Each face of a cube is divided into a grid of equal small squares, with 3 squares along each side of the face. How many small squares are there on the outside of the cube altogether?
9
18
36
54
162
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答案： D (54)
One face is a 3 by 3 grid of small squares. How many small squares on one face? 9
A cube has 6 faces, and every small square is on exactly one face. What is 6 × 9? 54
最快的方法： Count one face (k x k) and multiply by 6 faces — every small square is on exactly one face.
容易错的地方： multiplying by 4 faces, or counting edges instead of faces.
2 · AMC Middle Primary · 热身
How many minutes are there in four twelfths of an hour?
15
20
25
33
40
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答案： B (20)
An hour is 60 minutes. One twelfth of it is 60 ÷ 12. What is 60 ÷ 12? 5
You need 4 of those parts. What is 5 × 4? 20
最快的方法： An hour is 60 minutes; divide 60 by the denominator, then multiply by the numerator.
容易错的地方： using 100 minutes in an hour.
3 · AMC Middle Primary · 试卷中段
The pictograph shows the number of books for each year level. Each full symbol stands for 10 books; a half symbol stands for 5. How many books were there altogether?
9
70
75
80
85
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答案： E (85)
Year 3: 4 full symbols × 10. How many books for Year 3? 40
Year 4: 2 full symbols × 10. How many books for Year 4? 20
Year 5: 1 full symbol × 10. How many books for Year 5? 10
Year 6: 1 full symbol × 10, plus a half symbol worth 5. How many books for Year 6? 15
Add every row. What is 40 + 20 + 10 + 15? 85
最快的方法： Multiply full symbols by the key, add half a key for a half symbol, then compare or add the rows.
容易错的地方： counting symbols instead of what they stand for, or forgetting the half symbol.
4 · AMC Middle Primary · 试卷中段
Ava has 23 stamps. Ben has 3 more than Ava. Cara has 10 more than Ben. How many stamps does Cara have?
13
23
36
37
59
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答案： C (36)
One person at a time. Ben is '+3' compared with Ava, who has 23. How many does Ben have? 26
One person at a time. Cara is '+10' compared with Ben, who has 26. How many does Cara have? 36
最快的方法： Write each person's number on its own line, one step at a time, before adding anything.
容易错的地方： answering the last person's number when the question asks for a total, or applying a step to the wrong person.
5 · AMC Middle Primary · 最难题部分
A rectangle is cut into four smaller rectangles by one line across and one line down. The top-left piece has an area of 24 square centimetres, the top-right piece 48 square centimetres and the bottom-left piece 9 square centimetres. What is the area of the bottom-right piece, in square centimetres?
12
18
24
30
36
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答案： B (18)
The top two pieces share a height and the left two share a width. So top-left × bottom-right = top-right × bottom-left (each side is width × width × height × height). What is 48 × 9? 432
Divide by the top-left area. What is the bottom-right area? 18
最快的方法： Pieces in the same row share a height and pieces in the same column share a width, so the unknown area is (top-right x bottom-left) ÷ top-left.
容易错的地方： adding or subtracting the areas.
6 · AMC Middle Primary · 最难题部分
A gardener plants rows of seedlings. Each row takes one minute longer than the row before it. The first 6 rows take 39 minutes in total. How long do the next 3 rows take, in minutes?
24
27
30
33
36
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答案： D (33)
Row 2 takes 1 minute more than row 1, row 3 takes 2 more, … so the first 6 have step-ups of 0 + 1 + … + 5. What is 0 + 1 + … + 5? 15
Take the step-ups off the total; what is left is 6 copies of row 1. How many minutes does row 1 take? 4
The next 3 are row 7 to row 9: (4 + 6) + (4 + 7) + (4 + 8). How many minutes do the next 3 take? 33
最快的方法： Consecutive minutes are spread evenly: the middle hole is the average, so find the first hole, then continue the pattern.
容易错的地方： dividing the total by the number of holes and using that for the next holes.