作為英國(guó)九大公學(xué)之一，溫切斯特公學(xué)是英國(guó)頂尖的私立學(xué)校，該校的學(xué)術(shù)成績(jī)十分優(yōu)異，每年有99%的學(xué)生升讀大學(xué)，其中37%的學(xué)生升讀牛劍，并且該校還為學(xué)生提供了豐富多彩的課余活動(dòng)，因此，越來(lái)越多的學(xué)生去該校留學(xué)，可是，入讀私校筆試是必經(jīng)的一項(xiàng)，下面，小編就為大家?guī)?lái)了溫切斯特公學(xué)Winchester College 13+數(shù)學(xué)入學(xué)考試筆試題型，希望對(duì)大家有所幫助：

數(shù)學(xué)I(樣本筆試)

允許時(shí)間:1小時(shí)30分鐘

總分:100分

不允許使用計(jì)算器。

把你的答案寫(xiě)在這個(gè)小冊(cè)子上。如果您需要額外的空間，請(qǐng)寫(xiě)在A4紙上，并附在這本小冊(cè)子上。你可以用鉛筆畫(huà)圖表。你應(yīng)該展示你所有的作業(yè)，這樣部分正確的答案就可以得到學(xué)分。

如果你沒(méi)有完成，也不要?dú)怵H。如果你得到60分以上，你就做得很好了。

1. Complete:

a)7×13 =

c)4321+(9753?4321) =

d)1×111+2×111+4×111 =

2.

b) Find 68% of ￡25

c) Find 0.05 of ￡440

d) evaluate 8-6×(-2)-6×18÷(-3)

e) evaluate 1010+1001×1009-1000×1009

3. Find in the simplest form:

4. a)p= 3 ,q=12 andr=?5 .

b)2(x+3)-(x-5)+4(x+2)=119. Findx.

5. a) The diagram below shows a regular decagon (ten equal sides with ten equal interior angles). Write down the value ofx.

b) The diagram below shows a regular hexagon and a regular pentagon (which share a side). Find the value ofb.

c) The diagram below shows a regular nonagon (nine sides), an equilateral triangle and part of a regular polygon (dotted) withnsides. Findn.

6.

b)10^a×10^b= 10⁷

10^a÷10^b= 10³

Find the value ofab.

d) By writing 2020 as a product of prime factors, find a three-digit numbernfor which 2020nis a square number.

7. a)

(i) Complete the table above.

(ii) Strip pattern k is 90% shaded. Findk.

b) Complete the table below (a match is one side of a small square).

c) Find a formula for the number of matches in trapezium pattern n (a match is one side of a small equilateral triangle).

d) Frank makes a rectangle pattern, using all the matches he has. He then rearranges these matches into a trapezium pattern and has no matches left. Find three possible values for the number of matches Frank started with.

8. a) Alice, Brenda and Clara share a pile of buttons in the ratio 7 :12: 21 . Clara gets ten more buttons than Alice and Brenda put together. How many buttons were in the pile?

b) Derek, Ethan, Fynn and Gerald share a big pile of sweets. Derek, Ethan and Fynn now have sweets in the ratio1: 4 : 6, and Ethan, Fynn and Gerald have sweets in the ratio 6 : 9 : 2. Derek and Gerald have 35 sweets between them. How many sweets does Gerald have?

c) Harriet and Imogen share sweets in the ratio 1: 2. Imogen gives Harriet 42 sweets. The sweets are now shared between Harriet and Imogen in the ratio 5: 4. How many sweets did they share?

9. a) In the diagram below AB=AC=AD , KA=KB=KC, KA is parallel to CL, and BKD is a

straight line.

Angle BAC = 54°. Findxandy.

b) ABCD is a rhombus and KLC is an equilateral triangle. The lengths of the sides of KLC are the same as the lengths of the sides of ABCD. Find z.

10. a) Find the shaded area in the diagram on the right.

b) The vertices of a triangle ABC are A(0, 0), B(8, 10) and C(12,k).

The area of the triangle ABC is 34.

(i) Plot the pointsAandBon the diagram.

(ii) Find the value ofk, given that 0k

(The height of point C in the diagram is not to scale.)

11. The diagram below shows a house comprising a cuboid and a pyramid. EDZ is a straight line. WX=12 , EB=17 , BC =9 and BX=10 . Find the volume of the house.

【微語(yǔ)】破千重關(guān)心懷天下，讀萬(wàn)卷書(shū)志在四方。