干货分享 剑桥圣玛丽中学St Mary’s School, Cambridge Year 10数学入学考试笔试题!

　　在英国，有这么一所顶尖的私立女校，它创建于1898年，已有100多年的历史，并且该校位于剑桥大学附近，学生可享受到全英最顶尖的教学资源，并且该校的学术成绩也十分优异，因此，每年都有一大批的学子前往该校求学，可是，入读私校要经过笔试，下面，小编就为大家带来了剑桥圣玛丽中学St Mary’s School, Cambridge Year 10数学入学考试笔试题，希望对大家有所帮助：

　　Year 10数学

　　允许时间:60分钟

　　说明

　　1. 你不能使用计算器。

　　2. 尽可能多地做题。

　　3.方法完整的解决方案将获得满分。

　　4. 如果你不懂一个问题，跳过它，继续下一个问题。

　　5. 当你做完所有你能做的事情后，再回到你错过的问题上。

　　1.For each expression, multiply out the brackets and simplify:

　　(a)5c+2(3c – 1) =

　　………………(2)

　　(b)7p – 5(4 – p) 

　　………………(2)

　　2. Solve these equations. Show your method clearly.

　　(a) 3(x + 6) = 5x + 12 (b) 5p – 8 = 7p – 9

　　x = ……… p = ………

　　3. Solve this number puzzle. Show all your working clearly.

　　Jack and Harry think of the same number.

　　Jack adds 2 to his number, and then multiplies by 5.

　　Harry multiplies his number by 7 and then subtracts 6.

　　They both get the same answer.

　　What number did they both think of?

　　……………………………………….

　　4.Maya earns £6.50 per hour.

　　Her pay is increased by 4%. Calculate her new hourly rate of pay.

　　……..…… (3)

　　5. Work these out.

　　6. Change each of these to a decimal. State whether your answer is a terminating or recurring decimal.

　　7. A regular polygon has 20 sides. Calculate

　　(a) the size of each exterior angle

　　……………° (2)

　　(b) the size of each interior angle

　　……….……° (2)

　　The sizes of the angles, in degrees, of the quadrilateral are

　　x + 10

　　2x

　　x + 90

　　x + 20

　　(a) Use this information to write down an equation in terms of x.

　　.......................................................... (2)

　　(b) Use your answer to part (a) to work out the size of the smallest angle of the quadrilateral.

　　................................... ˚ (3)

　　8. On the diagram below, draw the following journey

　　A to Q: 55 km on a bearing of 070°

　　Q to R: 30 km on a bearing of 325°

　　9. Calculate the average speed of a car which travels 165 miles in 3 hours

　　……… m.p.h.

　　10. The cheetah is the fastest mammal in the world. It can run at a maximum speed of 29 metres per second.

　　If it maintained this speed, how far would it travel in one minute?

　　……………m

　　11. Calculate the time taken by a cyclist who goes 70 km at a speed of 20 km/h

　　……… hours

　　12. This table shows information about the weight of apples picked from different trees in an orchard.

　　(a) Write down the class interval that contains the median.

　　………………………

　　(b) What is the modal interval?

　　……… ………………

　　(c) Calculate an estimate of the mean weight of apples picked from a tree.

　　……… g

　　13. Mr Brown sows 200 flower seeds.

　　For each flower seed the probability that it will produce a flower is 0.85

　　Work out an estimate for the number of these flower seeds that will produce a flower.

　　.......................... (2)

　　14. Calculate the length of the hypotenuse of this triangle.

　　15. Mary bakes a cake with a diameter of 18cm.

　　(a) Work out the area of the top of the cake. Leave your answer in terms of π.

　　………………………cm²

　　(b) What length of ribbon would Mary need to fit exactly around the circumference of the

　　cake? Leave your answer in terms of π.

　　………………………cm

　　17.

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