好消息 伦敦城市学校City of London School Year7数学入学考试笔试真题!

　　作为英国顶尖的私立男校，伦敦城市学校可谓是私立男校教育的典范，这里不仅有着超高的学术成绩，而且还为学生提供了丰富多彩的课外活动，比如马术、射箭、艺术等等，因此，越来越多的学生去该校留学，可是，入读私校要经过笔试，下面，小编就为大家带来了伦敦城市学校City of London School Year7数学入学考试笔试真题，希望对大家有所帮助：

　　说明

　　•本文是入学考试内容的指示。

　　•在提供的空白处尽可能多地回答问题。

　　•清楚地展示你所有的工作。

　　•注意不要在任何一个问题上花太长时间。

　　•不允许使用计算器。

　　1. For this question you can do rough working on the left hand side of the page if required. Put answers only in the spaces on the right.

　　3. I buy 7 drinks at 72p each, and 9 sandwiches at £1.21 each.

　　How much change do I get from a £20 note?

　　4. Reflect the letters in the mirror line below. Three letters have been done for you.

　　6. The thermometers below show the temperature recorded at midday yesterday and midnight last night.

　　(i) What was the temperature midday yesterday in °F?

　　…………………….……………°F

　　(ii) What was the temperature midnight last night in °C?

　　…………………….……………°C

　　(iii) What was the difference in temperature between midday yesterday and midnight last night in °C?

　　7. How many minutes are there between 9.23 am and 1.06 pm?

　　8.

　　9. (i) Write 15% as a fraction in its simplest form.

　　(ii) Rowan sends 7 text messages each day.

　　A £5 credit buys him 140 text messages.

　　Today he received an extra 15% free text messages when he bought his £5 credit.

　　How many days should the credit last? Show your working.

　　11. The diagram below shows two overlapping rectangles.

　　i) Calculate the area of the larger rectangle only

　　ii) Calculate the total shaded area that the rectangles cover.

　　12. The diagram below shows a rectangle and a square. The diagrams are not drawn to scale.

　　If they have equal perimeters, what is the difference in their area?

　　13. Calculate the size of the missing angle in this triangle. The diagram is not drawn to scale.

　　14. (a) Find the size of angle ‘𝑎’ in the diagram below.

　　(b) Would you describe 100°? Acute, obtuse or reflex?

　　15. A right angled triangle is shown below. It is not drawn to scale.

　　(i) Calculate the perimeter of the triangle.

　　(ii) Calculate the area of the triangle.

　　16.

　　The diagram above is not drawn to scale.

　　(i) A box measures 20cm by 11cm by 15cm. Calculate the volume of the box.

　　(ii) A string is tied around the box with a bow at the top as shown in the diagram. If the length of the bow is 8 cm, calculate the total length of string used.

　　17.

　　Write one number from 20 to 30 that satisfies the descriptions below. Some numbers are used more than once.

　　(i) Prime?

　　(ii) Cube numbers?

　　(iii) Square numbers?

　　(iv) Fibonacci numbers?

　　The Fibonacci numbers follow the sequence 1, 1, 2, 3, 5, 8, 13…

　　(v) Triangular numbers?

　　The triangular numbers follow the sequence 1, 3, 6, 10, 15, …

　　(vi) Perfect numbers?

　　A perfect number is a number whose factors (not including itself) add up to itself.

　　e.g. 6 is a perfect number because 1 + 2 + 3 = 6.

　　(vii) Powerful numbers?

　　A powerful number has the property that for every prime number which divides into it, that prime number squared also divides into it.

　　e.g. 16 is a powerful number because both 2 and 22 are factors.

　　18. What is 4 − ((4 + 4) ÷ 4)?

　　19. 1001 = 𝑎 × 𝑏 × 𝑐, where a, b and c are prime numbers, with c is bigger than b, and b bigger than a.

　　Find a, b and c

　　20. Given that 2357 × 99 = 233 343, find:

　　(i) 233 343 ÷ 99

　　(ii) 235∙7 × 99

　　21. The symbol ⟴ has a special meaning in arithmetic.

　　𝑎 ⟴ 𝑏 means add 𝑎 and 𝑏 and then multiply by 𝑎.

　　For example:

　　4 ⟴ 2 = 4 × (4 + 2)

　　= 4 × 6

　　= 24

　　(a) Work out 4 ⟴ 5

　　(b) Work out 4 ⟴ (3 ⟴ 2)

　　(c) Work out the value of 𝑝 such that 6 ⟴ 𝑝 = 78

　　22. Four bells ring at intervals of 2, 8, 7 and 11 seconds.

　　If they are all rung at the same time, how many seconds will pass before they all ring at the same time again?

　　You should show some justification for your answer.

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