2025年圣保罗女校St Paul's Girls' School Year7数学入学考试笔试真题 赶紧收藏!

　　英国圣保罗女校可谓是英国私立女校教育的典范，这所学校不仅建校历史悠久，有着出色学术成绩，还有着高超的艺术水平和优越的地理位置，让女性在现代化和快速发展的世界中拥有一席之地，因此，越来越多的学生去圣保罗女校留学，可是，入读私校前要经过笔试和面试，下面，小编就为大家带来了2025年圣保罗女校St Paul's Girls' School Year7数学入学考试笔试真题，希望对大家有所帮助：

　　Section A

　　25分钟

　　请仔细阅读这些说明

　　用铅笔。不允许使用计算器、量角器或尺子。

　　一共有16道题。如果可以的话，回答所有问题。

　　在所提供的空白处列出你的所有作业，并将答案写在所提供的行上。如有必要，请使用后面的页。

　　请不要磨光你的工作。

　　如果你答不出一个问题，就把它放下，继续做下一个。稍后再试。

　　不要让老师给你解释问题。

　　如果你在25分钟内完成了，回去检查你的答案，并试着填上你遗漏的答案。

　　如果你没有完成，或者你不能理解所有的问题，不要担心。人们以不同的速度工作。

　　1. Fill in the blanks so that the calculation on the left is equal to the calculation on the right:

　　2. What number is 40% of 75?

　　3. Calculate (2.3 + 3.7) ÷ 9. Leave your answer as a simplified fraction.

　　4. Write the following in order of size (smallest first):

　　5. Find the missing numerator and denominator of the equivalent fractions below:

　　6. Calculate 391 divided by seventeen.

　　7. Write one number which fits all three of these statements:

　　It is a multiple of 3.

　　It is a multiple of 7.

　　It ends in a 2.

　　8. I think of a number n.

　　5n is more than 60, but n + 5 is less than 20. What are the possible values of n?

　　9. Sarah won a large jar of sweets in a Christmas raffle. If there are 486 sweets in the jar and she shares them equally with her 17 classmates, how many do they each get?

　　10. On 1st December 2008 my grandmother was 80 years old. Her daughter was 40 years old on 1st December 1996. How old was my grandmother when her daughter was born?

　　12. How many bags of crisps at 16p each can I buy for £2?

　　13. A shop sells bananas and pears.

　　Max buys 1 banana and 2 pears. He paid 94p.

　　Emily buys 1 banana and 1 pear. She paid 62p.

　　How much does 1 banana cost?

　　14. Put a circle around each the amounts that can be made with four coins. State which coins you would use

　　15. Benjamin walks dogs to earn some money. The formula below can be used to work out his pay.

　　Benjamin worked all day on Monday. He walked 13 dogs before lunch and 15 dogs afterwards.

　　Work out Benjamin’s pay on Monday.

　　16. The table shows the distances in miles between some towns in the West country.

　　a. One of the towns is 194km from Penzance. Which town is this?

　　b. Approximately how many times further is Exeter from Penzance than it is from Taunton?

　　A部分结束，现在回去检查你的答案。

　　Section B

　　25分钟

　　请仔细阅读这些说明

　　使用铅笔。不允许使用计算器、量角器或尺子。

　　有10个问题。如果可以的话，回答所有问题。

　　在所提供的空白处列出你的所有作业，并将答案写在所提供的行上。如有必要，请使用后面的页。

　　请不要磨光你的工作。

　　如果你答不出一个问题，就把它放下，继续做下一个。

　　稍后再试。

　　不要让老师给你解释问题。

　　如果你在25分钟内完成了，回去检查你的答案，并试着填上你遗漏的答案。

　　如果你没有完成，或者你不能理解所有的问题，不要担心。人们以不同的速度工作。

　　1

　　There are a number of coins on a table.

　　One quarter of the coins show heads.

　　If I turn over two coins, then one third show heads. How many coins are there altogether?

　　2

　　There are twenty gifts stacked up into four piles.

　　The first pile has 3 less than the second pile.

　　The second pile has two more than the third pile.

　　The fourth pile has twice as many as the second pile.

　　How many gifts are in each pile?

　　3

　　In Mathsland currency is arranged in alphas, betas and gammas where

　　1 Alpha=20 Betas and 1 Beta=5 Gammas.

　　a) How many Gammas in 5 Alphas, 6 Betas and 3 Gammas?

　　b) Using as many alphas as you can, and then betas, then gammas, how would you pay for something that costs 789 Gammas?

　　4

　　If 5 mugs cost £3.50 and 8 pens cost £6.80 how much change do I get from £10 if I buy 7 mugs and 5 pens? You MUST show your working.

