Noah compared the masses of three things on a balance scale. Which list puts them in order from heaviest to lightest?
melon, mango, apple
mango, apple, melon
melon, apple, mango
apple, melon, mango
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答案： C (melon, apple, mango)
On a balance the heavier side goes down. So the melon is heavier than the apple, and the apple is heavier than the mango. From heaviest: melon, apple, mango.
最快的方法： On each scale, the lower pan holds the heavier thing. The thing that is on both scales is in the middle.
容易错的地方： thinking the higher pan is heavier, which turns the whole order round
2 · ICAS Paper B · Mathematics · 热身
Max buys a puzzle for $6.70 and a magazine for $1.10. He pays with a $20 note. How much change should Max get?
$7.80
$12.20
$18.90
$13.30
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答案： B ($12.20)
Altogether the two things cost $6.70 + $1.10 = $7.80, so the change is $20 − $7.80 = $12.20.
最快的方法： Count on from the cost to the note (to the next dollar first), or subtract and check by adding back.
容易错的地方： taking away only one of the prices, or giving the total cost instead of the change
3 · ICAS Paper B · Mathematics · 试卷中段
A number machine uses the same rule every time. When 5 goes in, 12 comes out. When 4 goes in, 11 comes out. Which rule could the machine be using?
Double the number, then add 2
Multiply the number by 3, then take away 3
Add 7
Add 1, then double the answer
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答案： C (Add 7)
'Add 7' turns 5 into 12 and 4 into 11. Each other rule fits the first pair but not the second.
最快的方法： Test each rule on the number that goes in, step by step, and check EVERY pair.
容易错的地方： checking only the first pair, or doing the two steps of a rule in the wrong order
4 · ICAS Paper B · Mathematics · 试卷中段
The marks on a number line are equally spaced. The second mark is 500 and the sixth mark is 600. What number is at the ninth mark?
700
650
675
660
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答案： C (675)
From the second to the sixth mark there are 4 gaps covering 600 − 500 = 100, so each gap is 25. The ninth mark is 3 gaps after 600: 600 + 3 × 25 = 675.
最快的方法： Count the GAPS between the two labelled marks, find what one gap is worth, then count on.
容易错的地方： counting the marks instead of the gaps, so each gap seems smaller
5 · ICAS Paper B · Mathematics · 最难题部分
Hugo joined five identical squares to make a rectangle 5 squares long and 1 square wide. The perimeter of the rectangle is 48 cm. What is the perimeter of one small square?
16 cm
4 cm
12 cm
20 cm
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答案： A (16 cm)
Going round the outside of the rectangle you pass 12 sides of small squares. So one side is 48 ÷ 12 = 4 cm, and the perimeter of one small square is 4 × 4 = 16 cm.
最快的方法： Perimeter is the distance all the way round. Count the 1 cm edges, or find one side first and then go round.
容易错的地方： dividing the perimeter by the number of squares, or giving the length of one side instead of the perimeter
6 · ICAS Paper B · Mathematics · 最难题部分
In this number sentence, each ★ stands for the same number. 52 − ★ = 10 + ★ What number does ★ stand for?
20
42
22
21
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答案： D (21)
Try ★ = 21: 52 − 21 = 31 and 10 + 21 = 31. Both sides match. (The gap 52 − 10 = 42 is shared among the 2 stars: 42 ÷ 2 = 21.)
最快的方法： Both sides must be equal; try a value for ★ in BOTH places, then adjust.
容易错的地方： working out the difference of the numbers and forgetting that the star is used more than once