides of the trapezoid. What is the minimum length of the fence? (Find the area first and then find the perimeter, but the perimeter of the trapezoid needs to know two waists - assuming it is an isosceles trapezoid, the waist length is calculated using Pythagorean theorem: half-base difference = 1.5m, waist = √ (1.5² + 4²) = √ 18.25 ≈ 4.27m)🏔️
K3-9T5+T2+T7A fish tank: internal dimensions 0.8m×0.5m×0.6m. Once filled, scoop out the water using a 2.5 liter bucket. How many buckets can be scooped at most? (Volume of fish tank ÷ capacity of each barrel, note m³→L)🏔️
K3-10T5+T4+T7+T9L-shaped composite three-dimensional: bottom layer 10cm×8cm×4cm, upper layer 4cm×8cm×3cm (placed at one end of the bottom layer). Find: total volume, total surface area (note: joint surfaces are not counted as surface area). Four traps!🏔️
K3-11T4+T5+T7+T2A cube has a side length of 0.25 meters. Saw it all into small cubes with 5 cm sides. How many pieces can it be sawed into? How much more is the total surface area of ​​all the small cubes than the original large cube?🏔️
K3-12T4+T5+T2+T7+T9The length of the base of a triangle = the length of the side of a cube (0.4 meters). Height of triangle = volume of cube ÷ area of ​​base of cube. Area of ​​triangle = ? cm². Then use the area of ​​this triangle as the base area and add the height of 0.15 meters to form a triangular prism volume = ? cm³. (Five traps ultimate geometry question)🏔️
═══════════════ PAGE 8: KP4 — Ultimate Mixed Killer Question ═══════════════
Knowledge point 4: The ultimate mixed killer question🔴🔴 - no classification, purely comprehensive, each question contains 4+ traps
Features |||SEP|||: No obvious topic tags - calculations + text comprehension + units + geometry are all mixed togetherStrategy |||SEP|||: Mark all traps first→decompose into sub-questions→solve one by one→merge answers
SSPA Live |||SEP|||: This is the closest to the real SSPA finale question (the last 2-3 of each volume of Volume 1 and Volume 2) Difficulty of questions)Completion standard |||SEP|||: Can complete at least 5/9 questions correctly within the time limit, that is, you have the ability to achieve full SSPA score
SSPA Live: This is the difficulty closest to the real SSPA final questions (the last 2-3 questions of Paper 1 and Paper 2)
Completion standards: Able to complete at least 5/9 questions correctly within the time limit, that is, you have the ability to achieve SSPA full score
⚠️ WARNING: The following 9 questions are among the most difficult this school year. Each question contains 4 or more traps. It is recommended to list all the traps on a scratch paper before starting the calculation.
Ultimate mixed practice (total 9 questions - full 🏔️ level, perquestion≥4 trap)
#QuestionDifficultyWorking Space (first column trap→againcalculate)
End 1T2+T9+T3+T1A farmer has 250.5 kg of rice. He sells35and gives the remaining 0.25 to his neighbor. Finally he divided the remaining rice into 12.5kg bags. Q: How many bags can be divided into at most? How many kilograms are left? (Four traps: fractions + decimals + remaining understanding + division by pack)🏔️
End 2T4+T5+T7+T2A rectangular swimming pool: 0.05 km long, 25 m wide, average water depth 1.8 m. There is water in the pool45Full. How many minutes will it take to drain the pool using a pump that pumps 450 liters of water per minute? (Pool volume → water volume → time, all traps)🏔️
End 3T3+T9+T2+T7+T1Xiao Ming, Xiao Hua, and Xiao Mei share a lump sum of $1,500. Xiao Ming gets |||SEP|||, Xiao Hua gets 0.75 times what Xiao Ming gets, and Xiao Mei gets the rest. Xiaomei saves25of her money and donates the rest to charity. Question: How much did she donate? (Five traps, super long question)13Save it and donate the rest to charity. Question: How much did she donate? (Five traps, super long question)🏔️
#QuestionDifficultyWorking Space
End 4T5+T4+T7+T9+T2An L-shaped composite solid: the bottom cuboid A (60cm×40cm×25cm), and the upper cuboid B (20cm×40cm×15cm) are placed above the right end of A. Find: (a) Total volume =? cm³ (b) Total surface area =? cm² (joint surfaces are not counted) (c) If the entire solid body is sunk into a water tank (the bottom area of ​​the tank is 5000cm²), how many centimeters will the water level rise? (Five Trap Geometry Ultimate Question)🏔️
End 5T2+T9+T3+T7+T1The original water capacity of a water tank is 45.5 liters. First withdraw |||SEP|||, then inject 8750 ml, then withdraw the remaining 0.4, and finally inject 12.25 liters. How many milliliters of water is in the tank now? (Five traps: fractions + decimals + mixing units + remaining understanding + large number operations)15, inject another 8750 ml, withdraw the remaining 0.4, and finally inject 12.25 liters. How many milliliters of water is in the tank now? (Five traps: fractions + decimals + mixing units + remaining understanding + large number operations)🏔️