　　6

　　A box of biscuits contains 36 biscuits. 20 biscuits have foil wrappers. 15 are chocolate biscuits with foil wrappers. If 9 are not chocolate and do not have a foil wrapper, then how many chocolate biscuits are there?

　　7

　　All the long edges of the shape above have the same length and each long edge is twice as long as each short edge. All angles are 90° or 270°. If the area of the figure is 200cm², what is the perimeter?

　　8

　　Work out the missing length.

　　9

　　In this number tower the value in each block is the sum of the two below it. What is the value of block T?

　　10

　　Jenny passes 40 electricity poles along the straight road from school to her home.

　　The distance between every 2 poles is 30 metres.

　　If her school is exactly half way between 2 poles and her home is also exactly halfway between 2 poles, then

　　(a) Find the distance from her school to her home in 𝑘m.

　　(b) If she walks at a speed of 8 𝑘m/ℎ, how long does it take her to get to school from home?

　　SECTION B结束。

　　现在回去检查你的答案

　　Section C

　　25分钟

　　请仔细阅读这些说明

　　使用铅笔。不允许使用计算器、量角器或尺子。

　　有5个问题。如果可以的话，回答所有问题。

　　在所提供的空白处列出你的所有作业，并将答案写在所提供的行上。如有必要，请使用后面的页。

　　请不要磨光你的工作。

　　如果你答不出一个问题，就把它放下，继续做下一个。

　　稍后再试。

　　不要让老师给你解释问题。

　　如果你在25分钟内完成了，回去检查你的答案，并试着填上你遗漏的答案。

　　如果你没有完成，或者你不能理解所有的问题，不要担心。人们以不同的速度工作。

　　1.

　　a. Mila adds odd numbers together and writes down her results as follows:

　　1 = 1 = 1²

　　1 + 3 = 4 = 2²

　　1 + 3 + 5 = 9 = 3²

　　i. Write down the next three lines of this pattern:

　　ii. Using this pattern, write down the line which contains 169 at the centre.

　　b. Mila then adds different odd numbers and puts her results in a table again:

　　1 = 1 = 1³

　　3 + 5 = 8 = 2³

　　7 + 9 + 11 = 27 = 3³

　　i. Write down the next three lines of this pattern:

　　ii. Using this pattern, how many numbers do you need to add together to get:

　　… = 1000 = …

　　c. Using your answers from parts a. and b. find three numbers 𝐴𝐴, 𝐵𝐵 and 𝐶𝐶 such that

　　𝐴 − 𝐵 = 𝐶

　　and

　　𝐴² − 𝐵² = 𝐶³

　　2. The symbol ϕ represents a mathematical rule.

　　The rule for ϕ is “add the two numbers and then multiply their sum by the second number”.

　　For example, 2 ϕ 3 = (2 + 3) × 3 = 5 × 3 = 15

　　Work out:

　　a. 2 ϕ 6 =

　　d. If 6 ϕ 𝑚 = 91, what positive number must 𝑚𝑚 be? Show all your working.

　　e. If 𝑝 ϕ 𝑝 = 72, what number must 𝑝 be? Show all your working

　　f. Explain why x ϕ y is not the same as y ϕ x.

　　3. The diagram below shows a road network connecting the villages A to H. The numbers between the letters show how far apart the villages are in miles. A route connects two villages by travelling along the straight lines.

　　An example of a route from E to D is EF – FC – CD.

　　a) What is the shortest route between A and E, and how long is it?

　　b) What is the shortest route between H and C, and how long is it?

　　c) What is the shortest route between A and H, and how long is it?

　　4. Eliza is calculating 32 × 37.

　　She has constructed this number pattern:

　　Fill in the missing numbers.

　　a. Explain how the pattern is made.

　　b. Using a similar method, work out 27 × 37.

　　c. Adapt this method to work out 972 ÷ 36.

　　5. Tilly decides to count using a clock.

　　She starts counting from 1 in the normal way, so:

　　But when she gets to 12, the count goes back to 1, so she counts:

　　...8, 9, 10, 11, 12, 1, 2, 3...

　　So, for example, using this method of counting, 4 + 9 = 1 and 10 + 5 = 3. Similarly, 3 × 5 = 3 and 2 × 13 = 2.

　　a. Using this counting method, complete the following:

　　b. Using this counting method, can you find two different positive numbers 𝑛 and 𝑚 such that 𝑛² = 𝑚²

　　c. Using this method, can you find two different numbers 𝑝 and 𝑞 such that 𝑝³ =𝑞³?

　　SECTION C结束

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