安妮公主就读私校—博耐顿女校Benenden School year12数学入学考试笔试题库!

　　作为英国唯一一所全寄宿制女校，博耐顿女校是英国最好的私立女校之一，距今已有99年的历史啦，是英国贵族、名人的最佳私校，这所学校除了安妮公主就读之外，赌王的女儿何超欣、日本演员海天佑都曾就读于这所私校，可是入读这所私校要经过笔试，下面，小编就为大家带来了博耐顿女校Benenden School year12数学入学考试笔试题库，希望对大家有所帮助：

　　数学

　　时间:1小时30分钟

　　考生须知:

　　•使用黑色墨水或圆珠笔。

　　•如果使用铅笔绘制图表/草图/图表，必须是深色的(HB或B)。彩色铅笔和荧光笔不能使用。

　　•本考试允许使用计算器和几何仪器。

　　•在提供的空白处回答问题——空白处可能比你需要的多。确保你对部分问题的答案标注清楚。

　　•你应该展示足够的工作，使你的方法清晰明了。没有实践的答案可能得不到完全的信任。

　　•当使用计算器时，答案应该给出一个适当的精确度。

　　信息

　　这次考试有21道题，这篇论文的总分是100分。

　　如果最后有时间，检查一下答案。

　　公式表

　　1. (a) The length of an Airbus A300 aeroplane is 54 m.

　　The ratio of the length of this aeroplane to its wingspan is 6 : 5

　　Work out the wingspan of the aeroplane.

　　(b) A model is made of the Airbus A300 aeroplane.

　　The length of the model is 36 cm.

　　The length of the real aeroplane is 54 m.

　　Find the ratio of the length of the model to the length of the real aeroplane. Give your ratio in the form 1 : n

　　2. A = 2x² + kx

　　(a) x = –3

　　k = 4

　　Work out the value of A.

　　(b) A = 38

　　x = 4

　　Work out the value of k.

　　(b) Round your answer to 2 significant figures:

　　4. (a) Write 2³ × 2⁶ as a single power of 2

　　5. A group of students take a test.

　　The group consists of 12 boys and 8 girls.

　　The mean mark for the boys is 18

　　The mean mark for the girls is 16.5

　　Calculate the mean mark for the whole group.

　　6. (a) Solve 3(2x – 1) = 6

　　Show clear algebraic working.

　　7. The table shows information about the snowfall in Ottawa in January one year.

　　Work out an estimate for the total snowfall in January.

　　8. Express 300 as a product of its prime factors.

　　9. Bhavik left his home at 12 00 to cycle to Sam’s house.

　　On the way Bhavik stopped for a rest, and then continued his journey. The distance-time graph shows his journey.

　　(a) (i) For how many minutes did Bhavik stop for a rest?

　　(ii) After his rest, how many more kilometres did Bhavik cycle to Sam’s house?

　　(b) Bhavik stayed at Sam’s house for 2 hours.

　　He then cycled back to his home.

　　He arrived home at 17 15.

　　Show all this information on the graph.

　　(c) Write down the times at which Bhavik was 24 kilometres from his home.

　　(d) Work out the average speed, in kilometres per hour, of Bhavik’s journey back to his home, from when he left Sam’s house.

　　Give your answer correct to 1 decimal place.

　　10.

　　(a) Describe fully the single transformation that maps shape P onto shape Q.

　　(b) On the grid, rotate shape P 90° clockwise about the point (2, 0). Label the new shape R.

　　12. On 9th May, 2009, there were 3440 people in the world with swine flu. Of these people, 1639 were in the USA.

　　(a) Express 1639 as a percentage of 3440

　　Give your answer correct to 1 decimal place.

　　The 3440 people who had swine flu on 9th May was an increase of 37.6% on the number of people who had swine flu on 8th May.

　　(b) Calculate the number of people who had swine flu on 8th May.

　　13. The mass of the Space Shuttle is 7.8 × 10⁴ kilograms.

　　(a) Write 7.8 × 104 as an ordinary number.

　　The Space Shuttle docks with the International Space Station.

　　The mass of the International Space Station is 4.62 × 10⁵ kilograms.

　　(b) Calculate the total mass of the Space Shuttle and the International Space Station. Give your answer in standard form.

　　14. Factorise the following:

　　(a) x²+ 5x - 24

　　(b) 2x² - 3x - 35

　　15.

　　Triangle PQR is an enlargement, centre O, of triangle ABC.

　　OAP and OCR are straight lines.

　　OA = 3 cm.

　　AP = 12 cm.

　　OC = 3.5 cm.

　　PR = 19 cm.

　　(a) Work out the length of CR.

　　(b) Work out the length of AC.

　　The area of triangle ABC is 2 cm²

　　(c) Work out the area of triangle PQR.

　　16.

　　The diagram shows two congruent regular pentagons and part of a regular n-sided polygon A.

　　Two sides of each of the regular pentagons and two sides of A meet at the point P.

　　Calculate the value of n.

　　Show your working clearly.

　　17. (a) The equation of a line L is 2x – 3y = 6

　　Find the gradient of L.

　　(b) Find the equation of the line which is parallel to L and passes through the point (6, 9).

　　B, C and D are points on a circle, centre O.

　　BOD is a diameter of the circle.

　　AB is the tangent to the circle at B.

　　AO = 8 cm. Angle BAO = 30° Angle CBD = 63°

　　Calculate the length of BC.

　　Give your answer correct to 3 significant figures

　　19. Find the point of intersection of the lines

　　2x + 3y = 9 and

　　6x - y = -13

　　20.

　　A, B, C and D are four points on a circle, centre O.

　　AD is a diameter of the circle.

　　Angle BAD = 58°

　　(a) Calculate the size of angle ADB.

　　(b) (i) Calculate the size of angle BCD.

　　(ii) Give a reason for your answer.

　　21.

　　Two solid spheres, each of radius r cm, fit exactly inside a hollow cylinder.

　　The radius of the cylinder is r cm.

　　The height of the cylinder is equal to 4r cm.

　　Calculate the value of r.

　　Show your working clearly.

　　这篇论文的总分是100分

　　检查你的作业，如果你有时间，试一下下面两个问题。

　　1. A rectangular piece of paper measures 12cm by 9cm.

　　It is folded so that two diagonally opposite corners lie together (ie corner B is moved left and up, to touch corner A and the paper is folded flat):

　　Work out the length of the fold.

　　2. An n x n square has four triangles cut off the corners, to form a regular octagon.

　　What is the area, in terms of n, which is removed from the square (ie the shaded area)?

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