End 6T4+T5+T7+T3+T9A trapezoidal garden: upper base 8.5 meters, lower base 11.5 meters, height 6 meters.35Plant roses in the flower garden. How many square meters is the area where roses are planted? If 4 roses are planted per square meter, how many roses are planted in total? If each rose requires 250 ml of water and is watered once a day, how many liters of water will be required in a week? (Five trap long chain questions - area → fraction → multiplication → unit conversion → time)🏔️
End 7T3+T2+T9+T1+T7Project: Team A will complete the project in 20 days, and Team B will complete the project in 30 days. After the two teams work together for 5 days, Team A takes a break and Team B completes the rest alone. How many more days will it take for Team B? (Engineering problem - first find their respective efficiencies: A =120/day, B =130/day. Five traps)🏔️
End 8T4+T5+T2+T7+T9A rectangular glass water tank: outer dimensions 52cm×32cm×42cm, glass thickness 1cm (without cover). Find: (a) Internal capacity =? Liters (round up) (b) How many cm² of glass are needed to make this tank? (c) If a stone with a volume of 4800cm³ is placed in34water, will the water overflow? If it overflows, how much will it overflow? (Six trap practical questions - internal and external dimensions + volume + area + fraction + overflow judgment)🏔️
end 9T1+T2+T3+T7+T9+T4The ultimate challenge: a circular garden 14 meters in diameter (π≈227). There is a square pool in the center of the garden (3.5 meters on a side).34of the garden is paved with grass, and the rest is paved with stone bricks. Grass is $45.50 per square meter and stone tiles are $68.25 per square meter. The cost of paving grass + the cost of paving stone bricks =? How does the total cost compare to $25,000? (SSPA level ultimate question - area of ​​circle + area of ​​square + fraction + multiplication of decimals + comparison of large numbers + six traps)🏔️
V.SSPA Killer Questions Summary of Survival Rules
Detect traps
After reading the question, mark all possible pitfalls
unified format
Unify all fractions and decimals
Segment calculation
No skipping steps in each step of verification
check answer
Unit and rationality backward verification
🧠 SSPA killer mantra: "Trap detection is the first step, uniform format is the basic skill, segment calculations are correct, and check the answers to ensure full marks."
VI. The Lessoncorecommon errorsummary
✅ Self-examination in this hall (tick after completion)
☐ I know the pitfalls of solving each knowledge point ☐ I can complete 🌱basic questions independently ☐ I can challenge 🌿advanced questions ☐ I remember the formula
🎯 Review of Learning Objectives - After completing this lesson you should be able to:
☐ Identify all trap types in our hall ☐ Solve 🌱basic questions independently (100% correct) ☐ Challenge🌿Advanced questions (80%+ correct) ☐ Explain the lesson formula to classmates
#common errorCorrect Approach
1A certain trapwas missed in the multi-trap question, resulting in local errors.For each question, pause for 10 seconds to scan and mark all possible traps before starting the calculation.
2In the word problem, the direction of "remainder" is reversed |||SEP|||, using the original number instead of the remainder, use the original number instead of the remainderDraw a line segment diagram: update the remaining amount after each "remainder" and use it as the base for the next step
3The units are not uniformly substituted into the formula |||SEP|||: cm and m are used together, L and mL are used together.: cm and m are used together, L and mL are used togetherAll lengths are first unified into the same units; 1m=100cm, 1L=1000mL, 1m³=1000L
4The area of ​​a triangle is ÷2 / the trapezoid formula is misrememberedWrite formula → Algebra → Calculate; triangle A=bh/2, trapezoid A=(a+b)h/2
5Composite three-dimensional joint surface repeated calculation of surface areaThe joint surface does not belong to the external surface and is deducted from the total
6Efficiency is reversed in engineering problems |||SEP|||: The more days, the lower the efficiency: The longer the number of days, the lower the efficiency.Efficiency = 1÷number of days; cooperation efficiency = the addition of efficiencies; time = workload÷efficiency
7The answer misses a unit, a sentence, or the unit is written incorrectly.SSPA scoring: 1-2 step points will be deducted for missed sentences; 0 points for wrong units
Lam Fung Academy · LF Academy · We don't teach math. We teach trap avoidance.
Print Ctrl+P PDF | 11 pages · 57 questions | LF-P5-S2-L39 v6 EN
📌 本講義由 AI 輔助生成,並經導師審閱。| AI Model: deepseek-v4-flash | 生成日期: 2026-06-11 | 審閱狀態: ⏳ 待審閱