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AMC Upper Primary · 免费练习题
AMC Upper Primary 练习：5、6 年级
5、6 年级参加澳大利亚数学竞赛（AMC）的 Upper Primary 组别。下面是六道该水平的练习题，从开头的题目到最难题部分，每道题都有分步解答。
测试
试卷共 30 道题：25 道选择题（A 到 E），5 道填写 0 到 999 之间整数的题。考试时间 60 分钟。
时间每年 8 月初在学校参加；2026 年的考试在 8 月 4 日至 6 日举行。
奖项Participation（参与）、Proficiency（合格）、Credit（优良）、Distinction（优异）、High Distinction（特优）和 Prize（奖），按全国排名颁发。
难度递进越往后题目越难，分值也越高；最高奖项由最后几道题决定。
六道练习题，由易到难
请先自己做，再打开答案：解题过程会指出答错时通常错在哪一步。
1 · AMC Upper Primary · 热身Tom is in a line for the slide. 14 children are ahead of him and three times as many are behind him. How many children are in the line?
- 45
- 48
- 51
- 54
- 57
显示答案和解题过程
答案： E (57)
- Behind: 3 × 14. How many are behind? 42
- Ahead + the person + behind: 14 + 1 + 42. How many in the line? 57
最快的方法： Count the people ahead, the person themself, and the people behind — three groups.
容易错的地方： forgetting to count the person in the line.
2 · AMC Upper Primary · 热身A bag of 140 counters holds red, blue and green counters in the ratio 5:4:1. How many green counters are there?
- 12
- 14
- 28
- 46
- 126
显示答案和解题过程
答案： B (14)
- Add the ratio numbers to see how many equal parts there are. What is 5 + 4 + 1? 10
- 140 is shared over those 10 parts, so one part is 140 ÷ 10. How big is one part? 14
- The asked share is 1 part. What is 14 × 1? 14
最快的方法： Add the ratio numbers to get the total number of parts, find the size of ONE part, then multiply by the part asked for.
容易错的地方： dividing the total by the number of items in the ratio instead of the sum of the parts.
3 · AMC Upper Primary · 试卷中段Two friends' scores in a quiz have an average of 28, and one score is 8 higher than the other. What is the lower score?
- 0
- 8
- 16
- 24
- 32
显示答案和解题过程
答案： D (24)
- The average 28 sits exactly halfway between the two numbers, so each is 8 ÷ 2 away from it. What is 8 ÷ 2? 4
- The smaller number is the average minus that. What is 28 − 4? 24
最快的方法： Average of two = the middle. Half the difference above the middle is the larger, half below is the smaller.
容易错的地方： adding the whole difference to the average.
4 · AMC Upper Primary · 试卷中段A courier charges $30 for the first 5 kg of a parcel and $5 for every 5 kg, or part of 5 kg, after that. How many dollars does it cost to send a 19 kg parcel?
- 18
- 27
- 36
- 45
- 54
显示答案和解题过程
答案： D (45)
- The base covers the first 5; what is left is 19 − 5. How much is charged in blocks? 14
- 14 in blocks of 5, 'or part' means round UP. How many blocks? 3
- Base plus 3 blocks at 5. What is 30 + 3 × 5? 45
最快的方法： Take off what the base covers; what remains is charged in blocks — if 'or part', round UP to whole blocks.
容易错的地方： charging the base amount again for the first block, or rounding down 'or part'.
5 · AMC Upper Primary · 最难题部分Ada's chess club have played 34 games this season and won 25 of them. There are 36 games still to play. How many of those must they win to have won exactly 70% of all their games for the season?
- 8
- 16
- 24
- 32
- 40
显示答案和解题过程
答案： C (24)
- The percentage is of the WHOLE season, so count all the games first. How many games are there in the season altogether? 70
- 70% of that is the number of wins wanted. How many wins is 70% of the season? 49
- 25 are already won. How many more wins are needed? 24
最快的方法： Work out the target number of wins for the whole season first, then take away the wins already banked.
容易错的地方： taking the percentage of the games left instead of the whole season.
6 · AMC Upper Primary · 最难题部分On a farm, a horse eats one bale of hay every 12 days, a cow eats one bale of hay every 2 days and a sheep eats one bale of hay every 3 days. For how many days will 33 bales feed one horse, one cow and one sheep together?
- 0
- 12
- 24
- 36
- 48
显示答案和解题过程
答案： D (36)
- Use a block of 12 days (a number all three of 12, 2, 3 divide into). In 12 days the horse eats 12 ÷ 12 bales, the cow 12 ÷ 2, the sheep 12 ÷ 3. How many bales do the three eat together in 12 days? 11
- So 11 bales last 12 days. Scale to 33 bales. How many days do the bales last? 36
最快的方法： Turn each 'one bale every d days' into a share of a bale per day, add the shares, then divide the bales by the daily total.
容易错的地方： adding the days.
题目涵盖的内容
- 数：倒推、应用题中的分数和比、整除、数字与数位谜题。
- 图形：面积和周长谜题、展开图和立方体、角、方格中的路径。
- 推理：有条理地计数、逻辑、延续的规律，以及试卷最后的多步骤难题。
练习是怎样进行的
- 先做一次免费诊断：找出孩子尚未掌握的技能，并指出每道错题错在哪一步。
- 之后每周：一份 20 道题的练习卷，练习这些技能；周六按真实考试时间做一次模拟考试；周日给您发送一份报告。
- 由代码批改；答错的题会先一步一步讲解，最后才显示正确答案。
家长常问的问题
我的孩子考 AMC 的哪个组别？
5、6 年级考 Upper Primary；3、4 年级考 Middle Primary。
怎样准备 AMC 的难题？
最后几道题反复用到的方法其实不多：倒推、有条理地数、找规律。在新题上一次练一种方法，逐个掌握。
这些是 AMC 的往年真题吗？
不是。每道题都是按官方往年真题建模的题族生成的新变式，原题从不展示。