Leo had 90 stickers. He took one-fifth of them to school. Then he gave away one-half of the stickers that he still had. How many stickers did Leo have after that?
18
36
27
72
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答案： B (36)
One-fifth of 90 is 18, leaving 72. One-half of 72 is 36, leaving 72 − 36 = 36.
最快的方法： Work one step at a time: the second fraction is a fraction of what is LEFT, not of the starting number.
容易错的地方： taking the second fraction of the starting number, or stopping after the first step
2 · ICAS Paper C · Mathematics · 热身
These thermometers show the temperature in two towns at the same time one afternoon. How much warmer was it in Hobart than in Cairns?
6 °C
4 °C
8 °C
10 °C
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答案： C (8 °C)
Each small mark is 2 degrees. Hobart shows 26 °C and Cairns shows 18 °C, so the difference is 26 − 18 = 8 °C.
最快的方法： Work out what one small mark is worth (the gap between two numbers ÷ the number of spaces), read each thermometer, then subtract.
容易错的地方： counting the marks between the two readings (4) as if each mark were one degree
3 · ICAS Paper C · Mathematics · 试卷中段
Omar bought 3 packets of balloons with 12 in each packet. Noah bought 5 more packets than Omar. How many balloons did they buy altogether?
101
120
96
132
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答案： D (132)
Noah bought 3 + 5 = 8 packets, so together they bought 3 + 8 = 11 packets, and 11 × 12 = 132.
最快的方法： Write each step as a number sentence: groups × amount in each, then add or compare.
容易错的地方： using 5 as Noah's number of packets instead of 5 MORE than Omar's
4 · ICAS Paper C · Mathematics · 试卷中段
Which of these gives the same answer as 47 × 6?
50 × 6 − 18
50 × 7 − 3
50 × 6 − 3
50 × 6 + 18
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答案： A (50 × 6 − 18)
47 is 3 less than 50, so 47 × 6 is 6 lots of 3 less than 50 × 6: 50 × 6 − 18 = 282.
最快的方法： Work out every option fully; the right answer is the one that matches (or the odd one out).
容易错的地方： taking away (or adding) just 3 once instead of 6 lots of 3
5 · ICAS Paper C · Mathematics · 最难题部分
Mia looked at a clock and said, "One hour from now, the time left until 5:00 pm will be three times as long as it will be four hours from now." At what time did Mia say this?
6:00 am
11:30 am
12:30 pm
3:30 pm
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答案： B (11:30 am)
Call the time left until 5:00 pm right now the wait. In 1 hour the wait is 1 hour shorter; in 4 hours it is 4 hours shorter, so those two waits differ by 4 − 1 = 3 hours. The first is three times the second, so the difference is 2 lots of the second wait: the second wait is 1 hour 30 minutes. So the wait now is 1 hour 30 minutes + 4 hours = 5 hours 30 minutes (check: in 1 hour the wait is 4 hours 30 minutes, in 4 hours it is 1 hour 30 minutes, and 4 hours 30 minutes is three times 1 hour 30 minutes). 5 hours 30 minutes before 5:00 pm is 11:30 am.
最快的方法： Turn the words into two waits, find how they are linked (one is so many times the other, and they differ by a known number of hours), then count back from the target time.
容易错的地方： giving the time 1 hour from now instead of the time now, or taking the difference of 3 hours as the wait now (it is 2 lots of the later wait)
6 · ICAS Paper C · Mathematics · 最难题部分
Max will turn the orange triangle about one of the marked points. After the turn, the orange triangle must sit exactly on top of the blue one. Which point should he turn it about?
point P
point Q
point R
point S
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答案： D (point S)
Turning about point S by a quarter turn anticlockwise sends every corner of the orange triangle to a corner of the blue one: each corner stays the same distance from S. Turning about any other marked point leaves the triangle somewhere else.
最快的方法： Match the corners (the right angle to the right angle). The centre of the turn is the same distance from a corner and from where that corner ends up.
容易错的地方： choosing the point halfway between the triangles, which works for a half turn only when the triangles face opposite ways